A switching event-triggered load frequency safety control method for microgrid systems

Abstract

The present invention proposes a method for safely controlling the load frequency of a microgrid system triggered by a switching event. The method constructs a microgrid load frequency control scheme under DoS attack scenarios and without attacks, respectively, which can save more bandwidth resources under the premise of system stability. For the algorithm model affected by delay, by constructing a high-order Lyapunov energy functional, obtaining derivatives and scaling, the microgrid system subjected to denial of service attack is modeled as a delay system, and the time-varying delay stability criterion is applied thereto, and a smaller conservatism is ensured to obtain a delay-dependent convergence criterion that takes into account conservatism and complexity, and the tolerance of the algorithm to delay can be judged in turn. Finally, it is proved through experiments that the controller design method proposed by the present invention can ensure the asymptotic stability of the system when a DoS attack occurs.

Description

Technical Field

[0001] The present invention belongs to the technical field of novel power system safety control, and in particular relates to a method for safely controlling load frequency of a microgrid system triggered by a switching event. Background Art

[0002] Microgrids can effectively improve the safety and reliability of power system operation, and are conducive to the construction of anti-attack and anti-disaster capabilities of power systems. At present, the development of my country's power industry is in the stage of large power grids, high voltage, long distances and large capacity. The regional power grids have been interconnected, and the network architecture is becoming increasingly complex. However, large-scale power exchange is prone to low-frequency oscillations and system instability, and its dynamic performance is difficult to control. On the other hand, compared with traditional centralized power systems, microgrids can form a more efficient and flexible new system with various existing energy forms. In power systems, power balance and frequency stability are the most basic requirements for the normal operation of the system. In modern power Internet, load frequency control maintains the power stability and frequency stability of the power system by adjusting the power maintenance of frequency-regulated generators in the region and the real-time balance of loads. However, in the future, the measurement and control data transmission of power systems will be more vulnerable to malicious network attacks with the help of open network space.

[0003] With the gradual development of microgrids, the informatization process of traditional power systems has driven the integration of information space and physical entities to be closer. This development has facilitated the management and control of power systems on the one hand, but it has also caused the transmission, storage and calculation of redundant data. These redundant data have little effect on improving the stability of the system. If the traditional periodic sampling mechanism is still used at this time, it will cause a lot of unnecessary information interaction in the microgrid system, thereby increasing the communication cost of the system. On the contrary, if criminals use information congestion to launch a denial of service attack on the system, it is more likely to cause the control system to collapse. Therefore, the security control method of the microgrid system under network attacks has become an important issue that needs to be studied urgently at this stage.

[0004] The literature [Heemels W, Donkers M, Teel A. Periodic Event-Triggered Control for Linear Systems [C]. 2013 IEEE 52nd Annual Conference on Decision and Control (CDC)] proposed a periodic event-triggered control method for linear systems, which periodically verifies the event trigger conditions to determine whether to calculate and send new measurement data and control signals at each sampling moment.

[0005] The literature [Peng C, Li J, Fei M. Resilient Event-Triggering H∞Load Frequency Control for Multi-Area Power Systems With Energy-Limited DoS Attacks[J]. IEEE Transactions on Power Systems, 2017, 32(5): 4110-4118] proposed a resilient event-triggered control method for multi-area power systems under denial of service attacks. This method carefully constructs a regional control error-related time-delay model and proposes a resilient event-triggered communication scheme that allows a certain degree of packet loss caused by denial of service attacks and effectively saves communication bandwidth resources. Finally, the Lyapunov theory is used to derive the stability criterion of the multi-area power system under denial of service attacks.

[0006] The paper [Yan S, Gu Z, Park J H. Memory-Event-Triggered H∞Load Frequency Control of Multi-Area Power Systems With Cyber-Attacks and Communication Delays[J]. IEEE Transactions on Network Science and Engineering, 2021, 8(2): 1571-1583] proposed an adaptive event-triggered communication scheme that can dynamically adjust the event trigger threshold to save more limited network communication resources while maintaining the expected control performance.

[0007] The literature [Peng C, Zhang J, Yan H. Adaptive Event-Triggering H∞Load Frequency Control for Network-Based Power Systems[J]. IEEE Transactions on Industrial Electronics, 2018, 65(2): 1685-1694] proposes a design method for load frequency H controller of multi-domain power systems under network attacks and communication delays.

[0008] The literature [Peng C, Sun H. Switching-Like Event-Triggered Control for Networked Control Systems Under Malicious Denial of Service Attacks[J]. IEEE Transactions on Automatic Control, 2020, 65(9): 3943-3949. Experimental comparative study in the following text] proposed a similar switching event communication control method using confirmation character technology based on the TCP / IP communication protocol. This method switches the event trigger threshold by determining whether there is packet loss caused by a denial of service attack to alleviate the impact of denial of service attacks on system stability.

[0009] The first three schemes recorded in the prior art all decide whether to trigger the measurement transmission action based on the degree of measurement signal change, which saves communication bandwidth resources while ensuring system stability. However, the thresholds used in these methods are fixed thresholds, which cannot meet the requirements of the system status in various scenarios, that is, the scenario adaptability of these methods is low. The threshold switching of the fourth scheme is based on the system status rather than the attack scenario. Therefore, when the system is subjected to a denial of service attack, this method cannot effectively resist the impact of the attack on the system. In the fifth scheme, the construction of the Lyapunov energy functional and the integral inequality scaling method are somewhat conservative, so the derived system stability criterion cannot obtain a relatively larger maximum allowable delay upper bound for the delay system. And this method is not effectively combined with the microgrid system. Summary of the invention

[0010] In order to solve the above problems existing in the prior art, the present invention provides a method for safely controlling the load frequency of a microgrid system triggered by a switching event. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0011] The present invention provides a method for safely controlling load frequency of a microgrid system triggered by a switching event, comprising:

[0012] Step 1, obtaining a microgrid system model designed according to the actual structure of the microgrid system, and constructing a new microgrid system model by adding an energy storage device and a denial of service attack to the microgrid system model;

[0013] Step 2: According to the DoS attack link in the novel microgrid system model, the time interval is divided into an attack interval and a non-attack interval, and a corresponding switching event triggering strategy is designed according to the different divided intervals;

[0014] Step 3, using the switching event triggering strategies corresponding to different intervals, converting the novel microgrid system model to construct a closed-loop microgrid system model;

[0015] Step 4, combining the switching event triggering strategy with the different divided intervals, constructing a Lyapunov-Krasovskii functional containing a time delay cubic polynomial;

[0016] Step 5, deriving the constructed Lyapunov-Krasovskii functional along the system trajectory, combining the cubic matrix polynomial positive / negative definiteness criterion with the integral high-order inequality scaling technology to obtain the stability criterion of the microgrid time-delay system;

[0017] Step 6: Determine the tolerance of the microgrid system to time delay using the stability criterion system, and perform time delay control on the microgrid system according to the tolerance.

[0018] Beneficial effects of the present invention:

[0019] The present invention proposes a method for safely controlling the load frequency of a microgrid system triggered by a switching event. The method constructs a microgrid load frequency control scheme under DoS attack scenarios and under no attack scenarios, respectively, and can save more bandwidth resources under the premise of system stability. For the algorithm model affected by delay, by constructing a high-order Lyapunov energy functional, obtaining derivatives and scaling, the microgrid system subjected to a denial of service attack is modeled as a delay system, and the time-varying delay stability criterion is applied thereto, and a smaller conservatism is ensured to obtain a delay-dependent convergence criterion that takes into account both conservatism and complexity, and the tolerance of the algorithm to delay can be judged in turn. Finally, it is proved through experiments that the controller design method proposed by the present invention can ensure the asymptotic stability of the system when a DoS attack occurs.

[0020] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is a flow chart of a method for safely controlling load frequency of a microgrid system triggered by a switching event provided by the present invention;

[0022] Figure 2a It is a microgrid load frequency control structure diagram under DoS attack provided by the present invention;

[0023] Figure 2b It is a switching event triggering timing diagram under a denial of service attack provided by the present invention;

[0024] Figure 3 It is a schematic diagram of a switching event triggering strategy under a DoS attack provided by the present invention;

[0025] Figure 4 It is a state corresponding curve and a schematic diagram of a simple event-triggered communication release time of scenario 1 provided by the present invention;

[0026] Figure 5 It is a state corresponding curve of scenario 2 provided by the present invention and a schematic diagram of a simple event-triggered communication release time (system instability);

[0027] Figure 6 It is a schematic diagram of the state corresponding curve and elastic event triggered communication release time of scenario 3 provided by the present invention;

[0028] Figure 7 It is a state corresponding curve and a schematic diagram of the adaptive event-triggered communication release time of scenario 4 provided by the present invention;

[0029] Figure 8 It is a schematic diagram of the state corresponding curve of scenario 5 provided by the present invention and the communication release time triggered by the switching event. DETAILED DESCRIPTION

[0030] 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.

[0031] The solution of the present invention is applied to the central controller of a microgrid. Since the control parameters of the local controller of the microgrid and the central controller are mutually coupled, the control solution of the central controller can be directly applied to the central controller.

[0032] like Figure 1 As shown, the present invention provides a method for safely controlling load frequency of a microgrid system triggered by a switching event, including:

[0033] Step 1, obtaining a microgrid system model designed according to the actual structure of the microgrid system, and constructing a new microgrid system model by adding an energy storage device and a denial of service attack to the microgrid system model;

[0034] Step 2: According to the DoS attack link in the novel microgrid system model, the time interval is divided into an attack interval and a non-attack interval, and a corresponding switching event triggering strategy is designed according to the different divided intervals;

[0035] Step 3, using the switching event triggering strategies corresponding to different intervals, converting the novel microgrid system model to construct a closed-loop microgrid system model;

[0036] Step 4, combining the switching event triggering strategy with the different divided intervals, constructing a Lyapunov-Krasovskii functional containing a time delay cubic polynomial;

[0037] Step 5, deriving the constructed Lyapunov-Krasovskii functional along the system trajectory, combining the cubic matrix polynomial positive / negative definiteness criterion with the integral high-order inequality scaling technology to obtain the stability criterion of the microgrid time-delay system;

[0038] Step 6: Determine the tolerance of the microgrid system to time delay using the stability criterion system, and perform time delay control on the microgrid system according to the tolerance.

[0039] refer to Figure 2a As shown, Figure 2a The schematic diagram of the system structure of the microgrid system with energy storage device is shown in Figure 2. The new microgrid system model is expressed as follows:

[0040]

[0041] Figure 2a The physical description of each symbol is as follows:

[0042] Table 1 Symbols and their physical meanings in microgrid system

[0043]

[0044]

[0045] In the table, an element in a vector is represented by a lowercase letter with a subscript.

[0046] F is the system matrix, To include k ic , k pc The system array, the system delay satisfies 0≤d1≤d(t)≤d2, Among them, d1, d2, μ1, and μ2 are constants. represents the derivative of the load disturbance.

[0047] Since external disturbances cannot affect the internal stability of the system, the disturbance term can be ignored in the stability analysis of the time-delay microgrid cyber-physical system. In formula (1), t represents the system operation time, is the system state vector of the transmission. The specific elements contained in the vector can be expressed as follows: x(t) = [R ic ∫ΔfdtΔP mt ΔP fc ΔP ss ΔP es Δf] T , and represents the system matrix, φ(t) represents the initial state of the system, ΔP l ′=ΔP l -ΔPpv -ΔP w , where ΔP l is the user load, ΔP pv The electrical energy provided by photovoltaic power generation, ΔP w The electric energy provided by the wind turbine; other matrices are expressed as:

[0048]

[0049] a 21 =0,

[0050]

[0051]

[0052]

[0053]

[0054] ΔP l =ΔP ld -ΔP pv -P w , (2)

[0055] K ic ∫Δfdt′=R ic Δf, (3)

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] ΔP l ′=[ΔP ΔP′] T , (8)

[0062] The model considered in the present invention uses a hierarchical control structure including a microgrid central controller and a microgrid local controller in order to achieve the control target of dynamically stabilizing the desired frequency of the microgrid system.

[0063] The effective attack interval is divided according to whether there is a denial of service attack:

[0064] Step 21, according to the DoS attack link in the novel microgrid system model, the time interval of the successful transmission sequence is divided into a D interval with attack and an S interval without attack;

[0065] Assuming that the sampling period of the sensor based on periodic triggering is h, the sensor sampling sequence can be described as However, in actual working conditions, not all sampling data packets need to be transmitted to the remote controller, so an event-triggered communication strategy is introduced:

[0066] s k+1 =s k +inf{ιh|e T (s k +ιh)Φe(s k +ιh)≥ε * e T (s k )Φe(s k )}, (9)

[0067] In the formula, s k Indicates the current sampling packet transmission time, s k+1 represents the next transmission time, h is the system sampling period, ι is a positive scalar, ιh represents the total duration of ι sampling periods, e(s k + ιh) = x(s) k +ιh)-x(s k ), indicating the current time (s k +ιh) system state state x(s k +ιh) and the most recent Second transmission time s k System state x(s k ), ε * and Φ are the event triggering thresholds to be designed and the constant matrices of appropriate dimensions;

[0068] In order to construct the event triggering strategy under DoS attack, the successful transmission sequence is divided into the following categories. According to the DoS attack situation, it can be classified into two types of intervals, such as Figure 2b In the left figure, t k and t k+1 If the transmission is triggered at two moments, then we can know that at [t k ,t k+1 ) between which no DoS attack occurs, it is determined to be interval S, and the threshold parameter for triggering the switching event in this interval is ε1; accordingly, Figure 2b In the right figure of k+1 A DoS attack occurs at time t, causing the transmission data triggered at this point to fail to be transmitted. Therefore, the transmission flag bit at this point is 0.k ,t k+1 ) is the D interval, and from t′ k+1 From the moment, the event trigger threshold parameter is switched to ε2.

[0069] In summary, in each successful transmission interval, it can be classified into two types of intervals according to the DoS attack situation:

[0070] S interval: In the time interval [t k ,t k+1 ) No DoS attack occurred;

[0071] D interval: In the time interval [t k ,t k+1 ) a DoS attack occurs within;

[0072] Among them, take represents the data packets t0, t1, ..., t that trigger the event triggering strategy and are successfully transmitted in the interval [0, t) k ,t k+1 ,... represents the moment of each successful trigger. It can be seen that the event trigger strategy can greatly reduce the amount of data sent to save bandwidth resources. ACK is a confirmation flag character in the communication protocol to confirm whether the information has been received.

[0073] Step 22, introduce the time-triggered communication strategy, and design the trigger threshold parameters of the D-interval and S-interval switching event trigger strategies respectively;

[0074] Step 23: construct an event triggering strategy according to the event triggering strategy triggering threshold parameter and the time triggered communication strategy.

[0075] exist Figure 3 According to the different ACKs, the threshold parameters can be switched from and to meet the data transmission requirements of the system at different stages. The above switching event triggering strategy can be constructed in the following form:

[0076]

[0077] In the formula, i k h=t k +ιh,ι=1,2,...,n.,i kh is the most recent sampling time, ε1 and ε2 are the trigger threshold parameters of the switching event trigger strategy, and Φ is a positive definite matrix of appropriate dimension to be designed; at a certain moment, the event trigger condition is met, and the confirmation character is 1, indicating that there is no DoS attack at this time and data can be sent successfully, then the trigger threshold parameter of the event trigger strategy in this interval is ε1; on the contrary, when the confirmation character is 0, the trigger threshold parameter is ε2 accordingly. It is worth noting that if the ACK data packet between the controller and the sensor is also lost due to the DoS attack, then in this case ACK is 0, and the event trigger parameter in the event trigger strategy selects ε2.

[0078] In a specific embodiment, step 3 includes:

[0079] To complete further analysis: define η(t) = ti k h, the time-varying delay η(t) is a A piecewise function of is the upper bound of the communication delay and does not necessarily have to satisfy the constraint

[0080] Combining the new microgrid system model and the switching event triggering strategy in different intervals, a closed-loop microgrid system model is constructed:

[0081]

[0082] Among them, the initial state of the system state x(t) is φ(t0) = x(t0), t0 is the initial time, φ(t) is the time in the interval A continuous function of μ1 and μ2 are three constants.

[0083] In a specific embodiment, step 4 includes:

[0084] Combining the switching event triggering strategy with the different divided intervals, a Lyapunov-Krasovskii functional containing a cubic polynomial of time delay is constructed:

[0085]

[0086] in:

[0087]

[0088]

[0089]

[0090]

[0091] In the formula, is the Lyapunov-Krasovskii subfunctional, which is related to time t and system state x t Related, Q1>0, Q2>0, R1>0, R2>0, Z1>0, Z2>0, and Q1, Q2, R1, R2, Z1, Z2 are the weight variables to be determined in each delay interval respectively, and the delay polynomial model P(η(t))=η 3 (t)P3+η 2 (t)P2+η(t)P1+P0, η(t) is the system delay and is the upper bound of the delay, P3, P2, P1, P0 are the delay coefficient matrices of each order, and φ1(t), φ2(s, t), φ3(s, t) are column vectors related to the system state, ξ(t) is the system augmented vector; and the detailed definitions are as follows:

[0092]

[0093]

[0094]

[0095]

[0096] Where υ1(t) and υ2(t) are integral operators, defined as follows:

[0097]

[0098]

[0099] The two integral terms in It contains more integrals of the system energy over each time interval, that is, the functional contains more information about the system state, which can effectively reduce the conservatism of the system. The attack characteristics of DoS attacks are included and the characteristics of various parameters of the switching event triggering strategy are considered.

[0100] In a specific embodiment, step 5 includes:

[0101] Along the system trajectory Taking the derivative, we can get the following result:

[0102]

[0103] in:

[0104]

[0105]

[0106]

[0107] exist Integral term as well as φ1(t), φ2(t,t), φ3(t-η(t),t), φ2(s,t), φ3(s,t) are system state column vectors, s, t are independent variables, and t represents time. is the transpose of the system state column vector φ1(t), φ2(t,t), φ3(t-η(t),t), is the time derivative of the time-varying delay η(t), is the time derivative of the system state, is the time derivative of the system state with independent variable s, x(t-η(t)) represents the system state under the time-varying delay η(t), represents the derivative of the system state under the time-varying delay η(t), It represents the partial derivative of vector φ2(s,t) with respect to time t, Represents the partial derivative of vector φ3(s,t) with respect to time t.

[0108] In a specific embodiment, the LKF delay term of the cubic delay polynomial in step 5 is expressed as:

[0109]

[0110] Where K n (s) represents a 2n-degree polynomial with respect to s, θ i (i=0,1,...,2n) is the corresponding s i The coefficients of the order, for the matrix-valued polynomial K in formula (14) n (s) where n≥1 is an integer, θ j , (j=0,1,2,…,2n) is a q×q dimensional symmetric matrix; if θ 2n =0, then

[0111] K n (s)=s 2n-1 θ 2n-1 +s 2n-2 θ 2n-2 +…+θ0,

[0112] For n = 1, when θ2 = 0, K1(s) is is a convex function. When θ2≠0, K1(s) is It is not necessarily a convex function;

[0113] In order to derive the necessary and sufficient conditions for K1(s) to be strictly less than 0 when θ2≠0, we first introduce the following method. The steps are as follows:

[0114] i) For If and only if there exists a matrix and the skew-symmetric matrix So that the following is true:

[0115]

[0116] ii) For K n (s)>0, If and only if there exists a matrix and the skew-symmetric matrix So that the following is true:

[0117]

[0118] In the formula, is a known constant matrix, Ω n It is composed of various order coefficients, each defined as follows:

[0119]

[0120]

[0121]

[0122] The step 6 is to integrate the functional derivative results of step 5, and finally form a result about the delay quartic polynomial, so as to derive the delay stability criterion of the microgrid system.

[0123] In a specific embodiment, step 6 includes:

[0124] For given constants μ1, μ2 and If there is Q i >0,Z i >0,T1,T2,T3,T4,Y1,Y2,Y3, The real symmetric matrix P0, P1, P2, P3 makes the following inequality hold, and the microgrid system is asymptotically stable:

[0125]

[0126]

[0127]

[0128] Where α is given by and η(t), κ i1 , κi1 (i=1,2) is the decision variable, and combined with the following formula, two trigger thresholds can be obtained:

[0129]

[0130]

[0131] Where M is the maximum number of consecutive packet losses induced by a DoS attack:

[0132]

[0133]

[0134] Where:

[0135]

[0136]

[0137]

[0138]

[0139]

[0140] Among them, C ij (i=1,2,3,4,5,6.j=1,2,3) is the augmented vector, Denotes the augmented vector C ij The transpose of D ij (i=1,2,3,4,5,6.j=1,2,3,4) are the augmented vectors corresponding to Q1 and Q2, C0=Ae1+BKe2, e i =[0 n×(i-1)n I n×n 0 n×(15-i)n ], (i=1,2,3,...,15) is a constant matrix, 0 n×(i-1)n represents an n×(i-1)n-dimensional zero matrix, I n×n represents an n×n dimensional 1 matrix, col{e1,e2,e3,e4,e5,e6,e7,e8,e9} is a 15×15 matrix e6 = col{e 6,1 ,e 6,2 ,e 6,3 ,e 6,4},e7=col{e 7,1 ,e 7,2 ,e 7,3 ,e 7,4},e 6,1 =e7,e 6,2 =e8,e 6,3=e9,e 6,4 =e 10 e 7,1 =e 11 ,e 7,2 =e 12 ,e 7,3 =e 13 ,e 7,4 =e 14 , C j =C j0 +η(t)C j1 +η 2 (t)C j2 (i=1,2,...,6), the other vectors are defined as follows:

[0141]

[0142]

[0143]

[0144]

[0145]

[0146]

[0147] C 31 =col{C0,e1,e1,e 40},C 32 =col{e 30 ,e 61 ,e 30},

[0148]

[0149]

[0150] C 51 =col{e4,e2,e1,e 40},C 52 =col{e 40 ,e 61 ,e 20},

[0151]

[0152]

[0153] C7=col{e1,e2,e6}, C8=col{e2,e3,e7},

[0154]

[0155]

[0156]

[0157]

[0158] D 10 =col{e1-e2,e 60},D 11 =col{0,e 61 ,e1,e 40},

[0159]

[0160]

[0161] D 23 =col{e 30 ,σ3,-σ2,e 20},D 24 =col{e 50 ,σ5,σ4},

[0162]

[0163]

[0164]

[0165]

[0166]

[0167]

[0168]

[0169]

[0170]

[0171]

[0172]

[0173]

[0174]

[0175] ρ0=e 71 -e3.

[0176]

[0177]

[0178]

[0179]

[0180]

[0181]

[0182]

[0183]

[0184] According to if there is Q i >0,Z i >0,T1,T2,T3,T4,Y1,Y2,Y3, Determine the tolerance of the microgrid system to time delay;

[0185] The tolerance of the microgrid system to delay is determined by controlling the delay of the closed-loop microgrid system by controlling the number of transmitted data packets within the allowed range of delay.

[0186] The tolerance of the system to delay can be judged according to the above conditions. Within the allowed range of delay, the above safety control method can ensure convergence. Under the premise of ensuring the stability of the system, the stability criterion proposed by the present invention has lower conservatism and can obtain a larger maximum allowable experimental upper bound. At the same time, by using the event triggering scheme, relatively fewer data packets can be transmitted, saving more bandwidth resources.

[0187] This application belongs to the field of networked control systems, and specifically relates to a load frequency control safety control method for microgrids based on switching event triggering under denial of service attacks, including: designing a new microgrid system model, constructing a high-order Lyapunov-Krasovskii functional for time delay, constructing a microgrid system switching event triggering strategy, and designing a time delay system stability criterion based on a high-order matrix value positive / negative definite judgment criterion and a high-order integral inequality scaling method to ensure that the system saves more bandwidth resources and has greater tolerance to delays while ensuring stability. The specific innovations are as follows:

[0188] (1) A switching event trigger control strategy with denial of service attack awareness is designed. The strategy can switch the trigger threshold parameters to save communication resources. Compared with existing studies, the designed event trigger strategy effectively reduces the impact of data transmission packet loss caused by denial of service attacks by selecting more suitable trigger thresholds at different stages.

[0189] (2) This design models the microgrid system that is subject to a denial of service attack as a time-delay system, applies the time-varying delay stability criterion to it, and ensures a smaller conservatism. Since the control parameters of the microgrid local controller and the central controller are mutually coupled, this design determines the local controller and proposes a design method for the central controller.

[0190] (3) The present invention uses numerical examples and examples of microgrid systems under denial of service attacks to verify the effectiveness of the proposed switching event triggering strategy, and simulates the simple event triggering strategy, the elastic event triggering strategy and the adaptive event triggering strategy. The event release interval and the data packet transmission volume of the trigger control method of the present invention are compared with those of the existing method.

[0191] The effect of the present invention is explained below in conjunction with actual simulation data.

[0192] Example 1:

[0193] To verify the superiority of the new delay stability criterion designed based on the Lyapunov energy functional under the denial of service attack scenario compared with the existing research, it is first necessary to verify it using numerical examples and obtain the corresponding maximum allowable delay upper bound. The system model takes the following form:

[0194]

[0195] In this scenario, given μ = -μ1 = μ2∈{0.1, 0.3, 0.5, 0.7, 0.8}, compared with the simulation results of existing methods, the upper bound of the maximum allowable delay can be obtained. It can be organized into Table 2:

[0196] Table 2 Comparison of upper bounds of maximum allowable delay (μ=-μ1=μ2)

[0197]

[0198] It is not difficult to see from the above table that the Lyapunov energy function and high-order integral inequality scaling method designed in this chapter are more accurate in describing each delay interval, so the resulting delay stability criterion is less conservative, and therefore a larger maximum allowable delay upper bound h can be obtained in the numerical example simulation.

[0199] Example 2

[0200] The present invention verifies the effectiveness of the proposed switching event triggering strategy by taking an example of a microgrid system that suffers from a DoS attack, and compares it with the simple event triggering strategy, the elastic event triggering strategy, and the adaptive event triggering strategy. The dynamic model of the microgrid system is:

[0201]

[0202] According to existing research, the parameters of the microgrid cyber-physical system can be defined as: M = 10, D = 1, R es =1,T es =1,R fc =1,T fc =4,R mt =0.04,R pl =1,R il =1,R ss =1,T ss =1. Set γ = 200, sampling period h = 0.02s, and simulation time is 300s. Specifically set the following five scenarios, and set the same DoS attack for scenarios 2 to 5, and compare the control effects of these schemes and the triggering status of communication transmission strategies.

[0203] Scenario 1: No DoS attack and no event-triggered communication strategy

[0204] This scenario simulates the control effect of a simple event-triggered control strategy without a DoS attack. According to step 3), the control and communication parameters based on the event-triggered strategy corresponding to ε1 = 0.2 can be calculated. By solving the linear matrix inequality, the corresponding feedback control gain matrix can be obtained as follows:

[0205] K1=[2.8351 0.1545] T

[0206] The system response curve and the action time of the simple event trigger mechanism are plotted on Figure 4 middle.

[0207] Scenario 2: DoS attack occurs and a simple event trigger policy is used:

[0208] This scenario simulates the control effect and trigger communication effect of the simple event trigger control mechanism when the system suffers from DoS attack and generates communication delay. Assuming that the maximum allowed number of continuous packet loss caused by DoS attack is M = 2, ε1 = 0.2 is obtained. The simulation results show that the microgrid system cannot guarantee stability under the control method of elastic event trigger strategy. The state response curve and the simple event trigger action time are plotted on Figure 5 middle.

[0209] Scenario 3: DoS attack occurs and elastic events are used to trigger policies:

[0210] This scenario simulates the control effect of the elastic event triggering strategy proposed by the prior art on the microgrid system under DoS attack. Taking the maximum number of consecutive packet losses caused by DoS attack M = 2, we can get ε2 = 0.00036. By solving the linear matrix inequality, the controller gain is as follows:

[0211] K2=[4.8196 0.2636] T

[0212] The system response curve and the action time of the elastic event triggering strategy are plotted on Figure 6 middle.

[0213] Scenario 4: DoS attack occurs and adaptive event triggering policy is used:

[0214] This scenario simulates the control effect of the adaptive event triggering strategy proposed by the prior art on the microgrid system under DoS attack. Take the maximum number of consecutive packet losses caused by DoS attack as M = 2, σ m =0.01,γ=15, by solving the linear matrix inequality, the controller gain can be obtained as follows:

[0215] K3=[3.2721 0.3948] T

[0216] The system response curve and the action moment of the adaptive event triggering strategy are plotted on Figure 7 middle.

[0217] Scenario 5: A DoS attack occurs and a switching event is used to trigger the policy:

[0218] This scenario simulates the main conclusion of this chapter, that is, the control effect of the switching event-triggered control strategy based on the ACK confirmation mechanism on the microgrid system under DoS attack. This method can save limited communication resources to a greater extent while maintaining the expected control performance. Set the same DoS attack length and attack frequency as the above scenario and M=2. When a DoS attack occurs, ACK=1, and take ε=ε1=0.2; when no DoS attack occurs, ACK=0, and according to step 3), ε=ε2=0.00036 is obtained. The control gain can be obtained by solving the linear matrix inequality:

[0219] K4=[6.3851 0.2717] T

[0220] The system response curve and the release time and interval of the adaptive event trigger strategy are plotted on Figure 8 middle.

[0221] The event triggering strategy parameters, data packet transmission quantity and microgrid system stability in the above scenario simulation can be summarized in Table 3:

[0222] Table 3 Event trigger parameters and system stability under each trigger control strategy

[0223]

[0224] By comparison, it can be seen that under the premise of ensuring the stability of the microgrid system, the number of data packet transmissions triggered by using different types of event triggering strategies is summarized in the above table as follows:

[0225] Simple event triggering strategies cannot effectively resist DoS attacks, that is, if a DoS attack occurs in a microgrid system, such triggering control strategies cannot guarantee the stability of the system.

[0226] The elastic event triggering strategy can ensure system stability to a certain extent, but at the cost of transmitting more measurement data, so it cannot save bandwidth resources very well.

[0227] Compared with the elastic event triggering strategy and the adaptive event triggering strategy, the switching event triggering control strategy saves more communication resources while ensuring system stability.

[0228] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0229] Although the present application is described herein in conjunction with various embodiments, in the process of implementing the claimed application, those skilled in the art may understand and implement other variations of the disclosed embodiments by reviewing the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality of components or steps.

[0230] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A method for safely controlling load frequency of a microgrid system triggered by a switching event, characterized in that: include: Step 1, obtaining a microgrid system model designed according to the actual structure of the microgrid system, and constructing a new microgrid system model by adding an energy storage device and a denial of service attack to the microgrid system model; Step 2: According to the DoS attack link in the novel microgrid system model, the time interval is divided into an attack interval and a non-attack interval, and a corresponding switching event triggering strategy is designed according to the different divided intervals; Step 3, using the switching event triggering strategies corresponding to different intervals, converting the novel microgrid system model to construct a closed-loop microgrid system model; Step 4, combining the switching event triggering strategy with the different divided intervals, constructing a Lyapunov-Krasovskii functional containing a time delay cubic polynomial; Step 5, deriving the constructed Lyapunov-Krasovskii functional along the system trajectory, combining the cubic matrix polynomial positive / negative definiteness criterion with the integral high-order inequality scaling technology to obtain the stability criterion of the microgrid time-delay system; Step 6, determining the tolerance of the microgrid system to time delay for the stability criterion system, and performing time delay control on the microgrid system according to the tolerance; Combining the switching event triggering strategy with the different divided intervals, a Lyapunov-Krasovskii functional containing a cubic polynomial of time delay is constructed: in: In the formula, is the Lyapunov-Krasovskii subfunctional, which is related to time t and system state x t Related, Q1>0, Q2>0, R1>0, R2>0, Z1>0, Z2>0, and Q1, Q2, R1, R2, Z1, Z2 are the weight variables to be determined in each delay interval respectively, and the delay polynomial model P(η(t))=η 3 (t)P3+η 2 (t)P2+η(t)P1+P0, η(t) is the system delay and is the upper bound of the delay, P3, P2, P1, P0 are the delay coefficient matrices of each order, and φ1(t), φ2(s, t), φ3(s, t) are column vectors related to the system state, ξ(t) is the system augmented vector, i k h=t k +ιh,ι=1,2,...,n.,i k h is the most recent sampling time, s and t are both independent variables, and t represents time. is the time derivative of the system state with independent variable s.

2. The method for safely controlling load frequency of a microgrid system triggered by a switching event according to claim 1, characterized in that: The new microgrid system model in step 1 is expressed as: in F is the system matrix, To include k ic , k pc The system array, the system delay satisfies 0≤d1≤d(t)≤d2, Where d1, d2, μ1, μ2 are constants, ΔP l ′ represents the derivative of load disturbance, t represents the system operation time, is the system state vector of the transmission. The specific elements contained in the vector are expressed as follows: x(t) = [R ic ∫ΔfdtΔP mt ΔP fc ΔP ss ΔP es Δf] T , and represents the system matrix, φ(t) represents the initial state of the system, ΔP l ′=ΔP l -ΔP pv -ΔP w , where ΔP l is the user load, ΔP pv The electrical energy provided by photovoltaic power generation, ΔP w The electric energy provided by the wind turbine; other matrices are expressed as: ΔP l =ΔP ld -ΔP pv -P w , (2) K ic ∫Δfdt′=R ic Δf, (3) Δf is the system or frequency deviation, ΔP es Indicates the power output of the electrolyzer system, ΔP fc represents the fuel cell power output, ΔP mt Indicates the output power change, ΔP l represents load disturbance, M represents generator moment of inertia, D represents generator damping constant, R es represents the electrolyzer system gain, T es Represents the electrolytic cell system time constant, R ss represents the energy storage device gain, T ss Represents the time constant of the energy storage device, R fc represents the fuel cell gain, T fc represents the fuel cell time constant, R mt represents the descent characteristics of the microturbine, K pl represents the microgrid local controller proportional coefficient vector, K il represents the microgrid local controller integral coefficient vector, K pc represents the proportional coefficient vector of the microgrid central controller, K ic Represents the integral coefficient vector of the microgrid central controller; an element in the vector is represented by a lowercase letter with a subscript.

3. The method for safely controlling load frequency of a microgrid system triggered by a switching event according to claim 2, characterized in that: Step 2 includes: Step 21, according to the DoS attack link in the novel microgrid system model, the time interval of the successful transmission sequence is divided into a D interval with attack and an S interval without attack; Step 22, introduce the time-triggered communication strategy, and design the trigger threshold parameters of the D-interval and S-interval switching event trigger strategies respectively; Step 23: construct an event triggering strategy according to the event triggering strategy triggering threshold parameter and the time triggered communication strategy.

4. The method for safely controlling load frequency of a microgrid system triggered by a switching event according to claim 3, characterized in that: Step 21 includes: The sampling period of the sensor based on periodic triggering is h, and the sensor sampling sequence is described as Not all sampling data packets need to be transmitted to the remote controller, so an event-triggered communication strategy is introduced: s k+1 =s k +inf{ιh|e T (s k +ιh)Φe(s k +ιh)≥ε * e T (s k )Φe(s k )}, (9) In the formula, s k Indicates the current sampling packet transmission time, s k+1 represents the next transmission time, h is the system sampling period, ι is a positive scalar, ιh represents the total duration of ι sampling periods, e(s k + ιh) = x(s) k +ιh)-x(s k ), indicating the current time (s k +ιh) system state state x(s k +ιh) and the time of the most recent transmission s k System state x(s k ), ε * and Φ are the event triggering thresholds to be designed and the constant matrices of appropriate dimensions; In each successful transmission sequence interval In the analysis, the DoS attack is classified into two categories according to the situation: S interval: In the time interval [t k ,t k+1 ) No DoS attack occurred; D interval: In the time interval [t k ,t k+1 ) a DoS attack occurs within; Among them, take represents the data packets t0, t1, ..., t that trigger the event triggering strategy and are successfully transmitted in the interval [0, t) k ,t k+1 ,...indicates the moment of each successful trigger.

5. The method for safely controlling load frequency of a microgrid system triggered by a switching event according to claim 4, characterized in that: The event triggering strategy in step 23 is expressed as: Where ε1 and ε2 are the trigger threshold parameters of the switching event trigger strategy, and Φ is a positive definite matrix of appropriate dimension to be designed; when the event trigger condition is met at a certain moment and the confirmation character is 1, it indicates that there is no DoS attack and data can be sent successfully, then the trigger threshold parameter of the event trigger strategy (11) in this interval is ε1; on the contrary, when the confirmation character is 0, the trigger threshold parameter is ε2 accordingly, and ACK is the confirmation flag character in the communication protocol to confirm whether the information is received.

6. The method for safely controlling load frequency of a microgrid system triggered by a switching event according to claim 5, characterized in that: Step 3 includes: Define η(t) = ti k h, the time-varying delay η(t) is a satisfying A piecewise function of is the upper bound of the communication delay and does not necessarily have to satisfy the constraint Combining the new microgrid system model and the switching event triggering strategy in different intervals, a closed-loop microgrid system model is constructed: Among them, the initial state of the system state x(t) is φ(t0) = x(t0), t0 is the initial time, φ(t) is the time in the interval A continuous function of μ1 and μ2 are three constants.

7. The method for safely controlling load frequency of a microgrid system triggered by a switching event according to claim 6, characterized in that: Step 5 includes: Along the system trajectory Taking the derivative, we can get the following result: in: exist Integral term as well as φ1(t), φ2(t,t), φ3(t-η(t),t), φ2(s,t), φ3(s,t) are the system state column vectors, is the transpose of the system state column vector φ1(t), φ2(t,t), φ3(t-η(t),t), is the time derivative of the time-varying delay η(t), is the time derivative of the system state, x(t-η(t)) represents the system state under the time-varying delay η(t), represents the derivative of the system state under the time-varying delay η(t), It represents the partial derivative of vector φ2(s,t) with respect to time t, Represents the partial derivative of vector φ3(s,t) with respect to time t.

8. The method for safely controlling load frequency of a microgrid system triggered by a switching event according to claim 7, characterized in that: The LKF delay term of the cubic delay polynomial in step 5 is expressed as: K n (s)=s 2n i 2n +s 2n-1 i 2n-1 +…+θ0, (14) Where K n (s) represents a 2n-degree polynomial with respect to s, θ i (i=0,1,...,2n) is the corresponding s i The coefficients of the order, for the matrix-valued polynomial K in formula (14) n (s) where n≥1 is an integer, θ j , (j=0,1,2,…,2n) is a q×q dimensional symmetric matrix; if θ 2n =0, then K n (s)=s 2n-1 i 2n-1 +s 2n-2 i 2n-2 +…+θ0, For n = 1, when θ2 = 0, K1(s) is a convex function in s∈[0,η], and when θ2≠0, K1(s) is a convex function in It is not necessarily a convex function; To derive the necessary and sufficient conditions for K1(s) to be strictly less than 0 when θ2≠0, the steps are as follows: i) For If and only if there exists a matrix and the skew-symmetric matrix So that the following is true: ii) For If and only if there exists a matrix and the skew-symmetric matrix So that the following is true: In the formula, is a known constant matrix, Ω n is composed of various order coefficients, each defined as follows:

9. The method for safely controlling load frequency of a microgrid system triggered by a switching event according to claim 8, characterized in that: Step 6 includes: For given constants μ1, μ2 and If there is Q i >0,Z i >0,T1,T2,T3,T4,Y1,Y2,Y3, The real symmetric matrix P0, P1, P2, P3 makes the following inequality hold, and the microgrid system is asymptotically stable: Where α is given by and η(t), κ i1 , κ i1 (i=1,2) is the decision variable, and combined with the following formula, two trigger thresholds can be obtained: Where M is the maximum number of consecutive packet losses induced by a DoS attack: According to if there is Q i >0,Z i >0,T1,T2,T3,T4,Y1,Y2,Y3, Determine the tolerance of the microgrid system to time delay; The tolerance of the microgrid system to delay is determined by controlling the delay of the closed-loop microgrid system by controlling the number of transmitted data packets within the allowed range of delay.

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