A model-free adaptive microgrid frequency control method against cyber attacks
By employing dynamic linearization technology and model-free adaptive control strategy, the problem of unknown model and hybrid network attack in microgrid frequency control systems has been solved, achieving stable and adaptive frequency control and overcoming the limitations of traditional methods.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHINA UNIV OF GEOSCIENCES (WUHAN)
- Filing Date
- 2026-03-09
- Publication Date
- 2026-07-10
AI Technical Summary
Existing technologies struggle to achieve effective frequency control when the microgrid frequency control system model is unknown and faces the threat of hybrid network attacks.
The nonlinear system is transformed into an equivalent linear data model by using dynamic linearization technology. A partial pseudo-derivative estimation algorithm and a model-free adaptive control law containing a decay function are designed. Frequency control is achieved by iteratively updating the time-varying partial pseudo-derivative matrix.
In complex communication environments, it adaptively maintains frequency stability and avoids control interruptions, demonstrating excellent adaptability and resilience, and breaking through the limitations of traditional methods.
Smart Images
Figure CN122371176A_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of microgrid frequency control, and more specifically, relates to a model-free adaptive microgrid frequency control method that resists network attacks. Background Technology
[0002] Microgrids with high renewable energy penetration rates exhibit characteristics such as low inertia, nonlinearity, and time-varying behavior. These characteristics, combined with limiting factors such as communication-induced time delays and network attacks in frequency control, constitute the core challenges to system stability.
[0003] In practical applications, microgrid frequency control systems are nonlinear systems that are difficult to model accurately. Existing research typically linearizes them and analyzes them as low-order linear models. This modeling method is effective for relatively simple systems. However, as the structure of microgrid frequency control systems becomes increasingly complex, it is necessary to explore more suitable modeling and control strategies.
[0004] Therefore, how to achieve effective frequency control when the microgrid frequency control system model is unknown and faces the threat of hybrid network attacks is an urgent problem to be solved. Summary of the Invention
[0005] To address the shortcomings of existing technologies, the purpose of this application is to provide a model-free adaptive microgrid frequency control method that can resist network attacks, enabling effective frequency control even when the microgrid frequency control system model is unknown and faces the threat of mixed network attacks.
[0006] To achieve the above objectives, in a first aspect, this application provides a model-free adaptive microgrid frequency control method to resist network attacks, comprising the following steps:
[0007] S10, considering the combined effects of denial-of-service attacks and spoofing attacks, a system output model including attack coefficients is established, and the microgrid frequency control system is modeled as a discrete-time nonlinear system. S20, using dynamic linearization technology, the nonlinear system is transformed into an equivalent linear data model, which is represented as follows: ,in To output the change vector, For the input change vector, It is a time-varying partial pseudo-derivative matrix; S30. For the linear data model, design a partial pseudo-derivative estimation algorithm and design a model-free adaptive control law containing a decay function. S40, the time-varying partial pseudo-derivative matrix is estimated using the partial pseudo-derivative estimation algorithm. The system performs iterative updates and calculates the control input at the current moment using the model-free adaptive control law based on the updated partial pseudo-derivative matrix, in order to control the microgrid frequency.
[0008] As a further preferred embodiment, in step S10, the attack coefficient is a Bernoulli sequence with a value of 0 or 1.
[0009] As a further preferred embodiment, in step S10, the discrete-time nonlinear system is represented as follows: ,in f (·) is a nonlinear function.
[0010] As a further preferred embodiment, in step S20, the time-varying partial pseudo-derivative matrix The input change vector ,in and for column vectors, and This represents the input change in the two input channels.
[0011] As a further preferred option, there exists a positive constant. and This makes it possible for any time k The time-varying partial pseudo-derivative matrix satisfies (i=1, 2), and satisfying ; and The sign of remains unchanged at all times, that is or Furthermore, these symbols do not change over time; to ensure that output changes are controlled by synchronous generation, conditions are added. .
[0012] As a further preferred embodiment, in step S30, the partial pseudo-derivative estimation algorithm is designed specifically as follows: based on the partial pseudo-derivative estimation criterion function... right and Estimate the value to obtain the estimated value. ,in This is the system output after an attack. for k Time and k The difference in system output after being attacked at time -1. These are the weighting coefficients used to adjust the partial pseudo-derivative parameters. .
[0013] As a further preferred embodiment, in step S30, designing the model-free adaptive control law specifically involves: based on the control input criterion function... Calculate the change in control input and ,in express k The system's target output value at time +1, and These are adjustable parameters used to adjust the output of the virtual inertia control loop and the secondary frequency control loop, respectively.
[0014] As a further preferred embodiment, in step S30, the attenuation function is used to adjust the control input during the duration of the denial-of-service attack, and is specifically defined as follows:
[0015] In the formula, i Indicates the channel number; and It is based on the historical maximum denial-of-service attack interval; and It is to satisfy The normal value controls the attenuation rate; Affecting the rate of change ; Indicates the end time of the denial-of-service attack; This indicates the moment the denial-of-service attack began.
[0016] As a further preferred option, a mechanism for resetting the partial pseudo-derivative matrix estimate is also included: , where is a given partial pseudo-derivative estimate.
[0017] Secondly, this application provides a control system for implementing the model-free adaptive microgrid frequency control method for resisting network attacks as described in any of the above claims, comprising: The model building module is used to consider the combined effects of denial-of-service attacks and spoofing attacks, and to build a system output model that includes attack coefficients, thus modeling the microgrid frequency control system as a discrete-time nonlinear system. The dynamic linearization module is used to transform the nonlinear system into an equivalent linear data model using dynamic linearization techniques. The linear data model is represented as follows: ,in To output the change vector, For the input change vector, It is a time-varying partial pseudo-derivative matrix; The controller module is used to design a partial pseudo-derivative estimation algorithm for the linear data model, and to design a model-free adaptive control law including a decay function; and to use the partial pseudo-derivative estimation algorithm to evaluate the time-varying partial pseudo-derivative matrix. The system performs iterative updates and calculates the control input at the current moment using the model-free adaptive control law based on the updated partial pseudo-derivative matrix, in order to control the microgrid frequency.
[0018] This application offers the following advantages: Addressing the challenge of unknown microgrid frequency control system models and the threat of mixed network attacks, it establishes a system output model incorporating attack coefficients. This enables the system to explicitly characterize the combined effects of denial-of-service and spoofing attacks on the control process, providing an accurate input-output basis for subsequent control strategy design. Furthermore, it employs a model-independent dynamic linearization technique to transform the unknown nonlinear system into an equivalent linear data model described by a time-varying partial pseudo-derivative matrix. This overcomes the limitations of traditional methods that rely on precise mathematical models, achieving a data-driven description of the complex, time-varying, and difficult-to-model dynamic characteristics of microgrids. Furthermore, a partial pseudo-derivative estimation algorithm and a model-free adaptive control law containing a decay function were designed for this data model. This enables the system to dynamically adjust the control strategy by estimating the time-varying partial pseudo-derivative matrix in real time without knowing the specific model parameters. At the same time, the introduction of the decay function ensures the continuity of control input during the duration of the network attack, avoiding the risk of instability caused by control interruption due to the attack. Finally, through iterative updates of the time-varying partial pseudo-derivative matrix and real-time calculation of control input, the entire control system can adaptively maintain frequency stability in complex communication environments with unknown models and mixed network attacks, demonstrating excellent adaptability and resilience. Attached Figure Description
[0019] Figure 1 This is a microgrid frequency control model with the participation of a virtual synchronous generator, as provided in the embodiments of this application. Figure 2 This is an internal structure diagram of the microgrid central controller provided in the embodiments of this application; Figure 3 This refers to the external disturbances experienced by the system provided in the embodiments of this application; Figure 4 This refers to the network attack suffered by the system provided in the embodiments of this application; Figure 5 This refers to the system frequency deviation change under scenario 1 provided in the embodiments of this application; Figure 6 This refers to the system frequency deviation change in scenario 2 provided in the embodiments of this application. Detailed Implementation
[0020] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.
[0021] This application proposes a data-driven, model-free adaptive control-based resilient cooperative frequency control strategy for microgrid frequency control systems with unknown dynamic models under the threat of hybrid network attacks, applicable to microgrids with low inertia levels. By employing dynamic linearization techniques to transform the nonlinear system into an equivalent linear data model, this method designs control laws and parameter estimation algorithms to ensure robustness, and further introduces a decay function to ensure input continuity during attacks. Simulations verify the effectiveness of this strategy under various communication network constraints, including time delays and hybrid network attacks. Results show that compared to existing methods, this approach maintains frequency stability and exhibits superior performance, highlighting its adaptability and resilience in complex communication environments. This work overcomes the limitations of traditional linearization models, providing a lightweight, adaptive, and secure control scheme for low-inertia microgrid frequency control systems under complex communication environments. Specifically, it includes the following steps.
[0022] Step 1: Establish a nonlinear discrete-time system model for the microgrid frequency control system under an open communication network. First, the microgrid frequency control system under consideration consists of renewable energy sources, diesel generator units, loads, and various energy storage systems. The inherent intermittency and volatility of renewable energy sources, along with load disturbances, are the main factors affecting system stability. The system achieves primary frequency control through the speed governors of the energy storage systems and generator units. However, primary frequency control typically cannot fully restore the frequency to its rated value, thus requiring secondary frequency control via an open communication network. Unlike traditional power grids where synchronous generators dominate, the inertia and damping levels of microgrids significantly decrease with the increasing penetration of renewable energy. Currently, short-term energy storage systems are commonly used to construct virtual synchronous generators to provide inertia and damping support. The constructed control loop includes a virtual primary frequency control loop and a virtual secondary frequency control loop. The virtual secondary frequency control is integrated with the secondary frequency control within the microgrid central controller. The received measurement signals are affected by various network-induced constraints in the communication network and face the threat of hybrid network attacks. The structure of the microgrid frequency control system is as follows: Figure 1 As shown.
[0023] The external disturbances experienced by the system mainly stem from fluctuations in photovoltaic power generation. Fluctuations in wind power generation The inherent intermittent and fluctuating characteristics of renewable energy, as well as load variations The resulting disturbances. Here, all the above disturbances are collectively attributed to external interferences experienced by the system. Some system parameters and symbols are shown in Table 1.
[0024] Table 1 System Parameters and Symbols
[0025] The hybrid network attacks considered in this application include DoS attacks and spoofing attacks. A characteristic of DoS attacks is the removal of control over input. Based on the denial-of-service condition, spoofing attacks were further considered. The core mechanism of a spoofing attack includes generating false data and transmitting it to the core control system. The control output of a system affected by spoofing and denial-of-service attacks can be expressed as: (1) in This means that any bounded signal satisfies , This is the attack coefficient, which uses a Bernoulli sequence and has a value of 0 or 1. Its probability distribution is as follows: , . It is a known constant. Here it will be... Defined as a DoS attack in the range The duration within.
[0026] In practical applications, microgrid frequency control systems are nonlinear systems that are difficult to model accurately. Existing research typically linearizes them and analyzes them as low-order linear models. This modeling method is effective for relatively simple systems. However, as the structure of microgrid frequency control systems becomes increasingly complex, it is necessary to explore more suitable modeling and control strategies. Dynamic linearization technology does not rely on a system model but is based on frequency deviation data measured during system operation. It estimates the time-varying parameters of the system through model-free adaptive control methods, thereby constructing an equivalent linear data model and providing a new solution to the frequency control problem of complex microgrids. Based on the above, a microgrid frequency control system can be considered as a discrete-time system with a single input and dual outputs, with the following structure: (2) Step 2: Design the model-free adaptive control law for the microgrid frequency control system Based on the above model, such as Figure 2 As shown, the pseudo partial derivative (PDD) estimator, DoS attack detector, and controller are integrated into the microgrid central controller, and their design is the core content of this application. The goal of this step is to fully consider the characteristics of DoS attacks by introducing a decay function to enhance the system's adaptability, and to fully consider the output requirements of the microgrid frequency control system by designing a data-driven model-free adaptive controller.
[0027] First, the following assumptions and lemmas are given.
[0028] Assumption 1: Function For control input The partial derivatives are continuous.
[0029] Assumption 2: System (2) satisfies the generalized Lipschitz condition, i.e. For any time k, we have , ,constant satisfy ,and .
[0030] Lemma 1: For a system that satisfies Assumptions 1 and 2, when At that time, there exists a time-varying PPD matrix. This allows the system to be represented as the following dynamic linearization model:
[0031] in , , , .
[0032] On this basis The corresponding expression can be written as:
[0033] in , .
[0034] Assumption 3: There exists a positive constant. and Such that for any time k, PPD satisfies (i=1,2), the vector norm satisfies ,and and The sign of remains unchanged at all times, that is or Furthermore, these symbols do not change over time. To ensure that output changes are controlled by synchronous generation, a condition is added here. .
[0035] Define the following estimation criterion function:
[0036] in, and These are the weighting factors for the two input channels, used to adjust and control the changes in the input.
[0037] Introducing step size factor and Its value range is Furthermore, using estimated values Replace unknown quantity The criterion function To each and Take the partial derivatives and set the results to 0. The final control law is then obtained as follows: (3) (4) Time-varying PPD parameters Precise values are difficult to obtain. Therefore, we introduce... The estimated value The following PPD estimation criterion function is defined:
[0038] in This represents the weighting factor.
[0039] Find them separately right and The partial derivatives are set to zero. A step factor is introduced. The parameter update law is obtained as follows: (5) (6) The reset mechanism is set as follows: (7) Combining equation (1), we can obtain the data-driven model-free adaptive controller as (3)-(7).
[0040] Here, we further introduce a decay function. By learning the maximum historical DoS attack interval To achieve adaptability, thereby balancing system performance and stability, the control input needs to be rewritten as follows:
[0041] in, This represents the input increment of channel i at the last moment before the attack begins. This is a decay function designed for channel i, and it is defined as follows:
[0042] in, and It is based on the historical maximum denial-of-service attack interval. and are positive constants that satisfy and control the decay rate, while affects the rate of change, .
[0043] Then, the estimation algorithm can be expressed as:
[0044] In summary, the data-driven model-free adaptive control strategy under hybrid network attack threats can be summarized as follows. First, the PPD estimation algorithm is:
[0045] The PPD reset algorithm is:
[0046] The input update algorithm is: ,
[0047]
[0048] Step 3: Simulate to verify the feasibility of the designed controller A simulation case study was conducted on the frequency control system of a low-inertia microgrid with hybrid network attack threats. For effective comparative analysis, the microgrid frequency control structure shown in the reference Wei C G, Shangguan X C, Yang Y H, et al. Delay-dependent robust frequency control in microgrids: Coordination of secondary frequency control and virtual inertia control[J]. IEEE Transactions on Industrial Informatics, 2025, 21(8): 6455-6465. was adopted, and the relevant parameters are listed in Table 2. A control system simulation platform was constructed in MATLAB / Simulink to verify the superior performance of the proposed control strategy compared with existing methods under hybrid network attack conditions. Figure 1
[0049] The first key technical point of this application is that it considers the threats of time delay and hybrid network attacks, and establishes a microgrid frequency control model under the threat of hybrid network attacks. The second key point is that it considers the threat of attacks and the impact of time delay, and designs a robust control strategy of coordinated control of secondary frequency control and virtual inertia control, which enables the microgrid frequency control system to cope with communication constraints and hybrid network attacks, and significantly improves the control effect.
[0050] To verify the effectiveness of the proposed method, simulation verification is performed here. First, the required system parameters are given in Table 2 of the appendix. The relevant parameters and initial values are set as follows: the discrete interval is set to... The desired frequency deviation is set to The initial control input is , The initial PPD estimate is , The parameter values are given below: , , , , , , , , , , .
[0051] Table 2 System Parameters
[0052] This section utilizes the established simulation platform to test and compare the performance of the microgrid frequency control system under two conditions: first, under the influence of time delays introduced by communication congestion; and second, under the threat of mixed network attacks with different control strategies. For system comparison, the following four control schemes are defined: Scheme 1 is the control strategy proposed in this application; Scheme 2 is the model predictive control strategy constructed in the reference Oshnoei S, Aghamohammadi MR, Oshnoei S, et al. A novel virtualinertia control strategy for frequency regulation of islanded microgrid using two-layer multiple model predictive control[J]. Applied Energy, 2023, 343:121233.; Scheme 3 is the Delay-dependent... The control method proposed in "robust frequency control in microgrids: Coordination of secondary frequency control and virtual inertia control" [J]. IEEE Transactions on Industrial Informatics, 2025, 21(8): 6455-6465 combines Lyapunov theory with intelligent optimization algorithms.
[0053] Consider the following two scenarios: (1) The inertia and damping of the microgrid are reduced by 50%. The system in When received The step disturbance is affected by a 2s time delay. (2) The inertia and damping of the microgrid are reduced by 50%, and it is affected by... Figure 3 The influence of random disturbances is considered, taking into account the effect of a 2-second time delay, and the system is subject to... Figure 4 The impact of hybrid cyberattacks in this context .
[0054] As can be seen from simulation images 5 and 6, the proposed control strategy can still ensure the stability of the low-inertia microgrid frequency control system under various negative impacts such as time delay and hybrid network attacks, and the control effect is superior to existing methods. This demonstrates that the proposed control strategy overcomes the limitations of traditional linearized models and provides a lightweight, adaptive safety control scheme for low-inertia microgrid frequency control systems in complex communication environments.
[0055] This application proposes a data-driven model-free adaptive control strategy for microgrid frequency control systems exhibiting low inertia, nonlinearity, and time-varying characteristics under inherent constraints and the threat of hybrid network attacks. First, the microgrid frequency control system is treated as a discrete-time nonlinear system, and the combined effects of DoS and spoofing attacks are considered, establishing a system output model under these attacks. Then, dynamic linearization techniques are employed to transform the nonlinear system into an equivalent linear data model, and control law and partial pseudo-derivative parameter estimation algorithms are designed. A decay function is introduced to handle input continuity during attacks, and control coefficients are considered to adjust the output of different control loops. Finally, simulation tests are conducted under various scenarios through multiple simulations, verifying the effectiveness and superiority of the proposed control strategy.
[0056] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.
Claims
1. A model-free adaptive microgrid frequency control method for resisting network attacks, characterized in that, Includes the following steps: S10, considering the combined effects of denial-of-service attacks and spoofing attacks, a system output model including attack coefficients is established, and the microgrid frequency control system is modeled as a discrete-time nonlinear system. S20, using dynamic linearization technology, the nonlinear system is transformed into an equivalent linear data model, which is represented as follows: ,in To output the change vector, For the input change vector, It is a time-varying partial pseudo-derivative matrix; S30. For the linear data model, design a partial pseudo-derivative estimation algorithm and design a model-free adaptive control law containing a decay function. S40, the time-varying partial pseudo-derivative matrix is estimated using the partial pseudo-derivative estimation algorithm. The system performs iterative updates and calculates the control input at the current moment using the model-free adaptive control law based on the updated partial pseudo-derivative matrix, in order to control the microgrid frequency.
2. The model-free adaptive microgrid frequency control method for resisting network attacks as described in claim 1, characterized in that, In step S10, the attack coefficient is a Bernoulli sequence with a value of 0 or 1.
3. The model-free adaptive microgrid frequency control method for resisting network attacks as described in claim 2, characterized in that, In step S10, the discrete-time nonlinear system is represented as: ,in f (·) is a nonlinear function.
4. The model-free adaptive microgrid frequency control method for resisting network attacks as described in claim 3, characterized in that, In step S20, the time-varying partial pseudo-derivative matrix The input change vector ,in and for column vectors, and This represents the input change in the two input channels.
5. The model-free adaptive microgrid frequency control method for resisting network attacks as described in claim 4, characterized in that, There exists a positive constant. and This makes it possible for any time k The time-varying partial pseudo-derivative matrix satisfies (i=1,2), and satisfy ; and The sign of remains unchanged at all times, that is or Furthermore, these symbols do not change over time; to ensure that output changes are controlled by synchronous generation, conditions are added. .
6. The model-free adaptive microgrid frequency control method for resisting network attacks as described in claim 4, characterized in that, In step S30, the partial pseudo-derivative estimation algorithm is designed specifically as follows: based on the partial pseudo-derivative estimation criterion function... right and Estimate the value to obtain the estimated value. ,in This is the system output after being attacked. for k Time and k The difference in system output after being attacked at time -1. These are the weighting coefficients. .
7. The model-free adaptive microgrid frequency control method for resisting network attacks as described in claim 4, characterized in that, In step S30, the design of the model-free adaptive control law specifically involves: based on the control input criterion function... Calculate the change in control input and ,in express k The system's target output value at time +1, and These are adjustable parameters used to adjust the output of the virtual inertia control loop and the secondary frequency control loop, respectively.
8. The model-free adaptive microgrid frequency control method for resisting network attacks as described in claim 4, characterized in that, In step S30, the attenuation function is used to adjust the control input during the duration of the denial-of-service attack, and is specifically defined as follows: In the formula, i Indicates the channel number; and It is based on the historical maximum denial-of-service attack interval; and It is to satisfy The normal value controls the attenuation rate; Affecting the rate of change ; Indicates the end time of the denial-of-service attack; This indicates the moment the denial-of-service attack began.
9. The model-free adaptive microgrid frequency control method for resisting network attacks as described in claim 8, characterized in that, It also includes a mechanism for resetting the estimates of the partial pseudo-derivative matrix: ,in b For a given partial pseudo-derivative estimate.
10. A control system for implementing the model-free adaptive microgrid frequency control method for resisting network attacks as described in any one of claims 1 to 9, characterized in that, include: The model building module is used to consider the combined effects of denial-of-service attacks and spoofing attacks, and to build a system output model that includes attack coefficients, thus modeling the microgrid frequency control system as a discrete-time nonlinear system. The dynamic linearization module is used to transform the nonlinear system into an equivalent linear data model using dynamic linearization techniques. The linear data model is represented as follows: ,in To output the change vector, For the input change vector, It is a time-varying partial pseudo-derivative matrix; The controller module is used to design a partial pseudo-derivative estimation algorithm for the linear data model, and to design a model-free adaptive control law including a decay function; and to use the partial pseudo-derivative estimation algorithm to evaluate the time-varying partial pseudo-derivative matrix. The system performs iterative updates and calculates the control input at the current moment using the model-free adaptive control law based on the updated partial pseudo-derivative matrix, in order to control the microgrid frequency.