Anti-DoS attack micro-grid event triggering rapid elastic distributed control method

Abstract

The invention provides an anti-DoS attack event-triggered rapid elastic distributed control method aiming at the problem when the distributed secondary control of the micro-grid faces the DoS attack, the method is a novel distributed elastic secondary control scheme, and the scheme effectively relieves the influence of the DoS attack on the micro-grid system by introducing an intermittent control strategy. According to the scheme, the fixed time lemma is applied, the time required for frequency recovery and active power sharing is shortened, and the electric energy quality is improved. Moreover, a dynamic event triggering mechanism is introduced in the implementation process to design the controller, so that the consumption of communication resources is greatly reduced, the pressure of a communication network is effectively relieved, and the efficient utilization of the communication resources is improved. Therefore, a brand new solution is provided for improving the stability and efficiency of the system when the secondary control of the micro-grid faces the DoS attack, and the method has remarkable beneficial effects.

Description

Technical Field

[0001] The present invention belongs to the technical field of microgrid security control, and particularly relates to a microgrid event-triggered fast elastic distributed control method against DoS attacks. Background Art

[0002] During the operation of a microgrid, accelerating the frequency recovery can effectively improve the power quality and enhance the reliability of the power system, which is of great significance for ensuring the power supply of important facilities, medical equipment, and residential use. In addition, the rapid sharing of active power enables distributed energy sources and loads to respond to each other's demands more quickly, thereby improving the energy utilization efficiency of the entire microgrid. However, the stable operation of a microgrid depends on a stable network environment, and an open communication network makes the system more vulnerable to network attack threats. Among these potential network attacks, denial-of-service (DoS) attacks can interrupt the information transmission of distributed generation units (DGs), affect the normal operation of the microgrid system, and even pose a risk of power outage accidents, affecting the daily life of the public and causing varying degrees of economic property losses. Therefore, it is of great significance to study the secure and fast control problem of the microgrid system.

[0003] To achieve rapid frequency restoration in a microgrid, a distributed fast convergence algorithm is used in the secondary control of the microgrid. Zhao et al. designed a fixed-time secondary control scheme for microgrid frequency restoration and power sharing in the literature "D. Zhao, C. Zhang, Y. Sun, S. Li, B. Sun, and Y. Li. Distributed robust frequency restoration and active power sharing for autonomous microgrids with event-triggered strate, IEEE Transactions on Smart Grid, 12(5): 3819 - 3834, 2021". The application of the static event-triggered mechanism saves communication resources. To resist the impact of DoS attacks, a distributed security control strategy has been applied to the frequency regulation of the microgrid. Jamali et al. proposed a resilient control strategy in the literature "M. Jamali, H. R. Baghaee, M. S. Sadabadi, G. B. Gharehpetian, and A. Anvari-Moghaddam. Distributed cooperative event-triggered control of cyber-physical AC microgrids subject to denial-of-service attacks, IEEE Transactions on Smart Grid, 14(6): 4467 - 4478, 2023" to ensure that the secondary controller in the microgrid converges exponentially under denial-of-service attacks, alleviating the impact of DoS attacks.

[0004] The secondary controllers designed in the above methods for studying frequency restoration and power sharing in a microgrid under DoS attacks all converge exponentially. In addition, in an ideal network communication environment, the existing fixed-time secondary controllers for microgrids all adopt a static event-triggered mechanism. To further save communication resources, it is necessary to develop and apply a dynamic event-triggered mechanism. Summary of the Invention

[0005] To solve the above problems existing in the prior art, the present invention provides a microgrid event-triggered fast resilient distributed control method against DoS attacks. The technical problems to be solved by the present invention are realized through the following technical solutions:

[0006] A microgrid event-triggered fast resilient distributed control method against DoS attacks, comprising:

[0007] S100. Describe the communication topology of a microgrid with multiple distributed generation units using an undirected graph to obtain the undirected graph of the microgrid system;

[0008] S200. Construct the control objective functions for frequency restoration and active power distribution of distributed generation units under DoS attacks;

[0009] S300. Use the ACK-based detection algorithm to detect whether the distributed generation units in the undirected graph of the microgrid system are under DoS attacks, and if so, obtain the detection results including the moment when the communication link returns to the available state after being attacked and the duration of the DoS attack;

[0010] S400. According to the detection results, the control objective function for frequency restoration, and the intermittent control fixed-time lemma for the system to tend to stability, and introduce a dynamic event-triggering mechanism to design a frequency auxiliary controller and an active power auxiliary controller respectively;

[0011] S500. Use the frequency auxiliary controller and the active power auxiliary controller to perform intermittent control on each node in the undirected graph of the microgrid system in the way of resting during the attack time and controlling when not under attack.

[0012] Beneficial effects:

[0013] In view of the problem that the distributed secondary control of the microgrid faces DoS attacks, the present invention proposes a microgrid event-triggered fast resilient distributed control method against DoS attacks. This method is a novel distributed resilient secondary control scheme. By introducing an intermittent control strategy, the impact of DoS attacks on the microgrid system is effectively alleviated. This scheme applies the intermittent control fixed-time lemma, which accelerates the time required for frequency restoration and active power sharing, and improves the power quality. And in the implementation process of the present invention, a dynamic event-triggering mechanism is introduced to design the controller, which not only significantly reduces the consumption of communication resources, but also effectively relieves the pressure on the communication network and improves the efficient utilization of communication resources. Therefore, the present invention provides a new solution for improving the stability and efficiency of the microgrid secondary control system in the face of DoS attacks, and has significant beneficial effects.

[0014] The following will further elaborate on the present invention in detail with reference to the drawings and embodiments. Description of the Drawings

[0015] Figure 1 is a schematic flowchart of a microgrid event-triggered fast resilient distributed control method against DoS attacks provided by the present invention;

[0016] Figure 2 is a schematic diagram of a DoS attack provided by the present invention;

[0017] Figure 3 It is a structural block diagram of the microgrid system provided by the present invention;

[0018] Figure 4 It is a schematic diagram of the communication topology of the distributed power generation unit provided by the present invention;

[0019] Figure 5 is a schematic diagram of a frequency signal of a distributed power generation unit provided by the present invention;

[0020] Figure 6 is a schematic diagram of an active power output signal of a distributed power generation unit provided by the present invention;

[0021] Figure 7 It is a schematic diagram of the triggering time of frequency recovery of the distributed power generation unit provided by the present invention;

[0022] Figure 8 It is a schematic diagram of the triggering time of active power recovery of the distributed power generation unit provided by the present invention. DETAILED DESCRIPTION

[0023] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0024] The present invention aims to solve the technical problem that when the system is attacked by a denial of service, the microgrid can still quickly restore the frequency and share the active power. First, an acknowledgment character (ACK) detection mechanism is introduced to identify the beginning and end of intermittent DoS attacks. Then, based on intermittent control, a novel distributed fixed-time elastic control strategy is proposed to achieve rapid frequency recovery and active power sharing. In addition, when designing the event trigger mechanism, internal dynamic variables are introduced to construct a dynamic event trigger mechanism, which further saves communication resources. Finally, a microgrid test system is used to verify the effectiveness of the proposed distributed fixed-time security control strategy.

[0025] like Figure 1 As shown, the present invention provides a microgrid event-triggered fast elastic distributed control method against DoS attacks, including:

[0026] S100, using an undirected graph to describe a microgrid communication topology structure having multiple distributed generation units to obtain an undirected graph of the microgrid system;

[0027] The undirected graph of the microgrid system consists of nodes and edges, and the node set is represented as Each node represents a distributed generation unit, and the edge set is represented as Edges represent communication links between corresponding nodes; It is used to represent the set of neighboring units of all distributed generation units. The corresponding adjacency matrix is ​​expressed as A = [aij N×N ; If then a ij > 0, otherwise a ij = 0; The degree matrix is expressed as The Laplacian matrix is defined as The adjacency matrix of the virtual leader is B = diag{b1, b2, b3, b4}. If the i-th distributed generation unit receives a reference signal, then b i = 1, otherwise b i = 0; Define the corresponding Laplacian matrix as

[0028] S200, construct the control objective functions for frequency restoration and active power distribution of distributed generation units under DoS attacks;

[0029] In the hierarchical control of a microgrid, droop control is usually used for primary control. However, droop control can cause the frequency to deviate from the rated value after load changes or operation mode switches. Therefore, it is necessary to adopt secondary control to correct these frequency deviations and ensure the reasonable distribution of active power by controlling the input Ω i The improved droop control can be expressed as:

[0030]

[0031] where ω i represents the frequency of the i-th distributed generation unit, is the rated frequency, m i is the active droop coefficient, and Ω i is the secondary control input. Taking the derivative of Ω i can obtain:

[0032]

[0033] With the help of feedback linearization, in the formula and respectively represent the auxiliary control inputs of the distributed generation unit frequency and active power. Accelerating the rate of frequency restoration and power sharing can improve the power quality.

[0034] Therefore, under a denial-of-service (DoS) attack, the control objective functions for frequency restoration and active power distribution are respectively expressed as:

[0035]

[0036] In the formula, ω i represents the frequency of the i-th distributed generation unit, ω ref is the rated reference frequency, T w is the frequency restoration time, T​p is the operating time of the active power, m i is related to P i corresponding active power droop coefficient, P i is the active power of the i-th distributed generation unit, m j is related to P j corresponding active power droop coefficient, P j is the active power of the j-th distributed generation unit, and t represents time.

[0037] S300, using the ACK-based detection algorithm, detects whether the distributed generation units in the undirected graph of the microgrid system are under DoS attacks, the moment when the communication link returns to the available state after being under DoS attacks, and the duration of the DoS attacks, and obtains the detection results;

[0038] Refer to Figure 2 As shown, after the system suffers the n-th attack, the moment when the communication link returns to the available state is recorded as r n , and the available duration is expressed as s n . Therefore, the normal operation interval of the microgrid is denoted as where Π N,n = [r n , s n + r n ). The DoS attack interval is denoted as where Π D,n = [s n + r n , s n+1 ).

[0039] Hypothesis 1:

[0040] Considering the energy-limited DoS attacks, the parameter ρ ∈ (0, 1) is used to describe the characteristics of the attacks,

[0041]

[0042] where |Π D (0, t)| represents the total duration of the DoS attacks, and the state of the communication network can be described by the following piecewise function

[0043]

[0044] DoS attacks will block the transmission of signals in the communication link, thereby affecting the performance of the microgrid.

[0045] To mitigate the impact of DoS attacks, a detection mechanism based on AKC is used to determine whether a DoS attack has occurred. Specifically, when the microgrid is under a DoS attack, the distributed generation units will not receive the ACK signal (ACK = 0). When the communication network resumes, the distributed generation units can receive the ACK signal (ACK = 1). The detection algorithm is expressed as:

[0046] r n = inf{t > s n-1 + r n-1 | ACK From 0 to 1}

[0047] s n + r n = inf{t > r n | ACK From 1 to 0}

[0048] In the formula, r n represents the moment when the communication link returns to the available state after the microgrid has been under the nth DoS attack; r n-1 represents the moment when the communication link returns to the available state after the microgrid has been under the (n - 1)th DoS attack; s n represents the duration when the communication link returns to the available state after the nth DoS attack; s n-1 represents the duration when the communication link returns to the available state after the (n - 1)th DoS attack; ACK From 0 to 1 means that the ACK received by the distributed generation unit jumps from 0 to 1; ACK From 1 to 0 means that the ACK received by the distributed generation unit jumps from 1 to 0.

[0049] S400. According to the detection results, the control objective function for frequency restoration, and the intermittent control fixed-time lemma for system stability, and introducing a dynamic event-triggering mechanism, respectively design a frequency auxiliary controller and an active power auxiliary controller;

[0050] This step aims at two situations where the detection result is that the microgrid is under a DoS attack and not under a DoS attack. According to the control objective function for frequency restoration and the intermittent control fixed-time lemma for system stability, and introducing a dynamic event-triggering mechanism, respectively design the frequency auxiliary controller and the active power auxiliary controller under DoS attack and without DoS attack.

[0051] When the microgrid is under a DoS attack, the distributed topology will change, which will affect the convergence of the system and even the stability of the microgrid. To mitigate the impact of DoS attacks, an intermittent control strategy is applied to the microgrid security control.

[0052]

[0053] In an intermittent control (a communication or control system architecture) scheme, it is usually necessary to obtain the distribution of control activation intervals in advance. An intelligent communication management center is introduced to monitor the communication environment and make decisions on network failures. A reliable and secure channel is used to transmit attack detection reports between each distributed generation unit (DGs) and the intelligent communication management center. When the DGs detect a DoS attack, it is sent to the intelligent communication management center, and then the intelligent communication management center sends the information of intermittent control to each DGs.

[0054] Lemma 1: Fixed-Time Lemma for the Microgrid to Tend to Stability

[0055] Consider the following microgrid system:

[0056]

[0057] where and the function g is a nonlinear mapping. If there exists a Lyapunov equation V(t) that satisfies

[0058]

[0059] where a1>0, a2>0, a3>0, p∈(1, ∞) and q∈(0, 1) represent the quotient of positive odd numbers, and the intervals [s n , s n +r n ) and [s n +r n , s n+1 ) represent the control interval and the rest interval of the nth control respectively. The microgrid will converge in a fixed-time manner, and the required time T for stability satisfies:

[0060]

[0061] where ρ represents the parameter used to describe the characteristics of the DoS attack. The control interval is the time interval without being attacked, and the rest interval is the time interval being attacked.

[0062] Proof: Construct the following dynamic equation:

[0063]

[0064] Combining (1.2) and (1.3) gives 0 ≤ V(t) ≤ R(t). When R(t) > 1, set:

[0065]

[0066] Then it can be obtained that:

[0067]

[0068] When \(0\leq R(t)\leq1\), let It can be obtained that

[0069]

[0070] It can be found that for the microgrid system (1.4), when \(W(t)\to0\), \(R(t)\to\infty\), and when \(W(t)\to1\), \(R(t)\to1\). Integrating Equation (1.4) gives

[0071]

[0072] where \(\Lambda\) c (0, t) is the control time of the system within \((0, t]\). Construct an increasing function that satisfies: \(W(t)\geq W_1(t)=W(0)+a_3(p - 1)(1 - \rho)t\). Therefore, there exists a time \(T_1\) * that satisfies That is Furthermore, \(T_1\) * is:

[0073]

[0074] Since \(W(0)\geq0\), thus

[0075]

[0076] Therefore, there exists a that satisfies Furthermore, it can be obtained that

[0077] For system (1.5), when \(W(t)\to1\), \(R(t)\to1\) and when \(W(t)\to0\), \(R(t)\to0\). It can be obtained that

[0078]

[0079] Therefore, there exists a decreasing function \(W_2(t)=W(0)+a_1(q - 1)(1 - \rho)t\). In addition, there exists a time that satisfies That is, \(W(0)+a_1(p - 1)(1 - \rho)t = 1\). Then it can be obtained that:

[0080]

[0081] When Equation, and can be expressed as

[0082]

[0083] where, since \(W(t)\leq W_2(t)\), satisfy and therefore when \(t\geq T\) * , \(V(t)\equiv0\).

[0084] Finally, the set time \(T\) can be obtained *

[0085]

[0086] The lemma is proved.

[0087] When the microgrid is under a DoS attack, the stability of the system will be affected. To ensure the stability of the system, the present invention proposes a fixed-time resilient controller to mitigate the impact of the DoS attack. First, for

[0088] the frequency restoration of the microgrid, the following auxiliary controller \(u\) ωi (t) is designed:

[0089] When the microgrid is not under attack, i.e., \(t\in[s\) n , \(s\) n +r n )

[0090]

[0091] where \(\gamma_1,\gamma_2,\gamma_3\) are positive control gains, \(p\in(1,\infty)\) and \(q\in(0,1)\) represent the quotient of positive odd numbers. Here, \(e\) ωi (t)=\(\omega\) i (t)-\(\omega\) r , so e ω =[e ω1 ,…,e ωN T .

[0092] is represented as the Laplacian matrix.

[0093] When the microgrid is under attack, i.e., \(t\in[s\) n +r n , \(s\) n+1 )

[0094] u ωi (t)=0

[0095]

[0096] To mitigate a communication resource, a dynamic event-triggering mechanism is introduced into the frequency restoration of the microgrid. Therefore, the frequency auxiliary controller under non-DoS attack and under attack is expressed as:

[0097]

[0098] where γ1, γ2, γ3 represent positive control gains represents the latest trigger time for the frequency recovery of the i-th distributed generation unit represents the next trigger time for the frequency recovery of the i-th distributed generation unit, and k represents the trigger ordinal number of frequency recovery is designed to be

[0099]

[0100] Define the dynamic event-triggered measurement error χ ωi (t) as follows:

[0101]

[0102] Therefore, the frequency assistance controller under no DoS attack is expressed as:

[0103]

[0104] where χ i (t) represents the dynamic event-triggered measurement error represents the frequency consistency error

[0105] An event-triggered equation is constructed as follows:

[0106]

[0107] where θ ∈ (0, 1), ∈ ∈ (0, 1). To further alleviate communication resources, internal dynamics are introduced into the communication of DGs

[0108]

[0109] where Υ ωi (0) > 0, δ ∈ (0, 1), ζ represents a positive parameter, δ represents a positive parameter, and γ5, γ6, γ7 are positive numbers. Therefore, the distributed frequency recovery dynamic event-triggered mechanism is designed as follows:

[0110] f wi (t) = ψ i (t) - Υ ωi (t) - ζ(1.6)

[0111] If Υ ωi (t) = 0, the trigger mechanism will become a static event-triggered mechanism. Then, Equation (1.6) is used to determine the trigger time of frequency communication

[0112]

[0113] The above equation ensures that the measurement error satisfies Therefore, the internal dynamic variable can be expressed as:

[0114]

[0115] Based on the above equation, we can obtain

[0116]

[0117] In the formula, It can be found that Υ ωi (t) is a positive parameter. Therefore, compared with the static event trigger, the trigger times can be significantly reduced, and the communication resources can be relieved.

[0118] Theorem 1: Assume that the undirected graph G is connected and at least one distributed generation unit can receive the reference signal ω ref . If the denial-of-service (DoS) attacks all meet the conditions of Hypothesis 1, then, using the dynamic event trigger and detection mechanism, the proposed distributed frequency controller can restore the frequency of the microgrid within a fixed time range. And, the convergence time of this frequency restoration meets the established requirements:

[0119]

[0120] In the formula,

[0121]

[0122] represents the second smallest eigenvalue of the matrix.

[0123] Proof: Select the following Lyapunov equation:

[0124] V(t) = V1(t) + V2(t)

[0125] In the formula, First, when the microgrid is not under DoS attack, that is, t ∈ Π N , taking the derivative of V(t) gives

[0126]

[0127] Substituting Equation (1.7) into the above equation gives

[0128]

[0129] Since and we can obtain:

[0130]

[0131] In the formula:

[0132]

[0133] When the microgrid is under a DoS attack, i.e., t ∈ Π D , taking the derivative of V(t) gives

[0134]

[0135] Combining Equation (1.9) and Equation (1.10), we get

[0136]

[0137] According to the intermittent control fixed-time lemma, when the time t required for V(t) = 0 satisfies t ≤ T ω , Q.E.D.

[0138] Theorem 2: Under the frequency restoration auxiliary control input and the dynamic event-triggering mechanism, Zeno behavior will be avoided.

[0139] Proof: In the proof of Theorem 1, we have where Then we have:

[0140]

[0141] In the formula

[0142] is the triggering time of the j-th distributed generation unit.

[0143] Integrating Equation (1.11) gives

[0144]

[0145] When , the triggering condition is satisfied:

[0146]

[0147] Combining (1.12), we get

[0148]

[0149] In the formula Therefore, Zeno behavior is avoided.

[0150] To achieve the sharing of active power under DoS attacks, an active power auxiliary controller designed using dynamic event triggering, i.e., the active power auxiliary controllers under DoS attacks and without DoS attacks are expressed as:

[0151]

[0152] where, represents the active power consistency error.

[0153] where is the latest trigger time when the active power of the i-th distributed generation unit recovers.

[0154] Define the active power measurement error as follows:

[0155]

[0156] The event trigger equation is defined as:

[0157]

[0158] The internal dynamic variable for the active power recovery of the distributed generation unit is defined as:

[0159]

[0160] Therefore, the distributed active power dynamic event trigger equation is

[0161] f Pi (t) = ψ Pi (t) - Υ Pi (t) - ζ(1.13)

[0162] If Υ ωi (t) = 0, the trigger mechanism will become a static event trigger mechanism. Then, Equation (1.13) is used to determine the trigger time of active power communication.

[0163] Theorem 3: Assume that the undirected graph G is connected and the DoS attack satisfies Assumption 1. The dynamic event-triggered active power controller will achieve power sharing within a fixed time T P and the time T P satisfies:

[0164]

[0165] where:

[0166]

[0167] Proof: The reasoning process of Theorem 3 is similar to the proof of Theorem 1. For the sake of brevity and to avoid repetition, the corresponding proof is omitted here.

[0168] Theorem 4: Under the active power auxiliary controller and the dynamic event-triggering mechanism, Zeno behavior will be avoided.

[0169] Proof: The proof of Theorem 4 is the same as that of Theorem 2. For the sake of brevity and to avoid repetition, the corresponding proof is omitted here.

[0170] S500, using the frequency auxiliary controller and the active power auxiliary controller, perform intermittent control on each node in the undirected graph of the microgrid system in the manner of resting at the attack time and controlling when not under attack.

[0171] Regarding the problem that the distributed secondary control of the microgrid faces Denial-of-Service (DoS) attacks, the present invention proposes a novel distributed resilient secondary control scheme. By introducing an intermittent control strategy, this scheme effectively alleviates the impact of DoS attacks on the microgrid system. This scheme utilizes the fixed-time lemma to accelerate the time required for frequency recovery and active power sharing, improving the power quality. And in the implementation process of the present invention, a dynamic event-triggering mechanism is introduced to design the controller, which not only significantly reduces the consumption of communication resources but also effectively alleviates the pressure on the communication network and improves the efficient utilization of communication resources. Therefore, the present invention provides a new solution for improving the stability and performance of the microgrid secondary control system in the face of DoS attacks, with remarkable beneficial effects.

[0172] The effects of the present invention can be further illustrated by the following simulation experiments.

[0173] 1. Simulation conditions

[0174] The present invention conducts simulations using MATLAB 2023b developed by MathWorks, Inc. in the United States on a central processing unit of Inter(R) Core(TM) i7-4790 3.60GHz CPU, NVIDIA Titan X GPU, and Ubuntu 16.04 operating system.

[0175] 1. Simulation content

[0176] An AC microgrid model is built in the MATLAB / SIMULINK toolbox to verify the effectiveness of the proposed dynamic event-triggering distributed resilient secondary control scheme. Figure 3 The physical components of the microgrid are shown, including 4 distributed generation units and 2 local loads. The detailed electrical parameters and control parameters of the distributed generation units are described in Tables 1 and 2.

[0177] Table 1 Microgrid system parameters

[0178]

[0179] Table 2 Controller Parameters

[0180]

[0181] The communication topology is as Figure 4 shown, and only the first distributed generation unit can receive the reference signal ω ref . If the i-th distributed generation unit establishes a communication connection with the j-th distributed generation unit, then a ij = 1. According to Figure 2 the topological structure, the weighted adjacency matrix A and the virtual adjacency matrix B can be obtained.

[0182] To verify the effectiveness of the proposed resilient secondary control, the step load change and the impact of DoS attacks are considered in the simulation experiment. At t = 0 s, the first load is connected to the system, and only droop control is implemented in the microgrid. At t = 0.5 s, the proposed secondary control scheme is implemented. At t = 3 s, the second load is connected to the microgrid and disconnected from the microgrid at t = 5 s.

[0183] The frequency response curves of all DGs are as Figure 5 shown. In the initial 0.5 s, only droop control is applied, and the frequency deviates when the system is stable because the essence of droop control is droop control. When t = 0.5 s, after the resilient secondary control scheme is implemented, the frequency quickly recovers to ω ref = 50 Hz, and the required time is 0.62 s. When t = 3 s, load 2 is instantaneously connected to the microgrid system, and the frequency deviates. The implementation of secondary control quickly realizes the frequency recovery, and the required time is 0.34 s. When t = 5 s, the second load is instantaneously removed from the microgrid system, and the frequency changes. The secondary control can still quickly realize the frequency recovery, and the required time is 0.3 s.

[0184] The corresponding response curves of the active power of all DGs are as Figure 6 shown. In the initial 0.5 s, droop control accurately realizes the sharing of active power through the droop coefficient. When t = 0.5 s, after a certain adjustment time, the secondary control can still ensure the sharing of active power, and the required time is 0.7 s. When t = 3 s, load 2 is instantaneously connected to the microgrid system, and the secondary control still ensures the sharing of active power by coordinating the DGs, and the required time is 0.6 s. When t = 5 s, the second load is instantaneously removed from the microgrid system, and the secondary control can still ensure the sharing of active power, and the required time is 0.53 s.

[0185] Figure 5 and Figure 6The shaded part in it is the time when the system suffers from a DoS attack. It can be seen that when the microgrid system suffers from a DoS, the proposed control scheme can still complete frequency restoration and active power sharing, verifying the effectiveness of the proposed elastic secondary control scheme. Figure 7 and Figure 8 are the triggering moments of frequency restoration and active power sharing respectively. It can be seen from the figure that the application of the dynamic event triggering mechanism significantly reduces the number of triggers, achieving the purpose of saving communication resources.

[0186] It should be noted that the terms "first" and "second" in the present invention are only for descriptive purposes and cannot be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, "a plurality" means two or more unless otherwise specifically defined.

[0187] Although the present application has been described in connection with various embodiments herein, however, in implementing the claimed present application, those skilled in the art can understand and realize other variations of the disclosed embodiments by viewing the accompanying drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "one" does not exclude a plurality of cases.

[0188] The above content is a further detailed description of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, and all should be regarded as belonging to the protection scope of the present invention.

Claims

1. A microgrid event-triggered fast elastic distributed control method against DoS attacks, characterized in that: include: S100, using an undirected graph to describe a microgrid communication topology structure having multiple distributed generation units to obtain an undirected graph of the microgrid system; S200, constructs the control objective function of frequency recovery and active power allocation of distributed generation units under DoS attacks; S300, using an ACK-based detection algorithm, detect whether the distributed generation units in the undirected graph of the microgrid system are under DoS attack, and obtain the detection result of the time when the communication link recovers to an available state after being attacked by DoS and the duration of the DoS attack; S400, according to the detection results, the control objective function of frequency recovery and the fixed time lemma of intermittent control that the system tends to be stable, and introducing a dynamic event trigger mechanism, the frequency auxiliary controller and the active power auxiliary controller are designed respectively; S500, using the frequency auxiliary controller and the active power auxiliary controller, intermittently control each node in the undirected graph of the microgrid system in a manner of resting during attack time and controlling during non-attack time.

2. The microgrid event-triggered fast elastic distributed control method against DoS attacks according to claim 1 is characterized in that: The undirected graph of the microgrid system consists of nodes and edges, and the node set is represented as Each node represents a distributed generation unit, and the edge set is represented as Edges represent communication links between corresponding nodes; It is used to represent the set of neighboring units of all distributed generation units. The corresponding adjacency matrix is ​​expressed as A = [a ij ] N×N ;if Then a ij >0, otherwise a ij =0; the degree matrix is ​​expressed as The Laplacian matrix is ​​defined as The adjacency matrix of the virtual leader is B = diag{b1, b2, b3, b4}. If the i-th distributed generation unit receives the reference signal, then b i =1, otherwise b i =0; define the corresponding Laplace matrix as 3. The microgrid event-triggered fast elastic distributed control method against DoS attacks according to claim 2 is characterized in that: The control objective functions of frequency recovery and active power distribution in S200 are expressed as: In the formula, ω i represents the frequency of the ith distributed generation unit, ω ref is the rated reference frequency, T w is the frequency recovery time, T p is the operating time of active power, m i is with P i The corresponding active power droop coefficient, P i is the active power of the ith distributed generation unit, m j is with P j The corresponding active power droop coefficient, P j is the active power of the jth distributed generation unit, and t represents time.

4. The microgrid event-triggered fast elastic distributed control method against DoS attacks according to claim 3 is characterized in that: The detection algorithm in S300 is expressed as: r n =inf{t>s n-1 +r n-1 |ACK From 0to 1} s n +r n =inf{t>r n |ACK From 1to 0} In the formula, r n represents the time when the communication link recovers to an available state after the microgrid is attacked by the nth DoS attack; r n-1 It indicates the time when the communication link recovers to the available state after the microgrid is attacked by the n-1th DoS attack; s n Indicates the duration of time it takes for the communication link to recover after the nth DoS attack; s n-1 It indicates the duration of time for the communication link to recover to an available state after the n-1th DoS attack; ACK From 0to 1 indicates that the ACK that the distributed generation unit can receive jumps from 0 to 1; ACK From 1to 0 indicates that the ACK that the distributed generation unit can receive jumps from 1 to 0.

5. The microgrid event-triggered fast elastic distributed control method against DoS attacks according to claim 4 is characterized in that: S400 includes: For the two cases where the detection results are under DoS attack and not under DoS attack, according to the control objective function of frequency recovery and the fixed time lemma of intermittent control that the system tends to be stable, a dynamic event trigger mechanism is introduced to design the frequency auxiliary controller and active power auxiliary controller under DoS attack and not under DoS attack respectively.

6. The microgrid event-triggered fast elastic distributed control method against DoS attacks according to claim 5 is characterized in that: The intermittent control fixed time lemma for the system to stabilize is expressed as: Microgrid system And the function g is a nonlinear mapping if there exists a Lyapunov equation V(t) that satisfies: Where a1>0, a2>0, a3>0, p∈(1,∞) and q∈(0,1) represent the quotient of positive odd numbers, and the interval [s n ,s n +r n ) and [s n +r n ,s n+1 ) represent the control interval and rest area of ​​the nth control respectively. The microgrid will converge in a fixed time manner, and the time required for stability T satisfies: Where ρ represents the parameter used to describe the characteristics of DoS attacks.

7. The microgrid event-triggered fast elastic distributed control method against DoS attacks according to claim 6 is characterized in that: The frequency auxiliary controller under no DoS attack and under attack is expressed as: In the formula, γ1, γ2, γ3 represent positive control gains, represents the latest triggering time of frequency recovery of the ith distributed generation unit, represents the next triggering time of frequency recovery of the i-th distributed generation unit, k represents the frequency recovery triggering sequence number, It is expressed as:

8. The microgrid event-triggered fast elastic distributed control method against DoS attacks according to claim 7 is characterized in that: The active power auxiliary controller under no DoS attack and under DoS attack is expressed as: In the formula, represents the latest triggering time of power sharing of the ith distributed generation unit, represents the next triggering moment of power sharing of the ith distributed generation unit, s represents the power sharing triggering sequence number, It is expressed as:

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