Method, system and device for analyzing stability of power grid load frequency under time delay attack

Abstract

The invention relates to the field of power grid load frequency analysis, and provides a power grid load frequency stability analysis method, system and device under time delay attack. Establishing a mathematical model of a load frequency control system; according to the mathematical model of the load frequency control system, establishing an LFC time delay attack model in a sampling control mode; and carrying out system stability analysis based on the LFC according to the LFC time delay attack model in the sampling control mode. The invention provides an active control method based on time delay compensation, which can compensate random time delay in real time and improve the robustness and dynamic performance of a system, and provides a solution capable of comprehensively processing various delay sources including sensing loop delay, control loop delay, calculation delay and communication waiting delay. Therefore, the multi-delay compensation capability of the LFC system is enhanced.

Description

Technical Field

[0001] The present invention relates to the field of power grid load frequency analysis, and provides a method, system and device for analyzing the stability of power grid load frequency under a time-lag attack. Background Art

[0002] At present, in power systems, LFC (load frequency control) is an important means to achieve frequency stability. Traditional LFC systems rely on dedicated communication channels to transmit measurement data and control signals, and usually assume that the communication delay is small and fixed. To address the problem of fixed time delay, existing technologies have proposed a variety of passive control methods, such as robust control-based schemes or event-triggered control strategies, which can adapt to fixed delays within a certain range and maintain system stability.

[0003] With the complexity of modern power systems and their dependence on open communication networks, the problem of random time delay has gradually emerged and has become an important factor affecting system performance. This random time delay mainly comes from the complexity of communication protocols, network load fluctuations, the diversity of communication lines, and the dynamic changes in routing selection. At the same time, malicious network attacks also pose a major threat to LFC systems. For example, time delay attacks deliberately damage the performance of LFC systems by injecting random delays in sensor loops or control loops, thereby affecting the safe operation of power systems.

[0004] In the prior art, some solutions have been proposed to address the delay problem, such as using network predictive control methods to compensate for communication delays, or using timestamp technology to mitigate the effects of some delays in the sensor loop. However, these solutions are usually limited to compensating for fixed delays or partial delay sources, and cannot cope with complex situations under random time delays or the combined effects of multiple delay sources. In addition, since there is usually a large update cycle (e.g., 2-4 seconds) in actual LFC systems, the control accuracy of existing predictive control methods decreases significantly under long update cycle conditions, making it difficult to meet the system's requirements for dynamic performance. Summary of the invention

[0005] The present invention aims to solve at least one of the technical problems existing in the related art. To this end, the present invention provides a method, system and device for analyzing the stability of power grid load frequency under time delay attack, which can solve the problem of insufficient performance of the prior art under the conditions of random time delay, comprehensive influence of multiple delay sources and large update cycle through dynamic time delay compensation mechanism and redundant communication design, thereby significantly improving the control accuracy, robustness and reliability of the LFC system.

[0006] The present invention provides a method for analyzing the stability of power grid load frequency under a time-delay attack, comprising the following steps: S1: Establish a linearized LFC model, define state variables, and establish a mathematical model of the load frequency control system based on the linearized LFC model and state variables; S2: Calculate the total delay, and establish an LFC delay attack model under the sampling control mode according to the mathematical model of the load frequency control system and the total delay; S3: Observe the system state to obtain a control input matrix, and perform LFC-based system stability analysis on the control input matrix according to the LFC delay attack model under the sampling control mode.

[0007] According to a method for analyzing the stability of power grid load frequency under a time-delay attack provided by the present invention, the steps of establishing a mathematical model of the load frequency control system are as follows: S11: Establishment Linearized LFC model for each region: in, For the The control input of each zone, For the The valve position deviation in each area, For the Mechanical output deviation in each area, For the The load variation in the area For the The frequency deviation of the region, For the The frequency deviation of the region, For the The power exchange deviation of the tie line in each area, For the The speed reduction rate of each area, For the The moment of inertia of the area, For the The load damping factor of the region, For the The turbine time constant of each region is For the The regulator time constant of each region, Indicates and The synchronization coefficient of the connecting lines between regions, is the regional ordinal number, is another region ordinal number, is the total number of regions, , , , for The first derivative of for The first derivative of for The first derivative of for The first derivative of S12: To simplify the LFC setup, define the state variables: in, is the system state matrix, is the output signal matrix, is the disturbance variable, For the The frequency deviation coefficient of the region, No. The regional control error signal of each region, For the The weighted frequency deviation of the region, Transpose the matrix; The first The state space model of a region is: in, is the first parameter matrix, is the second parameter matrix, is the third parameter matrix, is the parameter matrix to be measured, for The first derivative of is the control input matrix; S13: Since the state space model has stability equivalent to the origin, , the state space model is rewritten as: The mathematical model of the load frequency control system is obtained.

[0008] According to a method for analyzing the stability of power grid load frequency under a time delay attack provided by the present invention, the steps of establishing an LFC time delay attack model under a sampling control mode are as follows: S21: Define the delay of the perception loop as , the control loop delay is defined as , define the experimental delay as , calculate the loop time delay in, is the upper limit of the time delay, For time; S22: Due to the sampling data control, the loop time is delayed Discretization is translated into discretized loop time delay : in, is the delay of the discretized sensing loop, is the time delay of the discretized control loop, To discretize the experimental delay, is the sampling time, , is a set of natural numbers, is the cycle length, is the number of cycles, , is the upper bound of the period number; S23: Define waiting time Total delay for ; S24: Using the total time delay as a time interval, discretize the mathematical model of the load frequency control system to obtain an LFC time delay attack model: in, is the sensor sampling matrix, is the actuator sampling matrix, The sampling time is The system state matrix at time , The sampling time is The system state matrix at time , The sampling time is The control input matrix when The sampling time is The output signal matrix when .

[0009] According to a method for analyzing the stability of power grid load frequency under a time-delay attack provided by the present invention, step S3 includes the following steps: S31: Use the state observer to perform state estimation and obtain the control input matrix; S32: predicting the control signal of the system model according to the control input matrix to obtain a reference model of the system state; S33: performing TDC-based LFC system stability analysis according to the LFC time delay attack model, control input matrix and reference model of system state in the sampling control mode.

[0010] According to a method for analyzing the stability of power grid load frequency under a time-delay attack provided by the present invention, step S31 includes the following steps: S311: Estimate system state using state observer: in, The gain matrix of the state observer, The sampling time is The estimated value of the system state matrix at time The sampling time is The estimated value of the system state matrix at time ; S312: Update the control input matrix according to the estimated value of the system state matrix: in, is the state feedback controller gain.

[0011] According to a method for analyzing the stability of power grid load frequency under a time-delay attack provided by the present invention, step S32 includes the following steps: S321: According to the network predictive control model, the sampling time is System state prediction state , in, The sampling time is The predicted state of the system state at time t; future The formula for predicting the system state at a sampling time is: in, To predict the number of sampling moments, , To predict the maximum value at the sampling time, For prediction The predicted state of the system state at time , For prediction The sensor sampling matrix at the moment; predict The predicted state of the control input matrix at time for: ; S322: Introducing the reference model of system status: in, The sampling time is A reference model of the system state at the time The control input matrix is ​​translated as: .

[0012] According to a method for analyzing the stability of power grid load frequency under a time-delay attack provided by the present invention, step S33 includes the following steps: S331: Get system status response: in, The sampling time is The first error at The sampling time is The second error at The sampling time is The third error at The sampling time is The first error at The sampling time is The second error at The sampling time is The third error at is the identity matrix; S332: Define simplified state variables: in, The sampling time is The simplified state variables when The sampling time is The simplified state variables when To simplify the transformation matrix, To simplify the first parameter of the transformation matrix, To simplify the second parameter of the transformation matrix, To simplify the third parameter of the transformation matrix, To simplify the fourth parameter of the transformation matrix, To simplify the fifth parameter of the transformation matrix, To simplify the sixth parameter of the transformation matrix; S333: Define the second sampling moment , in, is the ordinal number of the second sampling instant time, , is the maximum value of the ordinal number of the second sampling instant time, is a Markov random function; definition: , ,in, for The left limit of for The right limit of , we can deduce: in, , , , is the first unit block matrix, is the second unit block matrix, is the third unit block matrix, is obtained after screening by Markov random function The simplified transformation matrix at time; S334: Derive stability conditions.

[0013] According to a method for analyzing the stability of power grid load frequency under a time-delay attack provided by the present invention, step S334 includes the following steps: S3341: Calculate the state transfer matrix: in, is the discrete parameter value, is the state transfer matrix, ,in, is the first parameter of the state transfer matrix, is the second parameter of the state transfer matrix, is the number of rows and columns of the state transfer matrix, is a diagonal matrix, is the probability function value, is the probability function, is the first probability value, is the second probability value; S3342: Existence positive definite symmetric matrix , , so that the following formula holds: in, is the discrete parameter value of the first parameter of the state transfer matrix, is the transfer matrix and the difference matrix, is a positive definite symmetric diagonal matrix.

[0014] A stability analysis system for power grid load frequency under time-delay attack, comprising: LFC model building module: establish a linearized LFC model, define state variables, and establish a mathematical model of the load frequency control system based on the linearized LFC model and the state variables; calculate the total delay, and establish an LFC delay attack model under the sampling control mode based on the mathematical model and the total delay of the load frequency control system; Stability analysis module: observe the system state to obtain the control input matrix, and perform LFC-based system stability analysis on the control input matrix according to the LFC delay attack model under the sampling control mode.

[0015] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of a method for analyzing the stability of a power grid load frequency under a time-delay attack as described in any one of the above are implemented.

[0016] The above one or more technical solutions in the embodiments of the present invention have at least one of the following technical effects: The present invention provides a method, system and device for analyzing the stability of power grid load frequency under time delay attacks. Based on the characteristics of random time delays and time delay attacks, a system modeling method for integrating multiple delay sources of perception loops, control loops and communication networks is proposed for the first time. The method can more accurately describe the comprehensive impact of time delays on the dynamic performance of load frequency control systems, laying a theoretical foundation for subsequent control strategy design.

[0017] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0019] Figure 1 It is a flow chart of a method for analyzing the stability of power grid load frequency under a time-lag attack provided by the present invention.

[0020] Figure 2 It is a structural schematic diagram of a stability analysis device for power grid load frequency under time-lag attack provided by the present invention.

[0021] Figure 3 It is a structural schematic diagram of the electronic device provided by the present invention.

[0022] Reference numerals: 101, LFC model building module; 102, stability analysis module; 810, processor; 820, communication interface; 830, memory; 840, communication bus. DETAILED DESCRIPTION

[0023] In order to make the purpose, technical scheme and advantages of the present invention clearer, the technical scheme in the present invention will be clearly and completely described below. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in the field without creative work are within the scope of protection of the present invention. The following embodiments are used to illustrate the present invention, but cannot be used to limit the scope of the present invention.

[0024] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the embodiment of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0025] Combine the following Figures 1 to 3 The present invention is described.

[0026] Example The embodiment of the present invention provides a method for analyzing the stability of power grid load frequency under time-delay attack, such as Figure 1 As shown, including: S1: Establish a linearized LFC model, define state variables, and establish a mathematical model of the load frequency control system based on the linearized LFC model and state variables; S2: Calculate the total delay, and establish an LFC delay attack model under the sampling control mode according to the mathematical model of the load frequency control system and the total delay; S3: Observe the system state to obtain a control input matrix, and perform LFC-based system stability analysis on the control input matrix according to the LFC delay attack model under the sampling control mode.

[0027] The multi-area power system consists of multiple control areas interconnected by tie lines. The linearized LFC model for a certain area includes the regulator, turbine, rotating masses and loads, and tie line power. In the system, the remote terminal unit is used to obtain the measurement values ​​through the SCADA system (Supervisory Control And Data Acquisition). It is assumed that the generators in each control area are equipped with non-reheat turbines.

[0028] Specifically, step S1 includes: S11: Establishment Linearized LFC model for each region: in, For the The control input of each zone, For the The valve position deviation in each area, For the Mechanical output deviation in each area, For the The load variation in the area For the The frequency deviation of the region, For the The power exchange deviation of the tie line in each area, For the The speed reduction rate of each area, For the The moment of inertia of the area, For the The load damping factor of the region, For the The turbine time constant of each region is For the The regulator time constant of each region, Indicates and The synchronization coefficient of the connecting lines between regions, is the regional ordinal number, is another region ordinal number, is the total number of regions, , , , for The first derivative of for The first derivative of for The first derivative of for The first derivative of S12: To simplify the LFC design, a decentralized control strategy is adopted, and the exchange of power in each regional tie line is regarded as a disturbance. At this time, the LFC design method of the single-region power system can be used to repeat the design for each region. Define the state variables: in, is the system state matrix, is the output signal matrix, is the disturbance variable, For the The frequency deviation coefficient of the region, No. The regional control error signal of each region, For the The weighted frequency deviation of the region, Transpose the matrix; The first The state space model of a region is: in, is the first parameter matrix, is the second parameter matrix, is the third parameter matrix, is the parameter matrix to be measured, for The first derivative of is the control input matrix; S13: Since the state space model has stability equivalent to the origin, , the state space model is rewritten as: The mathematical model of the load frequency control system is obtained.

[0029] In actual power systems, the LFC system is a sampled data system. The update cycle of the control signal is usually 2~4s. The measurement results of the RTU (Remote Terminal Unit) are not used directly, but are sampled at time intervals and sent to the control center. Then, the control signal generated by the control center is updated at another time interval on the actuator side. It is assumed that the sensor and actuator are synchronized and work in time-triggered mode, while the controller works in event-triggered mode. On the other hand, the signal transmission in the LFC scheme is not only affected by these intervals, but also by time delays.

[0030] Time delay comes from natural random time delay and delay attack. Natural time delay includes the delay caused by the network of sensor loop or control line and the calculation delay of the control center. For delay attack, when the hacker introduces time delay in the control system, the delay can be injected into the measurement signal of the sensor loop and the control signal of the control line. The combined effect of natural time delay and delay attack will be studied in this invention, and the combination is called delay.

[0031] Specifically, step S2 includes: S21: Define the delay of the perception loop as , the control loop delay is defined as , define the experimental delay as , calculate the loop time delay in, is the upper limit of the time delay, For time; S22: Due to the sampling data control, the loop time is delayed Discretization is translated into discretized loop time delay : in, is the delay of the discretized sensing loop, is the time delay of the discretized control loop, To discretize the experimental delay, is the sampling time, , is a natural number, is the number of cycles, , is the upper bound of the period number; S23: Define waiting time Total delay for ; S24: Using the total time delay as a time interval, discretize the mathematical model of the load frequency control system to obtain an LFC time delay attack model: in, is the sensor sampling matrix, is the actuator sampling matrix, The sampling time is The system state matrix at time , The sampling time is The system state matrix at time , The sampling time is The control input matrix when The sampling time is The output signal matrix when .

[0032] Specifically, step S3 includes: S31: Perform state estimation based on the state observer and obtain the control input matrix: S311: Estimate system state using state observer: in, The gain matrix of the state observer, The sampling time is The estimated value of the system state matrix at time The sampling time is The estimated value of the system state matrix at time ; S312: Update the control input matrix according to the estimated value of the system state matrix: in, is the state feedback controller gain.

[0033] S32: Predict the control signal of the system model according to the control input matrix to obtain a reference model of the system state: S321: According to the network predictive control model, the sampling time is System state prediction state , in, The sampling time is The predicted state of the system state at time t; future The formula for predicting the system state at a sampling time is: in, To predict the number of sampling moments, , To predict the total number of sampling moments, For prediction The predicted state of the system state at time , For prediction The sensor sampling matrix at the moment; predict The predicted state of the control input matrix at time for: ; S322: Introducing the reference model of system status: in, The sampling time is A reference model of the system state at the time The control input matrix is ​​translated as: .

[0034] S33: performing TDC-based LFC system stability analysis according to the LFC time delay attack model and the control input matrix in the sampling control mode.

[0035] S331: Get system status response: in, The sampling time is The first error at The sampling time is The second error at The sampling time is The third error at is the identity matrix; S332: Define simplified state variables: in, The sampling time is The simplified state variables when The sampling time is The simplified state variables when To simplify the transformation matrix, To simplify the first parameter of the transformation matrix, To simplify the second parameter of the transformation matrix, To simplify the third parameter of the transformation matrix, To simplify the fourth parameter of the transformation matrix, To simplify the fifth parameter of the transformation matrix, To simplify the sixth parameter of the transformation matrix; S333: Define the second sampling moment , in, is the ordinal number of the second sampling instant, , is the maximum value of the ordinal number of the second sampling instant time, is a Markov random function; definition: , ,in, for The left limit of for The right limit of , we can deduce: in, , , , is the first block identity matrix, is the second block identity matrix, is the third block identity matrix, is obtained after screening by Markov random function The simplified transformation matrix at time; S334: Derivation stability conditions: S3341: Calculate the state transfer matrix: in, is the discrete parameter value, is the state transfer matrix, ,in, is the first parameter of the state transfer matrix, is the second parameter of the state transfer matrix, is the number of rows and columns of the state transfer matrix, is a diagonal matrix; is the probability function value, is the probability function, is the first probability value, is the second probability value; S3342: Existence positive definite symmetric matrix , , so that the following formula holds: in, is the discrete parameter value of the first parameter of the state transfer matrix, is the transfer matrix and the difference matrix, is a positive definite symmetric diagonal matrix.

[0036] The embodiments of the present invention have the following advantages: 1. System modeling with comprehensive time delay effects Based on the characteristics of random time delay and time delay attack, this paper proposes for the first time a system modeling method that integrates multiple delay sources of perception loop, control loop and communication network. It can more accurately describe the comprehensive impact of time delay on the dynamic performance of load frequency control (LFC) system, and lays a theoretical foundation for the subsequent control strategy design.

[0037] 2. Improved robust control strategy The present invention adopts improved time delay compensation (TDC) technology, introduces a robust control strategy based on the dynamic adjustment of control parameters to resist malicious time delay attacks, and enhances the anti-interference ability of the LFC system in a random environment. This control strategy can significantly improve the stability and adaptability of the LFC system in a complex network environment.

[0038] 3. Prediction-based adaptive control mechanism The present invention designs an adaptive control mechanism based on network prediction, which can evaluate and adjust the control signal in real time to cope with the impact of long update cycle and multiple delay sources on system performance. By adaptively adjusting the control input, the present invention achieves higher control accuracy and better dynamic response under large update cycle.

[0039] 4. Scalability and compatibility The control strategy and network architecture proposed in the present invention have high scalability and can be applied to power systems of different sizes and types. At the same time, it is highly compatible with existing control schemes and can be upgraded and deployed on the basis of existing systems, significantly reducing the cost and complexity of practical applications.

[0040] like Figure 2 As shown, the embodiment of the present invention also includes a stability analysis system for power grid load frequency under time-delay attack, including: LFC model building module 101: building a linearized LFC model, defining state variables, building a mathematical model of a load frequency control system based on the linearized LFC model and the state variables; calculating the total delay, and building an LFC delay attack model under a sampling control mode based on the mathematical model of the load frequency control system and the total delay; Stability analysis module 102: observes the system state to obtain a control input matrix, and performs LFC-based system stability analysis on the control input matrix according to the LFC delay attack model under the sampling control mode.

[0041] Figure 3 An example of a physical structure diagram of an electronic device is shown in FIG. Figure 3 As shown, the electronic device may include: a processor 810, a communication interface 820, a memory 830 and a communication bus 840, wherein the processor 810, the communication interface 820, and the memory 830 communicate with each other through the communication bus 840. The processor 810 may call the logic instructions in the memory 830 to execute a method for controlling the stability of the load frequency of a power grid under a time-delay attack, the method comprising: S1: Establish a linearized LFC model, define state variables, and establish a mathematical model of the load frequency control system based on the linearized LFC model and state variables; S2: Calculate the total delay, and establish an LFC delay attack model under the sampling control mode according to the mathematical model of the load frequency control system and the total delay; S3: Observe the system state to obtain a control input matrix, and perform LFC-based system stability analysis on the control input matrix according to the LFC delay attack model under the sampling control mode.

[0042] In addition, the logic instructions in the above-mentioned memory 830 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when it is sold or used as an independent product. Based on this understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art or the part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program codes.

[0043] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

[0044] It should be noted that the embodiments of the present disclosure may be implemented by hardware, software, or a combination of software and hardware. The hardware portion may be implemented using dedicated logic: the software portion may be stored in a memory and executed by an appropriate instruction execution system such as a microprocessor or dedicated design hardware. Those skilled in the art will appreciate that the above-described apparatus and methods may be implemented using computer executable instructions and / or contained in a processor control code, such as a programmable memory or a data carrier such as an optical or electronic signal carrier providing such code.

[0045] In addition, although the operation of the method of the present disclosure is described in a particular order in the accompanying drawings, this does not require or imply that these operations must be performed in this particular order, or that all the operations shown must be performed to achieve the desired result. On the contrary, the steps depicted in the flow chart can change the order of execution. Additionally or alternatively, some steps can be omitted, multiple steps can be combined into one step for execution, and / or one step can be decomposed into multiple steps for execution. It should also be noted that the features and functions of two or more devices according to the present disclosure can be embodied in one device. Conversely, the features and functions of a device described above can be further divided into being embodied by multiple devices.

[0046] Although the present disclosure has been described with reference to several specific embodiments, it should be understood that the present disclosure is not limited to the specific embodiments disclosed. The present disclosure is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims

1. A method for analyzing the stability of power grid load frequency under time-delay attack, characterized in that: The following steps are involved: S1: Establish a linearized LFC model, define state variables, and establish a mathematical model of the load frequency control system based on the linearized LFC model and state variables; S2: Calculate the total delay, and establish an LFC delay attack model under the sampling control mode according to the mathematical model of the load frequency control system and the total delay; S3: Observe the system state to obtain a control input matrix, and perform LFC-based system stability analysis on the control input matrix according to the LFC delay attack model under the sampling control mode.

2. The method for analyzing the stability of power grid load frequency under time-delay attack according to claim 1 is characterized in that: The steps of establishing the mathematical model of the load frequency control system are: S11: Establishment Linearized LFC model for each region: in, For the The control input of each zone, For the The valve position deviation in each area, For the Mechanical output deviation in each area, For the The load variation in the area For the The frequency deviation of the region, For the The frequency deviation of the region, For the The power exchange deviation of the tie line in each area, For the The speed reduction rate of each area, For the The moment of inertia of the area, For the The load damping factor of the region, For the The turbine time constant of each region is For the The regulator time constant of each region, Indicates and The synchronization coefficient of the connecting lines between regions, is the regional ordinal number, is another region ordinal number, is the total number of regions, , , , for The first derivative of for The first derivative of for The first derivative of for The first derivative of S12: To simplify the LFC setup, define the state variables: in, is the system state matrix, is the output signal matrix, is the disturbance variable, For the The frequency deviation coefficient of the region, No. The regional control error signal of each region, For the The weighted frequency deviation of the region, Transpose the matrix; The first The state space model of a region is: in, is the first parameter matrix, is the second parameter matrix, is the third parameter matrix, is the parameter matrix to be measured, for The first derivative of is the control input matrix; S13: Since the state space model has stability equivalent to the origin, , the state space model is rewritten as: The mathematical model of the load frequency control system is obtained.

3. The method for analyzing the stability of power grid load frequency under time-delay attack according to claim 2 is characterized in that: The steps to establish the LFC delay attack model under sampling control mode are: S21: Define the delay of the perception loop as , the control loop delay is defined as , define the experimental delay as , calculate the loop time delay in, is the upper limit of the time delay, For time; S22: Due to the sampling data control, the loop time is delayed Discretization is translated into discretized loop time delay : in, is the delay of the discretized sensing loop, is the time delay of the discretized control loop, To discretize the experimental delay, is the sampling time, , is a set of natural numbers, is the cycle length, is the number of cycles, , is the upper bound of the period number; S23: Define waiting time Total delay for ； S24: Using the total time delay as a time interval, discretize the mathematical model of the load frequency control system to obtain an LFC time delay attack model: in, is the sensor sampling matrix, is the actuator sampling matrix, The sampling time is The system state matrix at time , The sampling time is The system state matrix at time , The sampling time is The control input matrix when The sampling time is The output signal matrix when .

4. The method for analyzing the stability of power grid load frequency under time-delay attack according to claim 3 is characterized in that: Step S3 includes the following steps: S31: Use the state observer to perform state estimation and obtain the control input matrix; S32: predicting the control signal of the system model according to the control input matrix to obtain a reference model of the system state; S33: performing TDC-based LFC system stability analysis according to the LFC time delay attack model, control input matrix and reference model of system state in the sampling control mode.

5. The method for analyzing the stability of power grid load frequency under time-delay attack according to claim 4 is characterized in that: Step S31 includes the following steps: S311: Estimate system state using state observer: in, The gain matrix of the state observer, The sampling time is The estimated value of the system state matrix at time The sampling time is The estimated value of the system state matrix at time ; S312: Update the control input matrix according to the estimated value of the system state matrix: in, is the state feedback controller gain.

6. The method for analyzing the stability of power grid load frequency under time-delay attack according to claim 5, characterized in that: Step S32 includes the following steps: S321: According to the network predictive control model, the sampling time is System state prediction state , in, The sampling time is The predicted state of the system state at time t; future The formula for predicting the system state at a sampling time is: in, To predict the number of sampling moments, , To predict the maximum value at the sampling time, For prediction The predicted state of the system state at time , For prediction The sensor sampling matrix at the moment; predict The predicted state of the control input matrix at time for: ； S322: Introducing the reference model of system status: in, The sampling time is A reference model of the system state at the time The control input matrix is ​​translated as: 。 7. The method for analyzing the stability of power grid load frequency under time-delay attack according to claim 6, characterized in that: Step S33 includes the following steps: S331: Get system status response: in, The sampling time is The first error at The sampling time is The second error at The sampling time is The third error at The sampling time is The first error at The sampling time is The second error at The sampling time is The third error at is the identity matrix; S332: Define simplified state variables: in, The sampling time is The simplified state variables when The sampling time is The simplified state variables when To simplify the transformation matrix, To simplify the first parameter of the transformation matrix, To simplify the second parameter of the transformation matrix, To simplify the third parameter of the transformation matrix, To simplify the fourth parameter of the transformation matrix, To simplify the fifth parameter of the transformation matrix, To simplify the sixth parameter of the transformation matrix; S333: Define the second sampling moment , in, is the ordinal number of the second sampling instant time, , is the maximum value of the ordinal number of the second sampling instant time, is a Markov random function; definition: , , ,in, for The left limit of for The right limit of It is deduced that: in, , , , is the first block identity matrix, is the second block identity matrix, is the third block identity matrix, is obtained after screening by Markov random function The simplified transformation matrix at time; S334: Derive stability conditions.

8. The method for analyzing the stability of power grid load frequency under time-delay attack according to claim 7, characterized in that: Step S334 includes the following steps: S3341: Calculate the state transfer matrix: in, is the discrete parameter value, is the state transfer matrix, ,in, is the first parameter of the state transfer matrix, is the second parameter of the state transfer matrix, is the number of rows and columns of the state transfer matrix, is a diagonal matrix, is the probability function value, is the probability function, is the first probability value, is the second probability value; S3342: If it exists positive definite symmetric matrix , , so that the following formula holds: in, is the discrete parameter value of the first parameter of the state transfer matrix, is the transfer matrix and the difference matrix, is a positive definite symmetric diagonal matrix, then the grid load frequency is stable; if it does not exist, then the grid load frequency is unstable.

9. A stability analysis system for power grid load frequency under time-delay attack, used to execute a stability analysis method for power grid load frequency under time-delay attack as claimed in any one of claims 1 to 8, characterized in that: include: LFC model building module: build a linearized LFC model, define state variables, and build a mathematical model of the load frequency control system based on the linearized LFC model and state variables; Calculate the total delay, and establish an LFC delay attack model under the sampling control mode according to the mathematical model of the load frequency control system and the total delay; Stability analysis module: observe the system state to obtain the control input matrix, and perform LFC-based system stability analysis on the control input matrix according to the LFC delay attack model under the sampling control mode.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the method for analyzing the stability of power grid load frequency under a time-delay attack as described in any one of claims 1 to 8 are implemented.

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