Method and system for frequency control of low-inertia micro-grid system under network attack

Abstract

The invention discloses a method and system for frequency control of a low-inertia micro-grid system under a network attack, and relates to the technical field of micro-grid control, and the method for frequency control of the low-inertia micro-grid system under the network attack mainly comprises the steps: constructing a micro-grid frequency control model in which a virtual generator influenced by the attack participates in frequency modulation, controller gain is obtained based on the Lyapunov stability theory and a stochastic analysis method; and performing frequency control on the low-inertia micro-grid system under the network attack according to the controller gain. By implementing the method and the system for frequency control of the low-inertia micro-grid system under the network attack provided by the invention, the influence of hybrid network attack, disturbance and inertia reduction can be reduced, and stable operation of the micro-grid is ensured.

Description

Technical Field

[0001] This invention relates to the field of microgrid control technology, and more specifically, to a method and system for frequency control of low-inertia microgrid systems under network attacks. Background Technology

[0002] With the large-scale integration of distributed renewable energy, microgrids are becoming increasingly popular as a key technology for improving energy flexibility and resilience. One of the core guarantees for their safe and stable operation is precise frequency control, which directly relates to power quality and system security. However, on the one hand, the high proportion of renewable energy integration significantly reduces the inertia level of microgrid frequency control systems when subjected to uncertain disturbances; on the other hand, microgrids heavily rely on open communication networks to transmit measurement signals and control commands, which face bandwidth limitations and cybersecurity threats. Therefore, comprehensively considering these issues and achieving better microgrid frequency control is crucial. Summary of the Invention

[0003] The purpose of this invention is to provide a method and system for frequency control of low-inertia microgrid systems under network attacks, which can reduce the impact of hybrid network attacks, disturbances and inertia reduction, and ensure the stable operation of the microgrid.

[0004] This invention provides a method for frequency control of a low-inertia microgrid system under network attacks, comprising the following steps: S1: Construct a microgrid frequency control model in which virtual generators affected by the attack participate in frequency regulation; S2: Based on the microgrid frequency control model, the controller gain is obtained using Lyapunov stability theory and stochastic analysis methods; S3: Perform frequency control on the low-inertia microgrid system under network attack based on the controller gain.

[0005] The present invention also provides a system for frequency control of a low-inertia microgrid system under network attacks, the system comprising the following modules: The microgrid frequency control model construction module is configured to: construct a microgrid frequency control model in which a virtual generator affected by an attack participates in frequency regulation; The controller gain generation module is configured to: obtain the controller gain based on the microgrid frequency control model, using Lyapunov stability theory and stochastic analysis methods; The frequency control module is configured to perform frequency control on a low-inertia microgrid system under network attacks based on the controller gain.

[0006] The method and system for frequency control of low-inertia microgrid systems under network attacks provided by this invention have the following beneficial effects: This invention addresses the challenges of time-delay and hybrid network attacks in microgrid frequency control systems. It proposes a cooperative control method combining secondary frequency control and virtual inertia control, which can tolerate high discrete periods. Robust Cooperative Control Strategy: First, a frequency control system model for a low-inertia microgrid with a virtual synchronous generator participating in frequency regulation is established and reorganized into a more realistic discrete-time model for analysis. Second, control laws are designed for the secondary frequency control loop and the virtual secondary control loop respectively. Based on Lyapunov theory, the conditions for ensuring the exponential mean square stability of the system are obtained and used to solve the linear matrix inequality of the cooperative controller gain. Finally, the robust controller gain under given conditions is obtained through matrix transformation, and the effectiveness of the proposed control strategy is verified through simulation.

[0007] This invention can effectively address the negative impacts of communication constraints, random disturbances, time delays, and reduced system inertia faced by microgrid frequency control systems under the influence of hybrid network attacks and large discrete intervals, reducing overshoot and helping the system recover stability more quickly. Attached Figure Description

[0008] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 This is a flowchart of a method for frequency control of a low-inertia microgrid system under network attacks provided by the present invention; Figure 2 This is a schematic diagram of a microgrid frequency control model with the participation of a virtual synchronous generator provided by the present invention; Figure 3 This is a schematic diagram illustrating the frequency deviation changes of the low-inertia microgrid frequency control system under different discrete intervals provided by this invention, under the influence of time delay and network attacks. Detailed Implementation

[0009] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0010] Figure 1 A schematic diagram of a method for frequency control of a low-inertia microgrid system under network attack, according to this embodiment, is shown. In this embodiment, the method for frequency control of a low-inertia microgrid system under network attack includes the following steps: S1: Construct a microgrid frequency control model in which virtual generators affected by the attack participate in frequency regulation.

[0011] In one exemplary embodiment, the microgrid frequency control model is described by the following formula:

[0012] , , , , , , , , , , , , , , , , , , in, , , express , , The state variable at any given time; express Random time-varying time delays at any given moment; , , Let be the state matrix of the system. , These represent the lower and upper bounds of the time delay, respectively. , This represents the state matrix of the system as it relates to past moments; , This represents the state matrix associated with the disturbance; , , These represent the set of past system states, the combination of attack-related states, and the set of microgrid states affected by external disturbances, respectively; the superscript T indicates matrix transpose; h represents the integration time constant. , These represent the combination of C matrices and the system's output state matrix, respectively. Represents a diagonal matrix; express External disturbances at any given moment; , , Bernoulli signals at different times are used to simulate the impact of an attack; , express Two independent Bernoulli sequences at time t; , express Combinations of items related to the attack at any given moment; , It is a constant; Represents the system's input state matrix; , , , This represents the combination of controller gain correlation matrices in the system; Represents the correlation matrix of the system disturbance state; , , , Indicates the gain of the controller to be designed; Represents the inertial constant of the virtual generator; Indicates the damping coefficient of the virtual generator; , , These represent the boundary values ​​of disturbances in the closed-loop system, the microgrid system, and the FDI attack, respectively. This indicates the expected value of the corresponding content; Represents the L2 norm of the corresponding content; Indicates the level of interference suppression; express Controlled output at any given moment.

[0013] S2: Based on the microgrid frequency control model, the controller gain is obtained using Lyapunov stability theory and stochastic analysis methods.

[0014] In one exemplary embodiment, the process of obtaining the controller gain includes: Based on the microgrid frequency control model, and using Lyapunov stability theory and stochastic analysis methods, the following are obtained to ensure the stability of the microgrid frequency control system: Sufficient conditions for performance; Based on the stated sufficient conditions, the controller gain is obtained using matrix transformation.

[0015] In one exemplary embodiment, the sufficient condition is: , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , in, This represents the linear matrix inequality used to solve for the controller gain. Represents the symmetric elements in a matrix; , , , , This represents a matrix related to the controller gain. , , Represent the matrix to be solved; Represents a combination of matrices; Indicates the orthogonal complement of the corresponding content; Represents the combination of matrices. , Represents a combination of matrices; Represents the combination of matrices. Represents the unknown term in a linear matrix inequality; Represents the combination of matrices. , , , , , , , Represents a combination of matrices; represents the unknown term in the linear matrix inequality; E represents the state matrix related to the control output. , Represent the unknown matrix in a linear matrix inequality; , These represent the lower and upper bounds of the time delay, respectively.

[0016] S3: Perform frequency control on the low-inertia microgrid system under network attack based on the controller gain.

[0017] This embodiment provides a system for frequency control of a low-inertia microgrid system under network attacks. The system includes the following modules: The microgrid frequency control model construction module is configured to: construct a microgrid frequency control model in which a virtual generator affected by an attack participates in frequency regulation; The controller gain generation module is configured to: obtain the controller gain based on the microgrid frequency control model, using Lyapunov stability theory and stochastic analysis methods; The frequency control module is configured to perform frequency control on a low-inertia microgrid system under network attacks based on the controller gain.

[0018] Specifically, the microgrid frequency control model is as follows:

[0019] , , , , , , , , , , , , , , , , , , in, , , express , , The state variable at any given time; express Random time-varying time delays at any given moment; , , Let be the state matrix of the system. , These represent the lower and upper bounds of the time delay, respectively. , This represents the state matrix of the system as it relates to past moments; , This represents the state matrix associated with the disturbance; , , These represent the set of past system states, the combination of attack-related states, and the set of microgrid states affected by external disturbances, respectively; the superscript T indicates matrix transpose; h represents the integration time constant. , These represent the combination of C matrices and the system's output state matrix, respectively. Represents a diagonal matrix; express External disturbances at any given moment; , , Bernoulli signals at different times are used to simulate the impact of an attack; , express Two independent Bernoulli sequences at time t; , express Combinations of items related to the attack at any given moment; , It is a constant; Represents the system's input state matrix; , , , This represents the combination of controller gain correlation matrices in the system; Represents the correlation matrix of the system disturbance state; , , , Indicates the gain of the controller to be designed; Represents the inertial constant of the virtual generator; Indicates the damping coefficient of the virtual generator; , , These represent the boundary values ​​of disturbances in the closed-loop system, the microgrid system, and the FDI attack, respectively. This indicates the expected value of the corresponding content; Represents the L2 norm of the corresponding content; Indicates the level of interference suppression; express Controlled output at any given moment.

[0020] Specifically, the process of obtaining the controller gain includes: based on the microgrid frequency control model, and using Lyapunov stability theory and stochastic analysis methods, obtaining the controller gain that guarantees the stability of the microgrid frequency control system. Sufficient conditions for performance; based on the sufficient conditions, the controller gain is obtained using matrix transformation.

[0021] Specifically, the sufficient condition is: , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , in, This represents the linear matrix inequality used to solve for the controller gain. Represents the symmetric elements in a matrix; , , , , This represents a matrix related to the controller gain. , , Represent the matrix to be solved; Represents a combination of matrices; Indicates the orthogonal complement of the corresponding content; Represents the combination of matrices. , Represents a combination of matrices; Represents the combination of matrices. Represents the unknown term in a linear matrix inequality; Represents the combination of matrices. , , , , , , , Represents a combination of matrices; represents the unknown term in the linear matrix inequality; E represents the state matrix related to the control output. , Represent the unknown matrix in a linear matrix inequality; , These represent the lower and upper bounds of the time delay, respectively.

[0022] In some embodiments, the above-described method for frequency control of low-inertia microgrid systems under network attacks can also be implemented in the following ways.

[0023] This embodiment constructs a microgrid frequency control model involving a virtual synchronous generator, considering hybrid network attacks. It designs a control law, analyzes it based on Lyapunov theory, obtains the conditions ensuring the exponential mean square stability of the system, and then utilizes matrix transformation to obtain a robust controller gain under given conditions. This ensures the normal operation of the low-inertia microgrid frequency control system under random disturbances and hybrid network attack threats. Specifically, it includes the following steps.

[0024] Step 1: Establish a microgrid frequency control model involving virtual generators The first step is to construct a microgrid frequency control model in which a virtual generator participates in frequency regulation, such as... Figure 2 As shown. The external disturbances experienced by this system mainly originate 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. External disturbances will disrupt the dynamic balance between power generation and consumption in the microgrid. When a frequency deviation occurs in the system, the diesel generator set, battery energy storage system, flywheel energy storage system, and fuel cell system will be the first to respond and participate in the primary frequency regulation process. These units are unaffected by time delays and have the ability to quickly respond to small frequency deviations. System parameters and symbols are shown in Table 1.

[0025] Table 1: System Parameters and Symbols

[0026] Since primary frequency control is often insufficient to maintain the system frequency at a reference value, synchronous generators in microgrids are equipped with both primary and secondary frequency control loops. The secondary control loop uses frequency deviation as a feedback signal and employs a PID controller to achieve frequency regulation. To address the inherent low inertia of microgrids, this embodiment utilizes a virtual synchronous generator, leveraging an energy storage system to simulate the dynamic characteristics of a synchronous motor and enhance system inertia. Power deficits caused by frequency deviations are offset by power compensation from the power source. The virtual synchronous generator model is constructed with two control loops: a virtual primary control loop and a virtual secondary control loop. It is important to note that both the secondary and virtual secondary frequency control loops are deployed within the microgrid's central controller, and their signal reception and transmission rely on an open communication network. Therefore, the control inputs must consider the effects of time delays and hybrid network attacks.

[0027] Selecting state variables External disturbances Control input Measurement output Controlled output The state-space expression of the microgrid frequency control system with the participation of virtual synchronous generators is shown below: (1) in , , , , , , .

[0028] Considering the sampling interval in microgrid frequency control in practical engineering The system (1) is discretized and rewritten as a linear discrete-time system as follows.

[0029] (2) The sampling time of the sensor is expressed as: , , , , .

[0030] A Denial-of-Service (DoS) attack is a malicious network attack method in which attackers use various methods to prevent a target system or network resource from providing normal services to legitimate users. Its goal is not to illegally obtain data, but to force service interruption and reduce business availability. Therefore, this study considers the scenario of a system being attacked by a DoS attack as one involving input control. The effects are offset. Building upon DoS attacks, we further consider the impact of False Data Injection (FDI) attacks. The core of an FDI attack is constructing false data and transmitting it to the core control system. The core control system, during decision analysis, uses this incorrect data input to implement incorrect control strategies, ultimately leading to damage to the power grid. Here, we consider a scenario where an FDI attack is implemented based on a DoS attack, specifically at the system control input... Further disturbances on top of being offset The impact of these two scenarios is modeled as follows:

[0031] in .

[0032] Therefore, the signal received by the microgrid central controller can be represented as: (3) Select two independent Bernoulli sequences and The value can be either 0 or 1, and its probability distribution is as follows:

[0033] in, and These are two known constants.

[0034] Taking all factors into consideration, it can be assumed that when , When the system is affected by a DoS attack, , The system is simultaneously affected by both DoS and FDI attacks. In other scenarios, the system operates normally without being affected by network attacks. Before signals threatened by mixed network attacks reach the microgrid's central controller, there will be a time delay due to bandwidth limitations of the open communication network.

[0035] In microgrid frequency control systems relying on open communication networks, communication delays are unavoidable due to bandwidth constraints during data transmission. This embodiment considers the system being subject to random time-varying delays. The effect of its time delay satisfies ,in and Let be constants, and represent the lower and upper bounds of the time delay, respectively. Therefore, the control input during normal system operation can be modeled as: (4) in, It is a scalar representing the length of time. , and The gain of the controller to be designed.

[0036] The process of virtual inertia control can be described as follows: (5) in, It is the gain of the controller to be designed.

[0037] Therefore, it can be written (6) in

[0038] Combining equations (3)-(6), system (2) can be written as: (7) in , , , , , , , , , , , , , , , , .

[0039] This embodiment aims to design an output feedback controller that ensures the system (7) is exponentially mean square stable while maintaining a given level of interference suppression. The system satisfies the following conditions. Performance constraints: (8) Step 2: Determine the controller gain of the microgrid frequency control system using the proposed method. Based on the above model, this embodiment utilizes Lyapunov stability theory and stochastic analysis techniques to establish sufficient conditions to guarantee the stability of the microgrid frequency control system (7) and Performance is assessed, and the controller gain is obtained using matrix transformations. Details are as follows.

[0040] Method 1: Given Performance indicators Time lag upper and lower bounds and The integral time length of the controller If a positive definite matrix exists... , and Solving the following linear matrix inequality yields the matrix related to the controller gain. , , , and .

[0041] (9) Then, based on the matrix relationships... (10) Calculate the controller gain. , , , , , , , , , , , , , , , , , , , , , , , , , , , .

[0042] Step 3: Simulation verification of the feasibility of the designed controller After calculating the gains of multiple controllers in the microgrid frequency control system with the participation of a virtual synchronous generator, simulation can be used to verify the control effect, ensuring that the system can operate stably under the influence of a given time delay and has high robustness sufficient to cope with the threat of hybrid network attacks. The simulation is built using MATLAB Simulink.

[0043] To verify the effectiveness of the method proposed in the embodiments, simulation verification is performed here. First, the system parameters required are given in Table 2 of the appendix.

[0044] Table 2: System Parameters

[0045] Given discrete sampling period Upper bound of time delay Interference suppression level The value is 1. Considering the hybrid network attack model... , The controller gain can be obtained by following the method described in Method 1 for solving the controller gain. , , , Simulation tests were conducted for the following scenarios to further verify the effectiveness and superiority of the proposed control strategy.

[0046] Assume that the microgrid frequency control system is subjected to a disturbance of 0.01 pu at the initial moment, and the system's inertial constant is... and damping coefficient Reduced The system was only subjected to DoS attacks in the first 100 seconds, and was subsequently affected by mixed network attacks. Simulation results at different discrete intervals are as follows: Figure 3 As shown, under the influence of time delay, hybrid network attacks, and large discrete intervals, the cooperative control method proposed in this embodiment can reduce overshoot, help the system recover stability faster, and better cope with problems such as communication constraints, hybrid network attacks, system inertia reduction, and random disturbances.

[0047] Results analysis: This embodiment proposes a robust cooperative control strategy for microgrid frequency control systems under the influence of time delays and hybrid network attacks. This strategy effectively addresses the negative impacts of random disturbances, time delays, hybrid network attacks, and reduced system inertia. First, a microgrid frequency control system model considering the participation of virtual synchronous generators in frequency regulation under the influence of hybrid network attacks is established. Second, a linear matrix inequality for solving the cooperative controller gain is obtained. Then, the final controller gain is obtained through matrix transformation. Finally, the effectiveness of the proposed control strategy is verified through simulation. Results show that this method effectively addresses the problems of random disturbances, time delays, and reduced system inertia faced by microgrid frequency control systems under the threat of hybrid network attacks. It can help microgrids operate better in practical engineering.

[0048] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for low-inertia microgrid system frequency control under cyber-attack, characterized in that, Includes the following steps: S1: Construct a microgrid frequency control model in which virtual generators affected by the attack participate in frequency regulation; S2: Based on the microgrid frequency control model, the controller gain is obtained using Lyapunov stability theory and stochastic analysis methods; S3: Perform frequency control on the low-inertia microgrid system under network attack based on the controller gain.

2. The method for low-inertia microgrid system frequency control under cyber-attacks according to claim 1, wherein, The microgrid frequency control model is as follows: ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， in, , , express , , The state variable at any given time; express Random time-varying time delays at any given moment; , , Let be the state matrix of the system. , These represent the lower and upper bounds of the time delay, respectively. , This represents the state matrix of the system as it relates to past moments; , This represents the state matrix associated with the disturbance; , , These represent the set of past system states, the combination of attack-related states, and the set of microgrid states affected by external disturbances, respectively; the superscript T indicates matrix transpose; h represents the integration time constant. , These represent the combination of C matrices and the system's output state matrix, respectively. Represents a diagonal matrix; express External disturbances at any given moment; , , Bernoulli signals at different times are used to simulate the impact of an attack; , express Two independent Bernoulli sequences at time t; , express Combinations of items related to the attack at any given moment; , It is a constant; Represents the system's input state matrix; , , , This represents the combination of controller gain correlation matrices in the system; Represents the correlation matrix of the system disturbance state; , , , Indicates the gain of the controller to be designed; Represents the inertial constant of the virtual generator; Indicates the damping coefficient of the virtual generator; , , These represent the boundary values ​​of disturbances in the closed-loop system, the microgrid system, and the FDI attack, respectively. This indicates the expected value of the corresponding content; Represents the L2 norm of the corresponding content; Indicates the level of interference suppression; express Controlled output at any given moment.

3. The method for frequency control of a low-inertia microgrid system under network attack according to claim 1, characterized in that, The process of obtaining the controller gain includes: based on the microgrid frequency control model, and using Lyapunov stability theory and stochastic analysis methods, obtaining the controller gain that guarantees the stability of the microgrid frequency control system. Sufficient conditions for performance; based on the sufficient conditions, the controller gain is obtained using matrix transformation.

4. The method for frequency control of a low-inertia microgrid system under network attack according to claim 3, characterized in that, The sufficient condition is: ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， in, This represents the linear matrix inequality used to solve for the controller gain. Represents the symmetric elements in a matrix; , , , , This represents a matrix related to the controller gain. , , Represent the matrix to be solved; Represents a combination of matrices; Indicates the orthogonal complement of the corresponding content; Represents the combination of matrices. , Represents a combination of matrices; Represents the combination of matrices. Represents the unknown term in a linear matrix inequality; Represents the combination of matrices. , , , , , , , Represents a combination of matrices; represents the unknown term in the linear matrix inequality; E represents the state matrix related to the control output. , Represent the unknown matrix in a linear matrix inequality; , These represent the lower and upper bounds of the time delay, respectively.

5. A system for frequency control of a low-inertia microgrid system under network attacks, characterized in that, The system includes the following modules: The microgrid frequency control model construction module is configured to: construct a microgrid frequency control model in which a virtual generator affected by an attack participates in frequency regulation; The controller gain generation module is configured to: obtain the controller gain based on the microgrid frequency control model, using Lyapunov stability theory and stochastic analysis methods; The frequency control module is configured to perform frequency control on a low-inertia microgrid system under network attacks based on the controller gain.

6. The system for frequency control of a low-inertia microgrid system under network attack according to claim 5, characterized in that, The microgrid frequency control model is as follows: ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， in, , , express , , The state variable at any given time; express Random time-varying time delays at any given moment; , , Let be the state matrix of the system. , These represent the lower and upper bounds of the time delay, respectively. , This represents the state matrix of the system as it relates to past moments; , This represents the state matrix associated with the disturbance; , , These represent the set of past system states, the combination of attack-related states, and the set of microgrid states affected by external disturbances, respectively; the superscript T indicates matrix transpose; h represents the integration time constant. , These represent the combination of C matrices and the system's output state matrix, respectively. Represents a diagonal matrix; express External disturbances at any given moment; , , Bernoulli signals at different times are used to simulate the impact of an attack; , express Two independent Bernoulli sequences at time t; , express Combinations of items related to the attack at any given moment; , It is a constant; Represents the system's input state matrix; , , , This represents the combination of controller gain correlation matrices in the system; Represents the correlation matrix of the system disturbance state; , , , Indicates the gain of the controller to be designed; Represents the inertial constant of the virtual generator; Indicates the damping coefficient of the virtual generator; , , These represent the boundary values ​​of disturbances in the closed-loop system, the microgrid system, and the FDI attack, respectively. This indicates the expected value of the corresponding content; Represents the L2 norm of the corresponding content; Indicates the level of interference suppression; express Controlled output at any given moment.

7. The system for frequency control of a low-inertia microgrid system under network attacks according to claim 5, characterized in that, The process of obtaining the controller gain includes: based on the microgrid frequency control model, and using Lyapunov stability theory and stochastic analysis methods, obtaining the controller gain that guarantees the stability of the microgrid frequency control system. Sufficient conditions for performance; based on the sufficient conditions, the controller gain is obtained using matrix transformation.

8. The system for frequency control of a low-inertia microgrid system under network attack according to claim 7, characterized in that, The sufficient condition is: ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， in, This represents the linear matrix inequality used to solve for the controller gain. Represents the symmetric elements in a matrix; , , , , This represents a matrix related to the controller gain. , , Represent the matrix to be solved; Represents a combination of matrices; Indicates the orthogonal complement of the corresponding content; Represents the combination of matrices. , Represents a combination of matrices; Represents the combination of matrices. Represents the unknown term in a linear matrix inequality; Represents the combination of matrices. , , , , , , , Represents a combination of matrices; represents the unknown term in the linear matrix inequality; E represents the state matrix related to the control output. , Represent the unknown matrix in a linear matrix inequality; , These represent the lower and upper bounds of the time delay, respectively.

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