Optimal false data injection attack method and system for load-frequency control in power system

Abstract

The invention relates to the technical field of power system data processing, in particular to an optimal false data injection attack method and system for load-frequency control in a power system, and proposes time domain formalized modeling to find an OFDIA, minimize successful attack time, construct an OFDIA model and optimize load attack quantity; load measurement values of the whole power grid are considered in a compromise mode, the influence of power system parameters on successful attacks is analyzed, and a load frequency model of the power grid is modeled; modeling the dynamic behavior of the power system in the time domain optimization framework; and establishing a false data injection attack model, constructing an OFDIA model, and optimizing the load attack quantity. According to the method, under the condition that an attacker completely accesses the data of the power system, the damaged measurement number and the starting time are reduced, meanwhile, the attack concealment is ensured, consideration is provided for a defense mechanism of a control center, and safe operation of a power grid is ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of power system data processing, and in particular to an optimal false data injection attack method and system for load-frequency control in a power system. Background Art

[0002] With the adoption of advanced information and communication technologies, traditional power grids are transforming into intelligent cyber-physical systems. Although this transformation brings benefits, it also makes the power grid vulnerable to cyber threats due to the increased reliance on communication and measurement technologies. False data injection attack (FDIA) is a major type of cyber attack that sends erroneous data to the power grid measurement / communication system, misleading the control center to make wrong decisions.

[0003] Grid frequency is one of the indicators that reflect the normal operation of the power system. Large frequency fluctuations need to be corrected, otherwise serious consequences may occur. After a grid disturbance, the main frequency responds and maintains the frequency by re-dispatching the generator. However, since the dispatch process relies on measurement and communication, FDIA in the closed-loop dispatch process may affect the frequency stability of the power system, resulting in false tripping of relays and system-wide consequences. Existing inventions have studied the impact of FDIA on grid frequency behavior, relay protection operation, generator dispatching process, etc., and there are also inventions that have studied the detection and mitigation of FDIAs. However, the FDIA models considered in many inventions are based on random attacks or limited predefined attack templates, and existing work has problems such as different scopes and lack of certain relay operations. Therefore, there is a need to improve the existing technology.

[0004] The above information is presented as background information only to assist with understanding the present disclosure and no determination or admission is made as to whether any of the above may be used as prior art with respect to the present disclosure. Summary of the invention

[0005] The present invention provides an optimal false data injection attack method and system for load-frequency control in an electric power system to solve the above-mentioned problems in the prior art.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] An optimal false data injection attack method for load-frequency control in a power system comprises the following steps:

[0008] Propose time domain formal modeling to find OFDIA, minimize successful attack time, build OFDIA model and optimize load attack volume;

[0009] The load frequency model of the power grid is modeled by considering the load measurements of the entire power grid and analyzing the impact of power system parameters on successful attacks;

[0010] Modeling the dynamic behavior of power systems in a time-domain optimization framework;

[0011] Establish a false data injection attack model, build an OFDIA model and optimize the load attack volume.

[0012] Furthermore, the proposed time domain formal modeling is used to find OFDIA, minimize the successful attack time, build the OFDIA model and optimize the load attack amount, including:

[0013] The optimizer is used to determine the optimal size of the load attack based on the load measurement value of the entire power grid, taking into account the actual structure and measurement of the power grid. At the same time, the optimization model formulated by the sequential process and the weighted objective function is used to find the minimum time for a successful attack, thereby constructing a time domain formal modeling.

[0014] The dynamic behavior of the power system is modeled and solved in a time domain optimization framework to obtain a perfect attack model.

[0015] Furthermore, the optimizer determines the optimal size of the load attack based on the load measurement value of the entire power grid, taking into account the actual structure and measurement of the power grid, and uses the optimization model formulated by the sequential process and the weighted objective function to find the minimum time for a successful attack, thereby constructing a time domain formal modeling, including:

[0016] Based on the actual structure and measurement of the power grid, the load measurement range that the attack focuses on is determined according to the load measurement value of the entire power grid, and the appropriate scale and direction of the load attack is determined based on the load measurement range in combination with the optimizer;

[0017] Analyze the influence of power system parameters, the accessibility of the attacker to the load on the possibility of a successful attack, and the minimum time required, and obtain the influencing factors; the power system parameters include the inertia of the generator set, the droop and time constant of the speed regulator;

[0018] Integrate the influencing factors into the weighted objective function to construct an optimization model that can effectively find the minimum attack time;

[0019] The dynamic behavior of the power system is modeled and solved in a time domain optimization framework to obtain a perfected attack model, including:

[0020] Model the load-frequency dynamics of the power grid based on the generator swing equations, the power grid model, and the actions of the controller, laying the foundation for overall modeling in the time domain framework;

[0021] The differential equations of the synchronous generator and the speed regulator as well as the DC power flow are considered to simulate the change of the rotor angle. The continuous format problem involving the dynamics of the power system is discretized into the Euler method to obtain a linear model that is easy to solve numerically, and the attack model construction within the time domain optimization framework is improved.

[0022] Further, the consideration of the load characteristics of the power grid includes compromising the load measurement value of the entire power grid and analyzing the impact of power system parameters on the successful attack, specifically:

[0023] By considering the load measurement value of the entire power grid, it is determined that FDIA is the load measurement value within the control area to determine the focus of the attack;

[0024] A comprehensive analysis of the impact of power system parameters such as the inertia of generator sets, droop and time constant of speed regulators, and the attacker’s accessibility to loads on the likelihood of a successful attack and the minimum time required provides a basis for attack strategies.

[0025] Further, the compromise considers the load measurement value of the entire power grid and determines that the FDIA is the load measurement value within the control area to determine the focus of the attack, including:

[0026] According to the actual situation of power grid load measurement, the load meter and the tie line sensor measurement quantity are compared to determine the rationality of taking the load measurement value in the control area as the attack focus;

[0027] Analyze the difference in the possibility of unsafe power meters and unsafe connection line sensor measurements to further clarify the attack direction;

[0028] The comprehensive analysis of the impact of power system parameters such as the inertia of the generator set, the droop and time constant of the governor, and the attacker's accessibility to the load on the possibility of a successful attack and the minimum time required provides a basis for the attack strategy, including:

[0029] The specific effects of the parameters such as the inertia of the generator set, the droop and time constant of the speed governor on the probability and minimum time of a successful attack are studied respectively;

[0030] Consider the attacker’s accessibility to the payload, evaluate its effect on the attack effect, and comprehensively derive influencing factors to guide the formulation of attack strategies.

[0031] Furthermore, the system dynamic behavior modeling includes modeling the load frequency model of the power grid and modeling the dynamic behavior of the power system in a time domain optimization framework, specifically:

[0032] The load frequency model of the power grid is modeled using multiple equations and controller actions to reflect the frequency dynamics and control mechanisms in actual power grid operation;

[0033] Modeling the dynamic behavior of the power system in a time-domain optimization framework ensures that the model is numerically solvable and can accurately simulate system changes;

[0034] The load frequency model of the power grid is modeled using a variety of equations and controller actions to reflect the frequency dynamics and control mechanisms in the actual operation of the power grid, including:

[0035] Model the load-frequency dynamics of the power grid using the generator swing equations, the grid model, and the controller actions, reflecting the impact of the inertia of the synchronous generator and the governor action on the frequency dynamics, and the process of maintaining the frequency by obtaining grid measurements and sending dispatch signals;

[0036] The dynamic behavior of the power system is modeled in the time domain optimization framework to ensure that the model can be solved by numerical methods and can accurately simulate system changes, including:

[0037] Considering the differential equations of synchronous generator and speed regulator as well as the change of rotor angle for DC power flow simulation, the backward Euler method is used to discretize the power system dynamics and obtain a linear model for numerical solution, which improves the scalability and accuracy of the model.

[0038] Furthermore, the attack optimization includes establishing a false data injection attack model and constructing an OFDIA model and optimizing the load attack volume, specifically:

[0039] Construct a false data injection attack model based on the power grid operation characteristics and control center actions, and clarify the settings and relationships of various parameters and variables;

[0040] Construct the OFDIA model, determine the optimized load attack volume and corresponding constraints, ensure the attack concealment and obtain the best attack effect.

[0041] Furthermore, the false data injection attack model is constructed based on the power grid operation characteristics and the control center actions, and the settings and interrelationships of various parameters and variables are clarified, including:

[0042] The basic framework of the false data injection attack model is constructed by fully considering key factors such as the size of the false data injected into the load measurement, the parameters / measurements after injection into FDIA, and the damaged load measurement values ​​used by the control center to update the dispatch signal;

[0043] The backward Euler method is used to discretize the continuous forms of the power system dynamic model and the control center action into specific relevant formulas such as load measurement attack, grid frequency dynamics, and control center operation. The expressions and mutual correlations of each variable in the model are clarified, and the operation of the RoCoF relay is simulated, and the FRO decision is made according to the predefined thresholds of frequency and RoCoF.

[0044] Furthermore, the OFDIA model is constructed to determine the optimized load attack amount and corresponding constraints to ensure the attack concealment and obtain the best attack effect, including:

[0045] When constructing the OFDIA model, we focus on optimizing the amount of load attack when RoCoF or frequency violation is initiated, and use slack variables to reformulate it as a linear programming problem. At the same time, we set many constraints including the power grid dynamic model, the role of the control center, and RoCoF calculation to reasonably optimize the size of the load attack;

[0046] By setting relevant thresholds such as preventing attacks from being too concentrated, ensuring the power range of generators, and limiting the changes in generator power output, the attack is kept hidden and can be avoided from being discovered by the detection algorithm. The weight factors are adjusted to balance the OFDIA components and ensure that the model can return the best attack in the system.

[0047] Starting from the initial dispatch cycle, OFDIA runs and checks whether there is a feasible attack that triggers the operation of related relays. If not, the dispatch cycle is increased successively and continues to run until a successful attack is found or the maximum number of dispatch cycles is reached. The model is implemented to finally achieve an attack on the load-frequency control of the power system. At the same time, the maximum number of dispatch cycles is reasonably determined according to the characteristics of different power grids to ensure the effectiveness of the attack implementation.

[0048] The present invention also provides an optimal false data injection attack system for load-frequency control in a power system, which is used to implement an optimal false data injection attack method for load-frequency control in a power system as described in any one of the above items, comprising:

[0049] An attack model building module, used to build an attack model based on time domain formal modeling, configured with an optimization unit, which can find the optimal false data injection attack through optimization means, minimize the time required for successfully launching an attack, and model based on the minimized time required for a successful attack;

[0050] The attack impact analysis module is used to consider the impact of grid-related characteristics and power system parameters on the attack and implement the attack process to achieve the attack on the load-frequency control of the power system;

[0051] The attack execution module is connected to the attack model construction module and the attack impact analysis module, and is used to implement a specific optimal false data injection attack operation on the load-frequency control of the power system based on the attack model and the impact analysis result according to a preset attack process.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] The present invention provides an optimal false data injection attack method and system for load-frequency control in an electric power system, which reduces the number of damaged measurements and the startup time when the attacker has full access to the electric power system data, while ensuring the concealment of the attack, providing considerations for the defense mechanism of the control center, and ensuring the safe operation of the power grid.

[0054] The present invention has other features and advantages, which will be apparent from or will be described in detail in the accompanying drawings and the following detailed description incorporated herein, which together serve to explain the specific principles of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in 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 only 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.

[0056] Figure 1 An example diagram of the generator dispatching process in the power grid regulating the grid frequency;

[0057] Figure 2 Schematic diagram of the virtual data injection attack and its impact on the power grid behavior;

[0058] Figure 3 Flowchart for running OFDIA in multiple scheduling cycles;

[0059] Figure 4 The present invention provides a flowchart of an optimal false data injection attack method for load-frequency control in a power system.

[0060] Figure 5 This is the IEEE39 bus system diagram;

[0061] Figure 6 A comparison diagram of the rotor angles of generator 33 and generator 35, the model accuracy adopted for generator 35, and the frequency characteristics developed in ePHASORSIM for generator 33;

[0062] Figure 7 Comparison of load measurement attack and frequency dynamics for optimal attack (OFDIA) and non-optimal attack (NOFDIA);

[0063] Figure 8Figure 2. OFDIA with frequency constraints only (F-OFDIA) versus RoCoF constraints only (R-OFDIA). DETAILED DESCRIPTION

[0064] In order to explain in detail the possible application scenarios, technical principles, specific schemes that can be implemented, and the purposes and effects that can be achieved, the following is a detailed description of the specific embodiments listed in conjunction with the accompanying drawings. The embodiments described herein are only used to more clearly illustrate the technical solutions of the present application, and are therefore only used as examples, and cannot be used to limit the scope of protection of the present application.

[0065] Reference to "embodiment" herein means that the specific features, structures or characteristics described in conjunction with the embodiment may be included in at least one embodiment of the present application. The term "embodiment" appearing in various places in the specification does not necessarily refer to the same embodiment, nor does it particularly limit its independence or association with other embodiments. In principle, in the present application, as long as there is no technical contradiction or conflict, the various technical features mentioned in the embodiments can be combined in any way to form a corresponding implementable technical solution.

[0066] Unless otherwise defined, the technical terms used in this document have the same meanings as those generally understood by those skilled in the art to which this application belongs; the use of relevant terms in this document is only for describing specific embodiments and is not intended to limit this application.

[0067] In the description of this application, the term "and / or" is an expression used to describe the logical relationship between objects, indicating that three relationships may exist, for example, A and / or B, which means: A exists, B exists, and A and B exist at the same time. In addition, the character " / " in this article generally indicates that the objects before and after are in an "or" logical relationship.

[0068] In the present application, terms such as “first” and “second” are merely used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship of quantity, priority or sequence between these entities or operations.

[0069] Without further limitations, in this application, the words "include", "comprises", "has" or other similar expressions used in the sentences are intended to cover non-exclusive inclusion. These expressions do not exclude the presence of additional elements in the process, method or product including the elements, so that the process, method or product including a series of elements may include not only those limited elements, but also other elements not explicitly listed, or also include elements inherent to such process, method or product.

[0070] With the adoption of advanced information and communication technologies, traditional power grids are transforming into smart cyber-physical systems. Although this transformation to smart grids brings some benefits to system operation, it also makes the grid vulnerable to cyber threats due to the increased dependence on communication and measurement technologies. Among various types of cyber attacks, false data injection attack (FDIA) is a major type of cyber attack that has been widely studied recently, such as Figure 2 The figure shows a schematic diagram of virtual data injection attack and its impact on power grid behavior.

[0071] Sending wrong data to the existing measurement / communication systems in the power grid, thereby misleading the control center / controller to make wrong control decisions. In the real world, there are several examples of attackers designing FDIA to disrupt the power grid. Although these attacks were not launched in the power system, such a complex attack with full access to data can also easily target the power system. Internal attackers can also attack the employees of the control center through social engineering to provide access to such high-level data. In summary, this paper studies the FDIA of the power system when the attacker has full access to the power system data.

[0072] Grid frequency is one of the indicators that reflect the normal operation of the power system. When there are large fluctuations in frequency, corrections need to be made to keep it within an acceptable range; otherwise, serious consequences may occur, including power outages. For example, the major blackouts in England and Wales in 2019 were caused by a drop in grid frequency, leaving about 1 million customers without electricity. After any disturbance in the grid, the main frequency response, including automatic decentralized control actions of the active output of generators, immediately determines the grid frequency. However, compared with the main frequency response, and on a slightly slower time scale, the grid frequency is maintained by re-dispatching generators. If the frequency fluctuates from the nominal value, re-dispatching generators adjusts the reference set point of the generators equipped with speed regulators to bring the frequency back into an acceptable range.

[0073] Since the dispatch process relies on measurement and communication, any FDIA in the closed-loop dispatch process can affect the frequency stability of the power system, resulting in false relay tripping and system-wide consequences. Among the several types of protective relays that can be affected by FDIA, rate-of-change-of-frequency (RoCoF) relays, underfrequency / overfrequency relays, and load shedding relays are directly affected by FDIA’s closed-loop control of the dispatch process. These relays assist in load generation balancing by disconnecting generators / loads at pre-defined locations as needed, tripping generators when the frequency is too high to protect the system from frequency instability, and preventing synchronous generator damage. Although as Figure 1As shown, most protection relays operate based on local measurements, but FDIA in the closed-loop control of the dispatch process can cause unnecessary frequency changes and ultimately lead to relay malfunction operation (FRO).

[0074] like Figure 3 As shown in Figure 1, a flowchart of running OFDIA in multiple dispatch cycles is shown. As a simple example of how a FRO attack can occur in a power system, assume that the attacker injects false data into the load measurements in dispatch cycle n to mislead the control center to reduce load consumption. This erroneous data causes the control center to have an erroneous power dispatch in the system and to determine an erroneous reference set point for the governor. By comparing the frequency deviation, the governor changes the mechanical input power of the generators, and therefore, the total power generation in the grid changes, while the actual load in the grid remains the same as the value before the attack (remember that the attacker only injected false data into the load measurements and did not change the actual load consumption). This imbalance in load generation causes some fluctuations in the frequency. If the fluctuations are large enough to satisfy at least one of the RoCoF and under / under frequency thresholds, the FRO is considered successful. Otherwise, the attacker needs to launch another attack in a subsequent dispatch cycle.

[0075] The impact of FDIA on grid frequency behavior and relay protection operation was studied. The impact of FDIA on the generator dispatch process was studied, and different FDIA templates such as signal scaling, ramping, surge and random noise were studied. The impact of the attack on the local controller of the load in the grid frequency was shown. In 2010, the authors demonstrated that FDIA can cause unnecessary grid frequency deviations, ultimately triggering load shedding. The impact of random FDIA on load triggering RoCoF relays was demonstrated. The impact of some limited FDIA predefined templates, such as constant or random packet delays, was also studied.

[0076] The detection and mitigation of FDIAs for load-frequency control of power systems have also been widely studied in the literature. An invention proposes an automatic generative control (AGC) detection and defense mechanism for FDIA based on a generative adversarial network. An invention uses the predicted area control error (ACE) to identify and mitigate FDIA on AGC. An invention treats FDIAs as unknown inputs and uses the estimated values ​​of FDIAs to compensate for the relevant impact on AGC. An invention proposes a control mechanism based on Kalman filtering and artificial neural networks to detect and mitigate the impact of FDIAs. However, the FDIA models considered in many inventions are based on random attacks or limited predefined attack templates, which may not be of interest to attackers in the real world.

[0077] In addition to the above inventions, there are other related FDIA works that are not studied in the context of the generator dispatch process, but are developing optimal attacks. One invention proposes a mechanism for finding the optimal attack that causes a transmission line outage.

[0078] However, the scope of these inventions (causing transmission line overload) is different from the scope of this work (attacking load-frequency control). Other inventions propose a Laplace domain optimization framework to study the vulnerability and impact of AC / HVDC load frequency control on FDIAs. There are some inventions that aim to find the optimal attack in the shortest time. However, these works consider multi-area interconnected power systems where all generators in one area are replaced with a single equivalent generator, while focusing on the tie-line sensor measurement trade-offs. In addition, there are inventions that lack the operation of generator RoCoF relays and load shedding low-frequency relays.

[0079] An intelligent FDIA can defeat the defense mechanism of the control center because it guarantees stealth. It is possible to launch a successful arbitrary FDIA, but to ensure stealth, arbitrary attacks require a long launch time to succeed. Such attacks may not be of interest to attackers. However, the optimal false data injection attack (OFDIA) proposed in this work can minimize the number of compromised measurements and the launch time, leaving a very short time for the control center's remedial actions. Therefore, the control center should consider possible OFDIA in its defense mechanism to ensure the safe operation of the power grid.

[0080] The present invention aims to provide a solution to solve the above-mentioned defects in the prior art.

[0081] Please refer to Figure 4 The present invention provides an optimal false data injection attack method for load-frequency control in a power system, comprising the following steps:

[0082] S1. Propose time domain formal modeling to find OFDIA, minimize successful attack time, build OFDIA model and optimize load attack volume;

[0083] S2, compromise the load measurements of the entire power grid, analyze the impact of power system parameters on successful attacks, and model the load frequency model of the power grid;

[0084] S3. Modeling the dynamic behavior of power systems in a time domain optimization framework;

[0085] S4. Establish a false data injection attack model, build an OFDIA model and optimize the load attack volume.

[0086] Firstly, a time-domain formal modeling is proposed to find OFDIA, minimize the successful attack time, build the OFDIA model and optimize the load attack volume.

[0087] In this process, the optimizer is used to determine the optimal size of the load attack based on the load measurement value of the entire power grid, taking into account the actual structure and measurement of the power grid. In this way, the attack scale is accurately determined by the optimizer in combination with the actual power grid situation, making the attack more targeted and improving the efficiency and accuracy of the attack. At the same time, the optimization model formulated by the sequential process and the weighted objective function is used to find the minimum time for a successful attack, thereby constructing a time domain formal modeling. Secondly, the dynamic behavior of the power system is modeled and solved in the time domain optimization framework to obtain a perfected attack model.

[0088] Specifically, the load-frequency dynamics of the power grid are modeled according to the swing equations of the generator, the power grid model, and the action of the controller, laying the foundation for the overall modeling within the time domain framework; the differential equations of the synchronous generator and the speed regulator and the DC power flow are considered to simulate the change of the rotor angle, and the continuous format problem involving the dynamics of the power system is discretized into the Euler method to obtain a linear model that is easy to solve numerically, thereby improving the construction of the attack model within the time domain optimization framework.

[0089] This step comprehensively models the dynamic behavior of the power system through a variety of equations and methods, so that the model can more accurately reflect the actual situation, improve the accuracy and operability of the attack model, and provide a more reliable basis for subsequent attacks.

[0090] Furthermore, the load measurements of the entire power grid are compromised, the impact of power system parameters on successful attacks is analyzed, and the load frequency model of the power grid is modeled.

[0091] The load frequency model of the power grid is specifically:

[0092] The load-frequency dynamics of the grid are modeled using the swing equations of the generators, the grid model, and the actions of the controllers, such as the governor and the operation of the relays, i.e., RoCoF and under-frequency / over-frequency relays. In the actual operation of the grid, the inertia of the synchronous generators and the governor actions continuously affects the frequency dynamics, i.e., the primary frequency response, and at regular time intervals, e.g., 2-45 seconds, grid measurements, such as grid frequency and parallel flow, are obtained, and the updated dispatch signals of the generators are sent to the dispatchable generators to maintain the frequency, i.e., the secondary frequency control.

[0093] The process of modeling the dynamic behavior of the power system in the time domain optimization framework is as follows:

[0094] The present invention considers the differential equations of the synchronous generator and the speed regulator and the DC power flow to simulate the change of the rotor angle. The DC power flow returns the new value of the rotor angle for any change in the power system (such as load fluctuations), which helps the present invention to evaluate the frequency behavior of the system. Then, in order to model these continuous format problems in an optimization environment, the present invention discretizes them using the backward Euler method. The dynamics of the power system are represented by nonlinear differential algebraic equations (DAEs), which cannot be solved analytically. Therefore, it is necessary to discretize the equations in order to solve them using numerical methods. In addition, the backward Euler method obtains a linear model of the dynamics after discretization, so the model is scalable compared to the nonlinear discretized model. However, the focus of the present invention is not on the computational gain brought by discretization, and the present invention uses available off-the-shelf solvers to solve the model.

[0095] The frequency behavior of a multi-machine power system can be expressed by the Swing equation as:

[0096]

[0097] Without loss of generality, the governor is represented by the TGOV1 model, which is a simplified representation of a steam turbine governor:

[0098]

[0099] Using the classical representation of a synchronous generator, its terminal voltage angle can be approximated by the rotor angle. Using the DC power flow formula, the grid model becomes:

[0100]

[0101] The dynamic models (1)-(4) determine the primary frequency response of the grid.

[0102] The secondary frequency control is as follows:

[0103] The control center can operate the DC power flow according to the measured value and obtain the steady-state reference set point (dispatch signal) Ps as:

[0104]

[0105] Specifically, the consideration of the grid load characteristics includes compromising the load measurement value of the entire grid and analyzing the impact of power system parameters on successful attacks, specifically:

[0106] By considering the load measurement value of the entire power grid, it is determined that FDIA is the load measurement value within the control area to determine the focus of the attack;

[0107] A comprehensive analysis of the impact of power system parameters such as the inertia of generator sets, droop and time constant of speed regulators, and the attacker’s accessibility to loads on the likelihood of a successful attack and the minimum time required provides a basis for attack strategies.

[0108] In this step, based on the actual situation of grid load measurement, the load meter and tie line sensor measurements are compared to determine the rationality of using the load measurement value in the control area as the focus of the attack. Determine the key attack area based on the actual measurement situation to improve the pertinence of the attack, make the attack more targeted, and increase the success rate of the attack.

[0109] Analyze the difference in the possibility of unsafe power meters and unsafe connection line sensor measurements to further clarify the attack direction.

[0110] It is understandable that a comprehensive analysis of the power system parameters such as the inertia of the generator set, the droop and time constant of the speed regulator, and the attacker's accessibility to the load on the possibility of a successful attack and the minimum time required provides a basis for the attack strategy. The specific effects of parameters such as the inertia of the generator set, the droop and time constant of the speed regulator on the possibility of a successful attack and the minimum time are studied separately; the attacker's accessibility to the load is considered, its effect on the attack effect is evaluated, and the influencing factors are comprehensively derived to guide the formulation of the attack strategy. The principle is to comprehensively consider the impact of various factors on the attack and formulate a more scientific attack strategy. The effect is to make the attack strategy more reasonable and increase the success rate of the attack.

[0111] Specifically, the system dynamic behavior modeling includes modeling the load frequency model of the power grid and modeling the dynamic behavior of the power system in a time domain optimization framework.

[0112] The load frequency model of the power grid is modeled using multiple equations and controller actions to reflect the frequency dynamics and control mechanisms in actual power grid operation. The load-frequency dynamics of the power grid are modeled using the generator swing equation, power grid model, and controller actions to reflect the impact of the inertia of synchronous generators and speed regulator actions on frequency dynamics, as well as the process of maintaining frequency by obtaining power grid measurements and sending dispatch signals.

[0113] The dynamic behavior of the power system is modeled in the time domain optimization framework to ensure that the model can be solved by numerical methods and can accurately simulate system changes. Considering the differential equations of the synchronous generator and the speed regulator and the change of the rotor angle for DC power flow simulation, the power system dynamics are discretized using the backward Euler method to obtain a linear model for numerical solution, improving the scalability and accuracy of the model.

[0114] It can be understood that through a comprehensive modeling and optimization framework, the dynamic behavior of the power system can be accurately reflected, which is convenient for solution and analysis, and can improve the accuracy and practicality of the attack model and provide stronger support for the attack.

[0115] Furthermore, implementing attack optimization includes establishing a false data injection attack model and building an OFDIA model and optimizing the load attack volume.

[0116] According to the operation characteristics of the power grid and the actions of the control center, a false data injection attack model is constructed to clarify the settings and relationships of various parameters and variables. Key factors such as the size of false data injected into the load measurement, the parameters / measurements after injection into FDIA, and the damaged load measurement values ​​used by the control center to update the dispatch signal are fully considered to construct the basic framework of the false data injection attack model.

[0117] The backward Euler method is used to discretize the continuous forms of the power system dynamic model and the control center action into specific relevant formulas such as load measurement attack, grid frequency dynamics, and control center operation. The expressions and mutual correlations of each variable in the model are clarified, and the operation of the RoCoF relay is simulated, and the FRO decision is made according to the predefined thresholds of frequency and RoCoF.

[0118] The specific false data injection attack model is as follows:

[0119] The dynamic characteristics of the power grid and the actions of the control center when the load measurements are compromised are considered, considering the size of the false data injected into the load measurements, the parameters / measurements after injection into the FDIA, and the compromised load measurements used by the control center to update the dispatch signals. The result of the control center running the dispatch process routine based on the compromised load measurements is the compromised reference set points of the controller. When these compromised reference set points are sent to the dispatcher, it causes load imbalance, resulting in frequency dynamics and possibly frequency instability. Therefore, the control center unknowingly participates in the attacker's goal of attacking the load-frequency control of the power grid.

[0120] The present invention uses the backward Euler method to discretize the continuous form of the power system dynamic model and the control center action into:

[0121] Load Measurement Attack:

[0122]

[0123] Grid frequency dynamics:

[0124]

[0125] Control Center Operation:

[0126]

[0127] Equation (6) shows the load measurement attack, where the measurement value for the load not included in the accessible load (A) is zero and remains constant during the dispatch period. Note that in Equations (7)-(12), the grid dynamics are modeled based on the actual load and the corrupted set points of the controller obtained from the control center, which results in corrupted power system variables / parameters. In (13) and (14), the corrupted dispatch signal is obtained based on the corrupted load measurement. Note that in (13), the variable P includes the amount of false data injected on the load measurement.

[0128] To simulate the operation of the RoCoF relay, the present invention performs the following calculations at the relay position:

[0129]

[0130] Then, the FRO decision is made based on the predefined thresholds of frequency and RoCoF:

[0131]

[0132] Construct the OFDIA model, determine the optimized load attack volume and corresponding constraints, ensure the attack concealment and obtain the best attack effect.

[0133] The OFDIA model is as follows:

[0134] The model optimizes the amount of load attack when a RoCoF or frequency violation is initiated. The relay operation logic defined in (16) is a non-smooth function, which complicates the formulation of the problem as it requires integer variables to model. Using slack variables, the present invention reformulates OFDIA as follows, making the problem essentially a linear programming, thus producing a tractable formulation. For a given dispatch period C, OFDIA optimizes the size of the load attack Σkeς(P[(K)) subject to constraints (7)-(16):

[0135] OFDIA:

[0136]

[0137] In addition, constraints (18)−(26),

[0138]

[0139] Where constraints (7)-(12) represent the dynamic model of the power grid, (13)-(14) represent the role of the control center, and (15) represents the RoCoF calculation. Equations (8) and (19) implement the RoCoF relay operation logic described in equation (16). Similarly, equations (20) and (21) model the operation of the frequency relay defined in equation (16). Equation (22) guarantees the positive slack variables. In (23), the present invention attempts to keep the load attack within [-t', t']% of the actual load on bus i. The main purpose of adding this constraint is to prevent OFDIA from attacking only certain load measurements while leaving the rest unchanged. This may be mathematically possible and result in a minimal OFDIA value; however, this would not be a realistic attack scenario with large differences between subsequent time steps.

[0140] Commonly used bad data detection algorithms are residual-based algorithms that use state estimation methods to discover the operating state of the power system. When the residual exceeds the allowed range, the data is classified as bad data. Generally, the attack is invisible when the change in (one or more) measurements keeps the difference between the reported measurement value and the estimated measurement value within a threshold. When this difference is zero, the stealth is at its best possible state. Therefore, in this article, the present invention considers an attack scenario in which the grid is fully visible. This means that there are enough measurements in the entire grid and the control center does not need to perform any state estimation to obtain visibility of the grid. Therefore, any attack on the measurement by the attacker will be directly transferred to the control center, affecting the dispatch process of the generator. In addition, the present invention considers some thresholds in the attack modeling, which can help the present invention represent attacks without observable changes. This ensures the concealment of the attack, so that no bad data detection and FDIA detection algorithms detect OFDIA. Equations (24)-(25) maintain the true value and the attacked value of the generator active power within the allowed range respectively. Equation (26) limits the change in generator power output over the next two dispatch cycles to within [-τg,τg]% of the generator output power. α, β, η, ζ, and γ are weight factors adjusted so that each OFDIA component does not overweight the rest. This helps OFDIA return the best attack in the system, regardless of its type (RoCoF / frequency). The objective function (17) together with the slack variables optimizes the attack vector to ensure that the frequency / RoCoF is pushed towards the upper / lower threshold of relay operation. Note that the above model may not be able to produce the optimal attack vector within one dispatch cycle, given the stealth constraint (23), the inertia of the generator, and the time constants of the equipment and controllers; therefore, the OFDIA model may need to run for multiple dispatch cycles.

[0141] In order to run OFDIA over multiple scheduling cycles, the present invention starts the optimization from C=1, runs OFDIA, and checks whether there is a feasible attack that triggers FRO defined in equation (15). If so, the loop terminates and the result is considered optimal. Otherwise, C is increased, and the process continues until the present invention finds a successful attack or the present invention reaches C equal to the maximum number of scheduling cycles, indicating that FRO is not feasible even over multiple scheduling cycles. The flowchart of this process is shown in Figure 3 As shown. There is no restriction on the choice of the maximum number of dispatch cycles, and the OFDIA proposed in this paper can take any maximum number of dispatch cycles and try to find the optimal attack within the desired time. However, if the maximum number of dispatch cycles is not large enough, the solver may not be able to find a successful attack. Basically, the appropriate maximum dispatch cycle value will be different for different power grids. For example, if a power grid mainly contains generators with large inertia, then the frequency in such a power grid will take a longer time to oscillate. Therefore, the frequency / RoCoF attack takes a longer time to be successfully launched in such a grid; that is, it requires a larger maximum number of dispatch cycles.

[0142] It is understandable that when constructing the OFDIA model, the focus is on optimizing the amount of load attack when RoCoF or frequency violation is initiated, and it is restated as a linear programming problem using slack variables. At the same time, many constraints including the grid dynamic model, the role of the control center, and rocof calculation are set to reasonably optimize the size of the load attack.

[0143] By setting relevant thresholds such as preventing attacks from being too concentrated, ensuring the power range of generators, and limiting the changes in generator power output, the concealment of the attack is ensured to avoid being discovered by the detection algorithm, and the weight factors are adjusted to balance the OFDIA components to ensure that the model can return the best attack in the system.

[0144] Among them, the model is implemented by starting from the initial dispatch cycle, running OFDIA and checking whether there is a feasible attack that triggers the operation of related relays. If not, the dispatch cycle is increased in sequence until a successful attack is found or the maximum number of dispatch cycles is reached. Finally, the attack on the load-frequency control of the power system is realized. At the same time, the maximum number of dispatch cycles is reasonably determined according to the characteristics of different power grids to ensure the effectiveness of the attack. The principle is to comprehensively consider various factors, build a perfect attack model and optimize it to ensure the concealment and effect of the attack. The effect is to improve the success rate and concealment of the attack and reduce the risk of being discovered.

[0145] The frequency-based relay operations are:

[0146] Generators are usually equipped with RoCoF and overfrequency relays and loads (bulk level) are equipped with underfrequency (or load shedding) relays to maintain load / generation balance by disconnecting excess load / generation in case of high frequency oscillations outside a predefined range. The underfrequency / overfrequency relays are triggered based on the frequency measurement, while the RoCoF relays are triggered based on the average rate of change of frequency at the relay position.

[0147] The present invention also provides an optimal false data injection attack system for load-frequency control in an electric power system, which is used to implement the above attack method and includes an attack model building module, an attack impact analysis module and an attack execution module.

[0148] The attack model construction module is used to construct an attack model based on time domain formal modeling. It is configured with an optimization unit, which can find the optimal false data injection attack through optimization means, minimize the time required to successfully launch an attack, and model based on minimizing the time required for a successful attack; the attack impact analysis module is used to consider the impact of power grid-related characteristics and power system parameters on the attack, and implement the attack process to achieve an attack on the load-frequency control of the power system; the attack execution module is connected to both the attack model construction module and the attack impact analysis module, and is used to implement specific optimal false data injection attack operations on the load-frequency control of the power system based on the attack model and the impact analysis results, according to the preset attack process.

[0149] The present invention realizes the optimal false data injection attack on the power system through the synergistic effect of various modules, provides system support for the implementation of the attack method, and improves the efficiency and success rate of the attack.

[0150] The following describes various embodiments of the present invention.

[0151] Example 1

[0152] like Figure 5 As shown, it is a diagram of the IEEE39 bus system. This embodiment uses the IEEE39 bus system as a case study to test the proposed formal attack model. The system has 10 synchronous generators, where S=1000MVA. For simplicity, this embodiment assumes Kp=0 for all generators. In addition, this embodiment ignores the subtransient reactance of the generator; therefore, the bus voltage angle is equal to the generator rotor angle. It is assumed that all generators have overfrequency relays and RoCoF relays, and all loads have underfrequency relays. It is assumed that the generators connected to the 30~35 bus are equipped with speed regulators participating in frequency regulation during the dispatch process, and the remaining generators have fixed mechanical input power. This embodiment assumes that the actual values ​​of the loads in the power grid, namely P, Vi and C, remain unchanged throughout the simulation process (<60 seconds). However, the formal model proposed in this embodiment can capture the actual changes in the load as well as the damaged measurements.

[0153] OFDIA is implemented using JuMP24028419, a domain-specific modeling language for mathematical optimization, and solved using Gurobi.

[0154] Example 2

[0155] In this section, this embodiment aims to verify the accuracy of the power system dynamics modeling adopted in this paper. To this end, this embodiment needs to ensure that the dynamic behavior of the test system is only due to the power system modeling represented by (7) to (15). Therefore, this embodiment sets all load measurement attack values ​​in (17) to zero, that is, P[K]=0, Vi∈A, Vk∈C, and disables constraints (18) to (26). Thereafter, this embodiment runs (17) to obtain a load disturbance of 500MW (25MW per load bus). The disturbance accounts for 8.13% of the total system load of 6150MW and lasts for 2s (from t=1s to t=3s).

[0156] Figure 6 33 and 35, the rotor angles of the generator 35, the model accuracy used for the generator 35, and the frequency characteristics developed in ePHASORSIM for the generator 33. Figure 6 Comparison of the frequency and rotor angle behavior of the generators at busbars 33 and 35 obtained in FIG. It can be seen that the dynamic response of the model adopted in the present invention is sufficient to reflect the actual dynamics of the test system. Note that the adopted method utilizes DC power flow to increase the scalability of the optimization model. The few observed differences in the results are due to the differences in the power flow methods used.

[0157] Example 3

[0158] To demonstrate the optimality of the proposed OFDIA, this example compares the results of a successful non-optimal FDIA (NOFDIA), which is a random feasible solution, with the results of the proposed OFDIA on load measurements and shows their impact on the frequency behavior of the power system. The information of this study is shown in Tables II, II, and IV.

[0159] Please refer to Figure 7 , Figure 7 Comparison of load measurement attack and frequency dynamics for optimal attack (OFDIA) and non-optimal attack (NOFDIA).

[0160] Specifically, Figure 7(a) shows the load attack values ​​measured for all loads in the test system. For OFDIA, it can be seen that all attack values ​​have small magnitudes and small variations between two consecutive cycles. This is due to the stealth constraints (18) to (25) in (17), which keep the attack volume within the allowed range. However, it is obvious from the figure that at least one of the NOFDIA attack values ​​is very large in magnitude and varies greatly between two consecutive cycles. Although such an attack will cause the protection relays of the power system to operate, it is most likely to be detected by the attack detection method in the control center before causing any problems due to the unobtrusive manipulation in the measurements. Figure 7 (b) also shows the frequency behavior of the system for both types of attacks. According to this figure, both OFDIA and NOFDIA can generate overfrequency (f>61.8Hz) in the system within the same time frame (12 seconds). While the operation of one protection relay in the system is considered a successful attack, NOFDIA causes overfrequency in all protection relays of the generators due to the non-optimal injection in the load measurement. However, OFDIA only causes overfrequency in some generators, which reflects the optimality of the proposed OFDIA method.

[0161] The present embodiment agrees that the problem can be formulated as a mixed integer linear program (MILP) by including "RoCoF or frequency" related constraints in the problem formulation. MILP type models do not scale up to larger systems; therefore, the present embodiment combines constraints by avoiding the use of slack variables with integer variables. However, the present embodiment has performed an additional simulation showing two cases: a) only RoCoF related constraints ((18)-(19)) and b) frequency related.

[0162] The results are as follows Figure 8 As shown, Figure 8 Figure 2. OFDIA with frequency constraints only (F-OFDIA) versus RoCoF constraints only (R-OFDIA). Figure 8 (a) shows the number of attacks launched against the load measurement (P) for attacks with the best frequency target (F-OFDIA) and RoCoF target (R-OFDIA). Activating different constraints (frequency or RoCoF) in OFDIA results in different PI, as shown in the figure. Figure 8 (b) also shows that the frequency oscillations in F-OFDIA exceed the threshold (60.8 Hz), while these oscillations in R-OFDIA remain below the threshold. This is because the main focus of R-OFDIA is to find the best P value to induce RoCoF attack in the system, regardless of the frequency value and its behavior. Figure 8 (b) and Figure 8(b) It can be found that the frequency oscillations of OFDIA and F-OFDIA are similar. This shows that the proposed OFDIA objective function returns the optimal attack on load measurement in the case of possible constraint violations, regardless of whether the frequency constraint and RoCoF constraint are activated simultaneously or separately.

[0163] Unless otherwise specified, the models of the components in the embodiments of the present invention are not limited, and any component that can complete the above functions may be used.

[0164] Those skilled in the art will appreciate that the accompanying drawing is only a schematic diagram of a preferred embodiment, and the serial numbers of the embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

[0165] Based on the foregoing embodiments, the contributions of the present invention are as follows:

[0166] This paper proposes a time-domain formal modeling to find OFDIA while minimizing the time of successful attack. This paper uses an optimizer to find the optimal size of the payload attack while implementing a sequential process to find the minimum time of successful attack. However, due to the non-convexity of the problem, the proposed method may not return the global optimum. In addition, the optimization model is formulated based on a weighted objective function; therefore, the method is sensitive to the choice of weights.

[0167] Unlike most of the inventions that focus on compromising tie-line sensor measurements, the formal modeling proposed in this invention aims to compromise load measurements for the entire grid. In other words, most of the current papers focus on control areas, while this invention considers FDIA to be load measurements within these control areas. This scenario seems more realistic because the number of load meters in the grid far exceeds the number of tie-line sensor measurements. Therefore, unsafe electricity meters are more likely to occur than unsafe tie-line sensor measurements.

[0168] Thereafter, using the proposed formal modeling, the present invention analyzes and comprehensively studies the impact of power system parameters, such as the inertia of the generator sets, the droop and time constant of the governor, and the attacker’s accessibility to the load on the likelihood and minimum time required for a successful attack.

[0169] The uniqueness of the present invention lies in:

[0170] Things like increasing the penetration of renewable energy in the grid and thus reducing the inertia of the power system can make the frequency stability of the power system more vulnerable to FDIA. In contrast, the combination of large governor time constant values ​​and small droop values ​​can increase the time required for a successful attack, making the frequency of the power system more stable against the attack. This paper proposes an OFDIA model to observe the feasibility of such an attack in a single-region power grid, which mainly includes load measurements, and then evaluates the feasibility of frequency-based relay protection FRO that affects the frequency security of the power system.

[0171] In summary, the present invention discloses an optimal false data injection attack (FDIA) method for load-frequency control in a power system, the method comprising: proposing an optimization-based formal model to find the optimal false data injection attack method (OFDIA) and cause frequency-dependent protection relay false operation (FRO) in the shortest time. The proposed model considers the dynamic behavior of the power system in an optimization framework to find the optimal attack scale within multiple generator dispatch cycles to minimize the attack startup time. Using the proposed modeling method, the present invention studies the impact of power system parameters (including inertia, governor droop, and time constant) and the attacker's accessibility to the load on the attack success and startup time. The results show that low-inertia systems are more susceptible to FDIA, while high-inertia systems are safer due to fewer generator protection relays being affected by FRO. In addition, the present invention also shows that protecting more load meters can increase the time to launch an attack in the system. In addition, the combination of large governor time constant values ​​and small governor droop values ​​can improve the time to a successful attack and make the system safer against FDIA.

[0172] Finally, it should be noted that although the above embodiments have been described in the specification and drawings of this application, this does not limit the scope of patent protection of this application. All technical solutions generated by replacing or modifying equivalent structures or equivalent processes based on the essential concept of this application using the contents recorded in the specification and drawings of this application, as well as directly or indirectly implementing the technical solutions of the above embodiments in other related technical fields, are included in the scope of patent protection of this application.

Claims

1. An optimal false data injection attack method for load-frequency control in a power system, characterized in that: The following steps are involved: Propose time domain formal modeling to find OFDIA, minimize successful attack time, build OFDIA model and optimize load attack volume; The load frequency model of the power grid is modeled by considering the load measurements of the entire power grid and analyzing the impact of power system parameters on successful attacks; Modeling the dynamic behavior of power systems in a time-domain optimization framework; Establish a false data injection attack model, build an OFDIA model and optimize the load attack volume.

2. The optimal false data injection attack method for load-frequency control in a power system according to claim 1, characterized in that: The proposed time domain formal modeling is used to find OFDIA, minimize the successful attack time, build the OFDIA model and optimize the load attack volume, including: The optimizer is used to determine the optimal size of the load attack based on the load measurement value of the entire power grid, taking into account the actual structure and measurement of the power grid. At the same time, the optimization model formulated by the sequential process and the weighted objective function is used to find the minimum time for a successful attack, thereby constructing a time domain formal modeling. The dynamic behavior of the power system is modeled and solved in a time domain optimization framework to obtain a perfect attack model.

3. The optimal false data injection attack method for load-frequency control in a power system according to claim 2, characterized in that: The optimizer determines the optimal size of the load attack based on the load measurement value of the entire power grid, taking into account the actual structure and measurement of the power grid. At the same time, the optimization model formulated by the sequential process and the weighted objective function is used to find the minimum time for a successful attack, thereby constructing a time domain formal modeling, including: Based on the actual structure and measurement of the power grid, the load measurement range that the attack focuses on is determined according to the load measurement value of the entire power grid, and the appropriate scale and direction of the load attack is determined based on the load measurement range in combination with the optimizer; Analyze the influence of power system parameters, the accessibility of the attacker to the load on the possibility of a successful attack, and the minimum time required, and obtain the influencing factors; the power system parameters include the inertia of the generator set, the droop and time constant of the speed regulator; Integrate the influencing factors into the weighted objective function to construct an optimization model that can effectively find the minimum attack time; The dynamic behavior of the power system is modeled and solved in a time domain optimization framework to obtain a perfected attack model, including: Model the load-frequency dynamics of the power grid based on the generator swing equations, the power grid model, and the actions of the controller, laying the foundation for overall modeling in the time domain framework; The differential equations of the synchronous generator and the speed regulator as well as the DC power flow are considered to simulate the change of the rotor angle. The continuous format problem involving the dynamics of the power system is discretized into the Euler method to obtain a linear model that is easy to solve numerically, and the attack model construction within the time domain optimization framework is improved.

4. The optimal false data injection attack method for load-frequency control in a power system according to claim 1, characterized in that: The consideration of the load characteristics of the power grid includes compromising the load measurement value of the entire power grid and analyzing the impact of power system parameters on successful attacks, specifically: By considering the load measurement value of the entire power grid, it is determined that FDIA is the load measurement value within the control area to determine the focus of the attack; A comprehensive analysis of the impact of power system parameters such as the inertia of generator sets, droop and time constant of speed regulators, and the attacker’s accessibility to loads on the likelihood of a successful attack and the minimum time required provides a basis for attack strategies.

5. The optimal false data injection attack method for load-frequency control in a power system according to claim 4, characterized in that: The compromise considers the load measurement values ​​of the entire power grid and determines that FDIA is the load measurement value within the control area to determine the focus of the attack, including: According to the actual situation of power grid load measurement, the load meter and the tie line sensor measurement quantity are compared to determine the rationality of taking the load measurement value in the control area as the attack focus; Analyze the difference in the possibility of unsafe power meters and unsafe connection line sensor measurements to further clarify the attack direction; The comprehensive analysis of the impact of power system parameters such as the inertia of the generator set, the droop and time constant of the governor, and the attacker's accessibility to the load on the possibility of a successful attack and the minimum time required provides a basis for the attack strategy, including: The specific effects of the parameters such as the inertia of the generator set, the droop and time constant of the speed governor on the probability and minimum time of a successful attack are studied respectively; Consider the attacker’s accessibility to the payload, evaluate its effect on the attack effect, and comprehensively derive influencing factors to guide the formulation of attack strategies.

6. The optimal false data injection attack method for load-frequency control in a power system according to claim 1, characterized in that: The system dynamic behavior modeling includes modeling the load frequency model of the power grid and modeling the dynamic behavior of the power system in a time domain optimization framework, specifically: The load frequency model of the power grid is modeled using multiple equations and controller actions to reflect the frequency dynamics and control mechanisms in actual power grid operation; Modeling the dynamic behavior of the power system in a time-domain optimization framework ensures that the model is numerically solvable and can accurately simulate system changes; The load frequency model of the power grid is modeled using a variety of equations and controller actions to reflect the frequency dynamics and control mechanisms in the actual operation of the power grid, including: Model the load-frequency dynamics of the power grid using the generator swing equations, the grid model, and the controller actions, reflecting the impact of the inertia of the synchronous generator and the governor action on the frequency dynamics, and the process of maintaining the frequency by obtaining grid measurements and sending dispatch signals; The dynamic behavior of the power system is modeled in the time domain optimization framework to ensure that the model can be solved by numerical methods and can accurately simulate system changes, including: Considering the differential equations of synchronous generator and speed regulator as well as the change of rotor angle for DC power flow simulation, the backward Euler method is used to discretize the power system dynamics and obtain a linear model for numerical solution, which improves the scalability and accuracy of the model.

7. The optimal false data injection attack method for load-frequency control in a power system according to claim 1, characterized in that: The attack optimization includes establishing a false data injection attack model, building an OFDIA model, and optimizing the load attack volume, specifically: Construct a false data injection attack model based on the power grid operation characteristics and control center actions, and clarify the settings and relationships of various parameters and variables; Construct the OFDIA model, determine the optimized load attack volume and corresponding constraints, ensure the attack concealment and obtain the best attack effect.

8. The optimal false data injection attack method for load-frequency control in a power system according to claim 7, characterized in that: The false data injection attack model is constructed based on the power grid operation characteristics and the control center actions, and the settings and relationships of various parameters and variables are clarified, including: The basic framework of the false data injection attack model is constructed by fully considering key factors such as the size of the false data injected into the load measurement, the parameters / measurements after injection into FDIA, and the damaged load measurement values ​​used by the control center to update the dispatch signal; The backward Euler method is used to discretize the continuous forms of the power system dynamic model and the control center action into specific relevant formulas such as load measurement attack, grid frequency dynamics, and control center operation. The expressions and mutual correlations of each variable in the model are clarified, and the operation of the RoCoF relay is simulated, and the FRO decision is made according to the predefined thresholds of frequency and RoCoF.

9. The optimal false data injection attack method for load-frequency control in a power system according to claim 7, characterized in that: The OFDIA model is constructed to determine the optimized load attack amount and corresponding constraints to ensure the attack concealment and obtain the best attack effect, including: When constructing the OFDIA model, we focus on optimizing the amount of load attack when RoCoF or frequency violation is initiated, and use slack variables to reformulate it as a linear programming problem. At the same time, we set many constraints including the power grid dynamic model, the role of the control center, and RoCoF calculation to reasonably optimize the size of the load attack; By setting relevant thresholds such as preventing attacks from being too concentrated, ensuring the power range of generators, and limiting the changes in generator power output, the attack is kept hidden and can be avoided from being discovered by the detection algorithm. The weight factors are adjusted to balance the OFDIA components and ensure that the model can return the best attack in the system. Starting from the initial dispatch cycle, OFDIA runs and checks whether there is a feasible attack that triggers the operation of related relays. If not, the dispatch cycle is increased successively and continues to run until a successful attack is found or the maximum number of dispatch cycles is reached. The model is implemented to finally achieve an attack on the load-frequency control of the power system. At the same time, the maximum number of dispatch cycles is reasonably determined according to the characteristics of different power grids to ensure the effectiveness of the attack implementation.

10. An optimal false data injection attack system for load-frequency control in a power system, characterized in that: A method for implementing an optimal false data injection attack on load-frequency control in a power system as claimed in any one of claims 1 to 9, comprising: An attack model building module, used to build an attack model based on time domain formal modeling, configured with an optimization unit, which can find the optimal false data injection attack through optimization means, minimize the time required for successfully launching an attack, and model based on the minimized time required for a successful attack; The attack impact analysis module is used to consider the impact of grid-related characteristics and power system parameters on the attack and implement the attack process to achieve the attack on the load-frequency control of the power system; The attack execution module is connected to the attack model construction module and the attack impact analysis module, and is used to implement a specific optimal false data injection attack operation on the load-frequency control of the power system based on the attack model and the impact analysis result according to a preset attack process.

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