Multi-zone power system event-triggered load frequency safety control method and system

Abstract

The application discloses a multi-region power system event-triggered load frequency safety control method and system, and the technical scheme points are as follows: in view of the problem that the existing load frequency control method generally assumes that the communication link is continuously available and is difficult to maintain stable operation under the condition of DoS attack, the system is modeled as a switching system when the DoS attack exists, and the control mode is switched in real time according to whether the link is subjected to the DoS attack: the conventional learning control is executed to optimize the frequency regulation performance when the communication is normal; the anti-attack control mode is switched to when the attack occurs, so that the closed-loop stability can be maintained and the frequency deviation and the tie-line power fluctuation can be inhibited under the condition that the communication is blocked, and the system safety is significantly improved; in addition, based on the RL method, the control strategy is obtained by online learning through interaction with the environment under the condition that the system model is unknown or the parameters are uncertain, so that the control energy minimization and the operation economy are realized without depending on the accurate system dynamics.

Description

Technical Field

[0001] This invention relates to the field of power control technology, and more specifically, to a method and system for event-triggered load frequency safety control in multi-regional power systems. Background Technology

[0002] Load frequency control is a crucial component of multi-regional power system operation control. Its primary objective is to achieve a dynamic balance between power generation and load demand under disturbances such as load fluctuations and random variations in renewable energy output, and to maintain the system frequency stably near its rated value, thereby ensuring power quality and the safe and stable operation of the system. With the deep integration of information and communication networks and control systems in new multi-regional power systems, the system's reliance on communication networks has significantly increased. However, due to the open and interconnected nature of communication networks, power systems are vulnerable to cyberattacks such as Denial of Service (DoS) attacks. DoS attacks can cause delays, packet loss, or even interruptions in the transmission of critical measurement data or control commands, leading to the controller's inability to obtain timely and effective feedback or output effective control quantities. This results in a decline in frequency regulation performance and, in severe cases, may cause frequency exceedances, increased power fluctuations on tie lines, or even power outages. Therefore, ensuring the safe and reliable operation of multi-regional power systems under cyberattack scenarios is of paramount importance.

[0003] In scenarios involving network attacks and limited communication resources, control systems not only need to maintain stability but also minimize performance losses caused by communication constraints and attacks, improving the system's adaptability and robustness against interference in complex environments. Existing load frequency safety control methods largely rely on accurate system mathematical models and stable communication conditions. When the system model has uncertainties or the communication link is attacked, control performance is prone to significant degradation, and closed-loop stability may even be difficult to guarantee. Reinforcement learning (RL), as a data-driven optimization method, can learn control strategies step-by-step through interaction with the dynamic environment when the system model is unknown or the parameters are uncertain, possessing a certain degree of adaptability and online optimization potential.

[0004] Therefore, in complex environments such as DoS attacks, limited communication resources, and unknown system models, how to design a RL-based event-triggered load frequency security control method and system for multi-regional power systems to effectively improve the performance of multi-regional power systems is a key technical problem that urgently needs to be solved. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a method and system for event-triggered load frequency security control in multi-regional power systems. When a DoS attack occurs, the system is modeled as a switching system, and the control mode is switched in real time according to whether the link is under DoS attack: when communication is normal, conventional learning control is performed to optimize frequency regulation performance; when an attack occurs, it switches to an anti-attack control mode, thereby maintaining closed-loop stability and suppressing frequency deviation and tie-line power fluctuations even when communication is blocked, significantly improving system security.

[0006] The above-mentioned technical objective of the present invention is achieved through the following technical solution: Firstly, a method for event-triggered load frequency security control in multi-regional power systems is provided, including the following steps: When facing a Denial-of-Service (DoS) attack, the multi-regional power system is modeled as a switching system, and a switching control law is established. The switching control law includes a first control mode executed in the safe interval where communication is normal and a second control mode executed in the attack interval where communication is blocked. For the switching system, an optimization objective function is established that includes system state, control input, and external disturbances, transforming the load frequency control problem into a zero-sum game problem, so as to minimize control energy consumption while suppressing external disturbances; Within the safe zone, an event-triggered transmission strategy is designed to transmit the system status information collected by the sensors to the controller when the triggering conditions are met. The data-driven composite strategy iterative algorithm learns and solves the optimal controller gain matrix corresponding to the optimization objective function by interacting with the environment. The composite strategy iterative algorithm automatically finds initialization parameters to ensure the convergence of the algorithm during the iteration process. The optimal controller gain matrix obtained by solving is applied to the switching control law to generate the final control command, thereby realizing the safe control of load frequency in a multi-regional power system under DoS attack.

[0007] Furthermore, the safe zone and the attack zone are divided in an alternating manner on the time axis; Within the safe zone, the switching control law adopts a first control mode calculated based on the latest successfully transmitted state information; Within the attack range, the switching control law switches to a second control mode based on the previous successful transmission and combined with historical data for maintenance or compensation.

[0008] Furthermore, within the attack range, when communication is blocked and new status information cannot be obtained, data compensation is also included: By utilizing the system state and control commands successfully transmitted last time before entering the attack zone, the control input at the current moment is generated by maintaining or predicting the system dynamics, so as to maintain the transient stability of the system and suppress the expansion of frequency deviation.

[0009] Furthermore, the data-driven composite strategy iterative algorithm specifically includes: Acquire the status data, control input data, and external interference data of the multi-regional power system during its operation; Based on the state data, control input data, and external disturbance data, a data matrix and vector containing the Kronecker product are constructed. By solving the least squares equations constructed based on the data matrix and the vector, the parameter matrix in policy evaluation and the controller gain matrix in policy improvement are updated online. The process is repeated iteratively until the controller gain matrix converges, and the converged gain matrix is ​​taken as the optimal controller gain matrix.

[0010] Furthermore, the automatic search for initialization parameters to ensure algorithm convergence specifically includes: Given an arbitrary initial controller gain matrix and initial parameters; The parameter matrix is ​​calculated by performing one iteration using the composite strategy iterative algorithm. Determine whether the parameter matrix is ​​a positive definite matrix; If not, the value of the initial parameter is increased by a fixed step size and recalculated until the parameter matrix is ​​a positive definite matrix. At this point, the initial parameter is used to ensure the convergence of subsequent iterations.

[0011] Furthermore, in constructing the data matrix, the method also includes: Probe noise is introduced into the control strategy input to the composite strategy iterative algorithm to ensure that the constructed data matrix has full rank so that the least squares equation has a solution.

[0012] Furthermore, the parameter matrix in the online update strategy evaluation includes: Based on the controller gain and system operating data from the previous iteration, a virtual matrix with adjusted parameters is constructed. The virtual matrix is ​​obtained by subtracting a scalar adjustment term related to the current iteration and ensuring stability from the original system matrix. Solve a Lyapunov equation consisting of the virtual matrix, the current controller gain, and the optimized weights. The unique positive definite solution of this equation is the parameter matrix to be obtained.

[0013] Furthermore, the optimization objective function is constructed as a performance index in the form of a zero-sum game, which is the sum of the integrals of the quadratic form of the system state deviation, the quadratic form of the control input energy, and the quadratic form of the scaled external disturbance energy from the current time to infinite future time. The objective of solving the optimal control strategy is to find a control input that minimizes the performance index, while considering a worst-case external disturbance that attempts to maximize the same performance index.

[0014] Furthermore, the triggering conditions of the event-triggered transmission strategy are set based on the comparison principle: A new data transmission is triggered when the squared norm of the error vector between the current control input and the most recently successfully transmitted control input exceeds a threshold consisting of a linear combination of the squared norms of the current system state vector and the linear combination of the squared norms of the most recently successfully transmitted control input. The linear combination coefficients used to construct the threshold are all pre-set normal numbers.

[0015] Secondly, a multi-regional power system event-triggered load frequency security control system is provided, including: The model building module is used to model a multi-regional power system as a switching system when facing a denial-of-service (DoS) attack, and to establish a switching control law. The switching control law includes a first control mode executed in a safe interval where communication is normal and a second control mode executed in an attack interval where communication is blocked. The problem optimization module is used to establish an optimization objective function for the switching system, which includes system state, control input and external disturbances, and transform the load frequency control problem into a zero-sum game problem, so as to minimize control energy consumption while suppressing external disturbances. The triggering mechanism module is used to design an event triggering transmission strategy within the safe zone, and to transmit the system status information collected by the sensor to the controller when the triggering conditions are met. An online learning module is used for a data-driven composite strategy iterative algorithm to learn and solve for the optimal controller gain matrix corresponding to the optimization objective function through interaction with the environment. The composite strategy iterative algorithm automatically finds initialization parameters to ensure the convergence of the algorithm during the iteration process. The control execution module is used to apply the solved optimal controller gain matrix to the switching control law to generate the final control command, thereby realizing the load frequency security control of the multi-regional power system under DoS attack.

[0016] Compared with the prior art, the present invention has the following beneficial effects: 1. The multi-regional power system event-triggered load frequency security control method provided by this invention addresses the problem that existing load frequency control methods generally assume continuous availability of communication links and are difficult to maintain stable operation under DoS attack conditions. When a DoS attack occurs, the system is modeled as a switching system, and the control mode is switched in real time according to whether the link is under DoS attack: when communication is normal, conventional learning control is performed to optimize frequency regulation performance; when an attack occurs, it switches to an anti-attack control mode, thereby maintaining closed-loop stability and suppressing frequency deviation and tie-line power fluctuations even when communication is blocked, significantly improving system security.

[0017] 2. This invention incorporates control energy consumption into the optimization objective without requiring a precise model, thus balancing economic efficiency and applicability. Existing load frequency security control methods often focus on system stability and communication resource conservation, neglecting to incorporate control energy consumption during unit regulation into a unified optimization framework. Furthermore, traditional model-based optimal control methods typically rely on precise system parameters and structural models. However, modern power systems are characterized by high parameter uncertainty, high load disturbance randomness, and significant fluctuations in renewable energy, making accurate system models difficult to obtain. Therefore, this invention, based on the RL method, obtains control strategies through online learning with the environment under conditions of unknown system models or uncertain parameters. This achieves the minimization of control energy consumption and improves operational economy without relying on precise system dynamics.

[0018] 3. This invention balances security control with communication resource constraints, using an event-triggered strategy and a data compensation method to synergistically reduce communication burden. Addressing the issues of redundant information, channel congestion, and increased network latency generated by traditional periodic sampling time-triggered communication mechanisms, and considering the risk of control performance degradation due to the loss of critical data / control commands caused by DoS attacks, this invention designs an event-triggered strategy under DoS attack and communication constraints, and introduces a data compensation mechanism during the attack. The synergistic effect of these two mechanisms effectively reduces unnecessary communication and continuous high-frequency transmission requirements, lowers bandwidth usage and transmission pressure, and improves frequency adjustment robustness under attack scenarios.

[0019] 4. This invention reduces the reliance on initial stable strategies and expert experience, accelerates learning convergence, and efficiently solves for optimal control strategies. Addressing the problems of existing RL-based strategy iteration algorithms requiring pre-set initial stable strategies, relying on expert experience for parameter tuning, and incurring high trial-and-error costs, as well as value iteration algorithms which, while allowing for more flexible initial strategies, suffer from numerous iterations and slow convergence, this invention proposes a data-driven composite strategy iteration algorithm. This algorithm achieves efficient convergence without requiring pre-set initial stable strategies, thus providing power systems with optimal control strategies that combine safety and economy in complex environments.

[0020] 5. This invention is applicable to complex multi-region interconnected systems and has strong scalability and adaptability. Designed for multi-region interconnected system structures, this invention can simultaneously handle complex factors such as regional coupling, tie-line power exchange, and the superposition of disturbances and attacks. It has good scalability and can be extended to new power system scenarios such as high-proportion renewable energy grid connection, energy storage participation in frequency regulation, flexible load regulation, and multi-control center collaborative control. Attached Figure Description

[0021] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings: Figure 1 This is a flowchart from Embodiment 1 of the present invention; Figure 2 This is a schematic diagram of the sensor sampling time and the controller update time under a DoS attack in Embodiment 1 of the present invention. (a) is the DoS attack interval and the sleep interval, (b) is the sampler sampling time, and (c) is the controller update time under a DoS attack. Figure 3 This is a schematic diagram of the control area of ​​the IEEE 39-node three-area interconnected power system in Embodiment 2 of the present invention; Figure 4 This is a schematic diagram of the system status response of each region under a DoS attack in Embodiment 2 of the present invention; Figure 5 This is a schematic diagram showing the instantaneous release time and interval of the event triggering mechanism in Embodiment 2 of the present invention; Figure 6 This is a schematic diagram of the controller response under DoS attack and limited communication resources in Embodiment 2 of the present invention; Figure 7 This is a system block diagram in Embodiment 3 of the present invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0023] Example 1: A method for event-triggered load frequency security control in multi-regional power systems, such as... Figure 1 As shown, it includes the following steps: S1: When facing a Denial-of-Service (DoS) attack, the multi-regional power system is modeled as a switching system, and a switching control law is established. The switching control law includes a first control mode executed in the safe zone where communication is normal and a second control mode executed in the attack zone where communication is blocked. S2: For switching systems, establish an optimization objective function that includes system state, control input and external disturbances, and transform the load frequency control problem into a zero-sum game problem, so as to minimize control energy consumption while suppressing external disturbances; S3: Within the safe zone, design an event-triggered transmission strategy to transmit the system status information collected by the sensor to the controller when the triggering conditions are met. S4: A data-driven composite policy iterative algorithm that learns and solves for the optimal controller gain matrix corresponding to the objective function by interacting with the environment. The composite policy iterative algorithm automatically finds initialization parameters to ensure the convergence of the algorithm during the iteration process. S5: Apply the obtained optimal controller gain matrix to the switching control law to generate the final control command, thereby achieving safe control of load frequency in a multi-regional power system under DoS attack.

[0024] First, consider the following multi-regional power system model: (1) in,

[0025]

[0026] in, It is the state vector of a multi-regional power system. It is the first The state vector of a regional power system It is the control input vector of a multi-regional power system. It is the first Control input vector of a regional power system It is the external disturbance vector of a multi-regional power system. Defined as the first External disturbance vector of a regional power system, index variable , It is the number of regions in a multi-regional interconnected power system. Represents the set of positive integers. These are the state weight matrix, control input weight matrix, and external disturbance weight matrix of a multi-regional power system, respectively. The first The state weight matrix, control input weight matrix, and external disturbance weight matrix of the regional power system For the first The regional power system and the first The weight matrix of the coupling of the regional power system. The first Frequency deviation and generator mechanical output deviation in each region The first Valve position deviation, connecting line power deviation, and area control error for each region. Defined as a linear combination of power exchange and frequency deviation between inter-regional tie lines, i.e. ,in Represents the frequency deviation coefficient. For the first Load deviation in each region These are the generator damping coefficient and the generator moment of inertia, respectively. Indicates the first and the Synchronization coefficient of the connecting lines between control areas These are the turbine time constant, the governor time constant, and the speed reduction parameter.

[0027] Because cyberattacks are energy-constrained, DoS attacks typically occur intermittently or randomly, meaning an attacker cannot launch consecutive DoS attacks. This invention uses... Indicates the first The instant at which the communication channel becomes accessible after a non-periodic DoS attack. This indicates the time interval during which the communication channel remains accessible. Specifically, it allows... Indicates the first The safe zone for this DoS attack. Indicates the first The communication interval affected by the DoS attack. Simultaneously, the DoS attack satisfies the following assumptions: Assumption 1: For DoS attack safe zone Scalar exists Make Furthermore, regarding the DoS attack range... Scalar exists Make .

[0028] Assumption 2: Let Representing an interval The number of DoS attacks within, of which Let represent the number of elements in the set. Then, does a scalar exist? , making Established.

[0029] Considering switching controllers, the system control input is: (2) in, Indicates an attack state. and Each attack state The control strategy and external disturbance strategy. Let , These are all gain matrices designed later.

[0030] Next, the optimal load frequency safety control strategy and the algebraic Riccati equation are designed as follows: for The cost function is defined as follows: (3) in, The weight matrix represents the state-related factors. This indicates the level of interference attenuation.

[0031] For convenience, the matrix in this invention is... , Representation matrix The transpose of .

[0032] Considering energy consumption control, load frequency security control can be transformed into a zero-sum game problem, the goal of which is to obtain the optimal strategy pair by solving the following problems. ,Right now (4) in For the optimal strategy pair The cost function under, The following conditions must be met: (5) in For optimal control strategy and arbitrary perturbation strategy The cost function under, For arbitrary control strategies and optimal perturbation strategy The cost function under this condition.

[0033] According to optimal control theory, equation (4) can be expressed in quadratic form of the current state as follows: , where the matrix It can be determined by the following algebraic Riccati equation: (6) Therefore, under a DoS attack, the optimal load frequency security control strategy is as follows: (7) in This is the optimal control gain.

[0034] Subsequently, an event-triggered mechanism was introduced into the controller design, supplemented by a data compensation strategy, to effectively conserve network resources while ensuring system performance. Specifically, as follows... Figure 2 As shown.

[0035] Based on DoS attack and event-triggered strategies, the load frequency security control strategy is designed as follows: (8) in, This represents the (s+1)th DoS attack safe zone. The sequence of successful internal transmission times. Indicates the supremacy. The set of natural numbers. For the most recently successfully transmitted control input With current control input The triggering error between them, the event triggering mechanism is designed as (9) in, All are normal numbers.

[0036] Therefore, under DoS attacks and resource constraints, the optimal security control strategy for event-triggered load frequency is as follows: (10) in Any attack state And the load frequency safety control strategy under the event-triggered strategy.

[0037] Finally, in order to solve the problem about Based on the algebraic Riccati equation (6), an improved policy iteration algorithm is proposed, which not only relaxes the requirements for the initial stable control policy pair, but also guarantees a certain convergence speed. Before introducing the data-driven composite policy iteration algorithm, a lemma and theorem are introduced.

[0038] Lemma 1: For each attack state Given an initial stable gain matrix Make ( For the first The gain matrix in the next iteration step is a Hurwitz matrix, with respect to the index variables. Repeat the following steps: Strategy evaluation: The first Lyapunov equation is obtained by solving the following Lyapunov equation. The positive definite matrix under the next iteration step

[0039] (11) Strategy Improvement: Update # Gain matrix under the next iteration step

[0040] (12) Therefore, the following property holds: For all index variables It is a Hurwitz matrix.

[0041] .

[0042] Lemma 1 provides a model-based policy iteration method for solving... However, its dependence on system dynamics and initial stable control strategies limits its practical application. Furthermore, determining a suitable stable control strategy is not easy and often heavily relies on expert experience; incorrect initialization can even lead to system failures or safety incidents. Therefore, this paper proposes a novel RL framework that adaptively learns the optimal solution to the algebraic Riccati equation (6) from system data. This eliminates the need for system dynamics and initial stability control strategies.

[0043] Theorem 1: For each ,make Let be any given initial positive definite matrix. Let be an arbitrary initial control gain. For the index variable... Perform the following iterative process: Strategy evaluation: Solve the positive definite matrix by solving the following Lyapunov equation.

[0044] (13) in, Represents the maximum value of a set. Let represent all the real parts of a vector. Represents the eigenvalues ​​of a matrix. Represents the smallest eigenvalue of the matrix. Represents the largest eigenvalue of the matrix. All are scalars. express An identity matrix of dimension 1.

[0045] Strategy Improvement: Update the Gain Matrix

[0046] (14) So, for all index variables It is a Hurwitz matrix and It is the only positive definite solution to equation (13).

[0047] Proof: This conclusion will be proved by mathematical induction. First, consider... For a given initial matrix ,have (15) According to scalar The definition can be easily observed. If the matrix is ​​a Hurwitz matrix, then equation (15) has a unique positive definite solution. Therefore, when This conclusion holds true at that time.

[0048] Next, assuming the above steps are correct... It also holds true, that is It is a Hurwitz matrix, and the matrix It is the unique positive definite solution to the following equation: (16) The control gain can be obtained based on equation (14). By Lemma 1, the matrix It is the unique positive definite solution to the following equation: (17) in, .

[0049] Finally, consider .Will From equation (17), we can obtain (18) This means It is a Hurwitz matrix. Therefore, equation (13) has a unique positive definite solution. Proof complete.

[0050] Based on Theorem 1, it can be easily proven that the sequence Monotonically decreasing if and only if the matrix It should be noted that Theorem 1 provides an efficient method for finding initial stable control policy pairs. More specifically, according to equations (13) and (14), the control gain pairs are obtained iteratively. Makes all index variables This is the Hurwitz matrix. Repeat this operation until the [number]th [number]. scalar under the next iteration Since the following inequality holds, we can obtain the first... Stable control gain in the next iteration : (19) Next, to propose a data-driven composite strategy iterative algorithm, system (1) can be rewritten as: (20) in .

[0051] Then, based on equations (13) and (20), The time derivative is calculated as follows: (twenty one) For convenience, for matrices ,in Represent a The set of 3D real matrices, defined ,in Represent a A set of dimensional column vectors, Representation matrix The Column vectors. For a symmetric matrix. .

[0052] definition in Representation matrix The Line 1 Column elements. For vectors. ,definition in Representing vectors The Each element. For both sides of equation (21) in Integrating points, among which Let a very small positive number be represented, and introduce the Kronecker product. This means that equation (21) can be rewritten as: (twenty two) To implement the data-driven learning algorithm, the following matrix equation is defined: (twenty three) in, It is a sufficiently large positive integer.

[0053] Therefore, equation (22) can be restated in the following more compact form: (twenty four) Among them, matrix Representation matrix The inverse matrix,

[0054] Therefore, let The control gain is the only solution to equation (13). It satisfies equation (14). It is worth noting that in the process of implementing Theorem 1, finding the scalar... These parameters are crucial. However, they depend on system dynamics. To relax this restriction, we propose the following approach: Similar to equation (24), for any Choose any positive definite matrix Arbitrary control gain pair and initial constants Then it exists: (25) Among them, matrix Representation matrix The inverse matrix,

[0055] Subsequently, according to Lyapunov's theorem and Theorem 1, if the matrix obtained from equation (25) It is positive definite, that is... Then equation (13) has a unique positive definite solution matrix. and Otherwise, update the parameters. ,in Set the step size and recalculate equation (25). Repeat this process until a positive definite solution matrix is ​​obtained. .

[0056] It should be noted that, using the least squares method, equation (24) only applies to matrices. The solution can only be found if the matrix is ​​invertible, which requires the matrix to be invertible. It must be full rank, that is ,in Representation matrix The rank of the matrix. However, the optimal control input is linearly related to the system state vector, which means that the matrix... It is unusual. To address this issue, the present invention will explore noise during the learning process. and Add to the control policy, where and All are real numbers greater than 0. This ensures the matrix... It is reversible.

[0057] Based on the above derivation, this invention develops the following data-driven composite strategy iterative algorithm.

[0058] ; Theorem 2: If The rank condition is satisfied for any given positive definite matrix. and arbitrary control gain The sequence obtained by the data-driven composite strategy iterative algorithm 1 is then... Each converges to its own optimal value. .

[0059] Proof: Under the condition that the rank condition is satisfied, equation (25) has a unique solution in each iteration step. Furthermore, by using steps 2-6 of the data-driven composite strategy iterative algorithm 1, a solution satisfying the condition can be found. scalar Therefore, the control gain obtained in step 7-11 can be used as a basis. It can guarantee the matrix It is Hurwitz stable.

[0060] Then, As the new initial control gain, and let the scalar If the result is 0, then substitute it into equation (25). From equations (13) and (14), it can be seen that the operations in steps 12-17 are equivalent to those in Lemma 1. Therefore, based on Lemma 1, the sequence generated by the data-driven composite strategy iterative algorithm 1 is... Convergence is guaranteed. Proof complete.

[0061] This invention proposes an event-triggered load frequency security control method for multi-regional power systems based on Reinforcement Learning (RL) to address the complex environments of DoS attacks and limited communication resources. Under DoS attacks, the system switches control modes to cope with different situations: during normal communication, it executes conventional control; when communication is blocked, it switches to an anti-attack mode, thus ensuring system stability during attacks. Furthermore, by combining an event-triggered mechanism and a data compensation strategy, redundant information transmission and high-frequency communication requirements are reduced, effectively lowering communication resource consumption and improving the system's robustness under DoS attacks. Unlike traditional methods that rely on precise system models, this invention employs a data-driven composite strategy iterative algorithm, enabling the system to automatically learn the optimal control strategy even when the model is uncertain or missing. This method significantly reduces the dependence on precise system dynamics and initial stability strategies, effectively optimizing control energy consumption and improving system economy.

[0062] Example 2: To verify the feasibility of the method, in a complex environment with DoS attacks and limited communication resources, consider an IEEE 39 node with 10 generators. For example... Figure 3 As shown, the system is divided into 3 control areas.

[0063] To simplify the description, this invention selects one generator in each control region for analysis. Table 1 lists some parameters for each region of the system.

[0064] Table 1 Parameters of each area of ​​the system ; choose And randomly select the initial control gain:

[0065] After calculation The real parts of the corresponding eigenvalues ​​are not all zero, which means that the system has control gain. It is not stable.

[0066] Assume all parameters of the power system are unknown. The initial state is set as follows:

[0067] Detection noise set to , in It is a random number that follows a uniform distribution in the interval [-50, 50].

[0068] make By executing steps 2-6 in Algorithm 1, we can obtain the condition that... parameters Continue executing steps 7-11 of Algorithm 1, obtaining the results at iterations 40 and 18 respectively. This indicates the control gain. This can stabilize the power system. Next, steps 12-17 of Algorithm 1 are executed, and the optimal gain pair is obtained after 27 iterations.

[0069] (26) By applying the controller with the optimal controller gain described above to a three-region power system, simulation results can be obtained. Figure 4 This demonstrates the system status response in each region under a DoS attack. Figure 5 The release time and interval of the event triggering mechanism. Figure 6 For controller responses under DoS attacks and limited communication resources.

[0070] Example 3: Multi-regional power system event-triggered load frequency security control system. This system is used to implement the multi-regional power system event-triggered load frequency security control method described in Example 1, such as... Figure 7 As shown, it includes a model building module, a problem optimization module, a triggering mechanism module, an online learning module, and a control execution module.

[0071] The system comprises the following modules: a model building module, used to model a multi-regional power system as a switching system when facing a Denial-of-Service (DoS) attack, and to establish a switching control law; the switching control law includes a first control mode executed within a safe interval where communication is normal and a second control mode executed within an attack interval where communication is blocked; a problem optimization module, used to establish an optimization objective function for the switching system, including system state, control input, and external disturbances, transforming the load frequency control problem into a zero-sum game problem to minimize control energy consumption while suppressing external disturbances; a triggering mechanism module, used to design an event-triggered transmission strategy within the safe interval, transmitting system state information collected by sensors to the controller when the triggering conditions are met; an online learning module, used to solve for the optimal controller gain matrix corresponding to the optimization objective function through interactive learning with the environment based on a data-driven composite strategy iterative algorithm, wherein the composite strategy iterative algorithm automatically finds initialization parameters to ensure algorithm convergence during the iteration process; and a control execution module, used to apply the solved optimal controller gain matrix to the switching control law to generate the final control command, thereby achieving safe load frequency control of the multi-regional power system under a DoS attack.

[0072] Working principle: When a DoS attack occurs, this invention models the system as a switching system and switches the control mode in real time according to whether the link is under DoS attack: when communication is normal, it performs conventional learning control to optimize frequency regulation performance; when an attack occurs, it switches to anti-attack control mode, so that it can maintain closed-loop stability and suppress frequency deviation and tie-line power fluctuations even when communication is blocked, thus significantly improving system security.

[0073] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0074] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0075] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0076] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0077] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for event-triggered load frequency security control in multi-regional power systems, characterized in that, Includes the following steps: When facing a Denial-of-Service (DoS) attack, the multi-regional power system is modeled as a switching system, and a switching control law is established. The switching control law includes a first control mode executed in the safe interval where communication is normal and a second control mode executed in the attack interval where communication is blocked. For the switching system, an optimization objective function is established that includes system state, control input, and external disturbances, transforming the load frequency control problem into a zero-sum game problem, so as to minimize control energy consumption while suppressing external disturbances; Within the safe zone, an event-triggered transmission strategy is designed to transmit the system status information collected by the sensors to the controller when the triggering conditions are met. The data-driven composite strategy iterative algorithm learns and solves the optimal controller gain matrix corresponding to the optimization objective function by interacting with the environment. The composite strategy iterative algorithm automatically finds initialization parameters to ensure the convergence of the algorithm during the iteration process. The optimal controller gain matrix obtained by solving is applied to the switching control law to generate the final control command, thereby realizing the safe control of the load frequency of the multi-regional power system under DoS attack. The data-driven composite strategy iterative algorithm specifically includes: Acquire the status data, control input data, and external interference data of the multi-regional power system during its operation; Based on the state data, control input data, and external disturbance data, a data matrix and vector containing the Kronecker product are constructed. By solving the least squares equations constructed based on the data matrix and the vector, the parameter matrix in policy evaluation and the controller gain matrix in policy improvement are updated online. The process is repeated iteratively until the controller gain matrix converges, and the converged gain matrix is ​​taken as the optimal controller gain matrix. The automatic search for initialization parameters to ensure algorithm convergence specifically includes: Given an arbitrary initial controller gain matrix and initial parameters; The parameter matrix is ​​calculated by performing one iteration using the composite strategy iterative algorithm. Determine whether the parameter matrix is ​​a positive definite matrix; If not, the value of the initial parameter is increased by a fixed step size and recalculated until the parameter matrix is ​​a positive definite matrix. The initial parameter at this time is the initialization parameter to ensure the convergence of subsequent iterations. The parameter matrix in the online update strategy evaluation includes: Based on the controller gain and system operating data from the previous iteration, a virtual matrix with adjusted parameters is constructed. The virtual matrix is ​​obtained by subtracting a scalar adjustment term related to the current iteration and ensuring stability from the original system matrix. Solve a Lyapunov equation consisting of the virtual matrix, the current controller gain, and the optimized weights. The unique positive definite solution of this equation is the parameter matrix to be obtained.

2. The multi-regional power system event-triggered load frequency security control method according to claim 1, characterized in that, The safe zone and the attack zone are divided into alternating sections on the timeline; Within the safe zone, the switching control law adopts a first control mode calculated based on the latest successfully transmitted state information; Within the attack range, the switching control law switches to a second control mode based on the previous successful transmission and combined with historical data for maintenance or compensation.

3. The multi-regional power system event-triggered load frequency security control method according to claim 1, characterized in that, Within the attack zone, when communication is blocked and new status information cannot be obtained, data compensation is also included: By utilizing the system state and control commands successfully transmitted last time before entering the attack zone, the control input at the current moment is generated by maintaining or predicting the system dynamics, so as to maintain the transient stability of the system and suppress the expansion of frequency deviation.

4. The multi-regional power system event-triggered load frequency security control method according to claim 1, characterized in that, When constructing the data matrix, the method further includes: Probe noise is introduced into the control strategy input to the composite strategy iterative algorithm to ensure that the constructed data matrix has full rank so that the least squares equation has a solution.

5. The multi-regional power system event-triggered load frequency security control method according to claim 1, characterized in that, The optimization objective function is constructed as a performance index in the form of a zero-sum game, which is the sum of the integrals of the quadratic form of the system state deviation, the quadratic form of the control input energy, and the quadratic form of the scaled external disturbance energy from the current time to infinite future time. The objective of finding the optimal control strategy is to find a control input that minimizes the performance index, while considering a worst-case external disturbance that attempts to maximize the same performance index.

6. The multi-regional power system event-triggered load frequency security control method according to claim 1, characterized in that, The triggering conditions for the event-triggered transmission strategy are set based on the comparison principle: A new data transmission is triggered when the squared norm of the error vector between the current control input and the most recently successfully transmitted control input exceeds a threshold consisting of a linear combination of the squared norms of the current system state vector and the linear combination of the squared norms of the most recently successfully transmitted control input. The linear combination coefficients used to construct the threshold are all pre-set normal numbers.

7. A multi-regional power system event-triggered load frequency safety control system, characterized in that, This system is used to implement the multi-regional power system event-triggered load frequency security control method according to any one of claims 1-6, comprising: The model building module is used to model a multi-regional power system as a switching system when facing a denial-of-service (DoS) attack, and to establish a switching control law. The switching control law includes a first control mode executed in a safe interval where communication is normal and a second control mode executed in an attack interval where communication is blocked. The problem optimization module is used to establish an optimization objective function for the switching system, which includes system state, control input and external disturbances, and transform the load frequency control problem into a zero-sum game problem, so as to minimize control energy consumption while suppressing external disturbances. The triggering mechanism module is used to design an event triggering transmission strategy within the safe zone, and to transmit the system status information collected by the sensor to the controller when the triggering conditions are met. An online learning module is used for a data-driven composite strategy iterative algorithm to learn and solve for the optimal controller gain matrix corresponding to the optimization objective function through interaction with the environment. The composite strategy iterative algorithm automatically finds initialization parameters to ensure the convergence of the algorithm during the iteration process. The control execution module is used to apply the solved optimal controller gain matrix to the switching control law to generate the final control command, thereby realizing the load frequency security control of the multi-regional power system under DoS attack.

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