Event-triggered control method for power system load frequency considering denial-of-service attacks

Abstract

The present invention relates to a load frequency event-triggered control method for a power system considering denial-of-service attacks. The method includes the following steps: S1, constructing a first state-space equation of a load frequency control system corresponding to the power system; S2, an adaptive event-triggered control scheme for bidirectionally adjusting a triggering threshold following the system output performance; S3, based on the first state-space equation and the adaptive event-triggered control scheme, establishing a second state-space equation of a frequency control system corresponding to an interconnected power grid considering transmission delay; S4, determining a scenario switching process under a random DoS attack according to the second state-space equation; S5, establishing a design criterion for event-triggered control parameters and updating the event-triggered control parameters according to an event-triggered control parameter update criterion to control the load frequency. Compared with the prior art, the present invention has the advantages of flexibly adjusting the triggering threshold and ensuring system sensitivity, etc.

Description

Technical Field

[0001] The present invention relates to the technical field of load frequency control, and in particular to an event-triggered control method for power system load frequency considering denial-of-service attacks. Background Art

[0002] As one of the most important characteristic parameters of the power system, frequency has a huge impact on the stable operation of the power system. Load Frequency Control (LFC), as an important means to ensure frequency stability, plays a huge role. It balances the fluctuations of the power consumed at the load end by adjusting the active power output of the generator units in the power system, maintains the exchanged power between the regional tie lines at the planned value, ensures that the system frequency is stable at the set value, and enables the safe and stable operation of the power system. With the development of computer technology and communication technology, the traditional dedicated communication channels in the power system have gradually been replaced by open communication networks. The addition of open communication networks brings convenience to the monitoring and resource scheduling of the power system, but its high openness and interconnectivity pose certain security risks to the acquisition and transmission of power system data, and are vulnerable to the impact of network attacks, thus threatening the stable operation of the power system. Among them, the denial-of-service attack blocks the communication network by sending a large amount of junk information, causing difficulties in data transmission. It has the characteristics of low attack cost, significant attack effect, low attack difficulty, and diverse attack methods, and is the number one threat in current network attacks.

[0003] With the continuous increase in the scale and complexity of interconnected power grids, the control center relies on the communication network to monitor the operating status of generators and issue control commands. In order to avoid competition for limited communication resources among real-time applications such as load frequency control systems, automatic voltage control, and wide-area damping control. In recent years, researchers have proposed an Event-triggered control (ETC) scheme. The basic idea of the existing event-triggered control is to set an event-triggered detector (ETD) on the controlled object side, and only trigger the transmission of system states and control quantities when the event-triggered detector detects that the state deviation exceeds a preset threshold. In the existing event-triggered load frequency control system scheme, the trigger threshold adaptive update mechanism adopts an exponential growth scheme and does not limit the upper limit. When the state deviation is effectively damped, the rapid growth of the trigger threshold will cause the power control center to quickly lose the monitoring sensitivity to the operating status of the load frequency control system, resulting in too long a frequency deviation recovery time or continuous oscillation of the tie line power. Summary of the Invention

[0004] The object of the present invention is to provide a power system load frequency event triggering control method considering denial-of-service attacks, which overcomes the problem that the monitoring sensitivity of the operation state of the load frequency control system is reduced because the trigger threshold adaptive update mechanism adopts an exponential growth scheme and does not limit the upper limit.

[0005] The object of the present invention can be achieved by the following technical solutions:

[0006] A power system load frequency event triggering control method considering denial-of-service attacks, the method comprising the following steps:

[0007] S1. Construct the first state space equation of the load frequency control system corresponding to the power system;

[0008] S2. An adaptive event triggering control scheme for bidirectionally adjusting the trigger threshold following the system output performance, wherein the time period between two adjacent trigger moments of the control instruction of the adaptive event triggering control scheme satisfies the bounded adaptive trigger threshold of δ(t k h) = min{δ M , max{δ m , λδ(t k-1 h)}}, where is the bounded adaptive trigger threshold, δ m , δ M are respectively the upper and lower bounds of the bounded adaptive trigger threshold, t k h, t k+1 h are two adjacent trigger moments, and λ is a control parameter, and the control parameter is specifically:

[0009]

[0010] where y(t k h), y(t k-1 h) are respectively the output quantities of the load frequency control system at the trigger moments t k h, t k+1 h, and the difference Δy(t k h) of the output quantities is:

[0011]

[0012] S3. Based on the first state space equation and the adaptive event triggering control scheme, establish the second state space equation of the frequency control system corresponding to the interconnected power grid considering transmission delay;

[0013] S4. Determine the scenario switching process under random DoS attacks according to the second state space equation;

[0014] S5. Design criteria for event-triggered control parameters in the switching process under stochastic DoS attacks are established according to Lyapunov stability theory, and the event-triggered control parameters are updated in accordance with the event-triggered control parameter update criterion to control the load frequency.

[0015] Furthermore, the control instruction of the adaptive event-triggered control scheme is:

[0016] u(t) = Kx(t k h),

[0017] where u(t) is the control instruction, K is the controller gain when working normally without DoS attacks, h is the sampling period, t k h and t k+1 h are respectively the adjacent two triggering moments, are respectively the transmission delays of the adjacent two triggering moments, and the upper bound of the transmission delay is , x(t k h) is the state quantity of the load frequency control system at the triggering moment t k h.

[0018] Furthermore, for the event-triggered communication mechanism of the adaptive event-triggered control scheme, the relationship between the adjacent two triggering moments is:

[0019]

[0020] where the sampling moment i k h = t k h + lh, lh is the time period between the adjacent two triggering moments, δ(t k h) is the bounded adaptive triggering threshold, e(i k h) is the difference between the state quantity of the load frequency control system at the sampling moment i k h and the state quantity of the load frequency control system at the previous triggering moment t k h, Φ and Ξ are both performance weight matrices, and x(t k h) is the state quantity of the load frequency control system at the triggering moment t k h.

[0021] Furthermore, the second state space equation of S4 is:

[0022]

[0023] where, where, x n (t) is the state space of region n, x n (t) = [Δf n , ΔP tie_n , ΔPmn , ΔP vn , ∫ACE n T , Δf n , where Δf is the frequency deviation of area n, and ΔP mn is the mechanical power output of the generator within area n, ΔP vn is the governor valve opening, and ΔP tie_n is the tie-line power fluctuation within area n, and ACE n is the control error of area n, and ACE n = β n Δf n + ΔP tie_n , where β n is the frequency deviation factor of area n

[0024] A = [A nj N×N , where

[0025]

[0026] where D n and M n are the generator damping coefficient and moment of inertia within area n respectively, T tn and T gn are the steam turbine and governor time constants within area n respectively, R n is the droop coefficient, and L nj is the tie-line synchronizing coefficient between areas n and j

[0027] B = diag{B n}, where

[0028]

[0029] K is the controller gain for normal operation without DoS attacks

[0030] is the sampling time i k and h is the transmission delay, and i k is t k , t k + 1, …, t k+1 ,

[0031] w(t) = [ΔP d1 , ΔP d2 , …, ΔP dN T , where ΔP dn is the load fluctuation of area n

[0032] F is F = diag{F​​​n}, where

[0033]

[0034] M n is the moment of inertia of the generator in area n;

[0035] e(i k h) is the difference between the state quantity of the load frequency control system at the sampling time i k h and the state quantity of the load frequency control system at the previous trigger time t k h;

[0036] y(t) is the observed quantity, C = diag{C n}

[0037]

[0038] where β n is the frequency deviation factor of area n.

[0039] Furthermore, in S4, assume that [h n , h n+1 is a complete DoS attack signal, where t ∈ [h n , h n +l n ), the DoS signal is in the sleep interval and does not act on the system, and when t ∈ [h n +l n , h n+1 ), the DoS attack is in the active interval and acts on the system. The second state space equation determines the scenario switching process under random DoS attacks as follows:

[0040] During the normal operation stage without DoS attacks in the time period t ∈ [h n , h n +l n ), the second state space equation remains unchanged;

[0041] During the stage of suffering from DoS attacks in the time period t ∈ [h n +l n , h n+1 ), the controller cannot receive the signal uploaded by the event trigger, and the control instruction u(t) = 0 of the adaptive event-triggered control scheme. At this time, the second state space equation is updated as:

[0042]

[0043] Furthermore, the first state space equation is:

[0044]

[0045] where \(u(t)\) is the control command and \(S\) DoS (t) is the DoS attack signal.

[0046] Furthermore, the DoS attack signal is:[[]]END]]

[0047]

[0048] where \(H\) n = [h n , h n + l n ), \(L\) n = [h n + l n , h n+1 correspond to the sleep interval and the active interval of the DoS attack respectively.

[0049] Furthermore, the event-triggered control parameter update criterion is:[[]]END]]

[0050] Let the load frequency control system be switched \(k\) times due to DoS attacks during the operation period \([t\) 0 , t\) 1 , and the switching times are \(T\) 1 , \(T\) 2 , …, \(T\) k , and the average dwell time \(T\) d and the number of switches satisfy \(k\leq1+(t\) 1 - t\) 0 ) / T\) d ;

[0051] Meanwhile, given scalars \(\lambda\), \(\sigma\), \(\gamma\), \(\rho>0\), if there exists a DoS attack time ratio coefficient \(\alpha\in[0,1)\) and the appropriate-dimensional matrices \(K\), \(X\) and the symmetric positive definite matrices \(\Lambda\) that satisfy the event-triggered control parameter design criterion and the inequality,[[]]END]]

[0052] Furthermore, the inequality to be satisfied is:[[]]END]]

[0053]

[0054] where \(T\) d is the average dwell time, \(\lambda\), \(\sigma\) are given scalars,[[]]END]] is the minimum required average dwell time, \(\alpha\) is the DoS attack time ratio coefficient,[[]]END]] is the upper bound of the transmission delay.[[]]END]]

[0055] Furthermore, the design criterion for the event-triggered control parameter is:[[]]END]]

[0056] Given scalars \(\lambda\), \(\gamma\), \(\rho>0\), if there exists an appropriate-dimensional matrix that satisfies the linear matrix inequality,[[]]END]] and a symmetric positive definite matrix Λ, Then it meets the design criteria of the event-triggered control parameters.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] The present invention adopts a variable bounded adaptive triggering threshold. When the system output performance deteriorates, the triggering threshold δ decreases, and the system output performance is restored by increasing the triggering times; conversely, when the system output performance improves, the triggering threshold δ increases, and the triggering times are reduced to save communication resources. At this time, the triggering threshold adjustment scheme can complete two-way dynamic adaptive adjustment according to the system output performance, which can better balance system performance and save communication network resources. Compared with the existing adaptive update mechanism with no upper bound on the triggering threshold, the present invention ensures that after the frequency deviation of the interconnected power grid is effectively controlled, the control center still has a certain sensitivity to the monitoring of the operation state of the load frequency control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 is a flowchart of the present invention;

[0060] Figure 2 is a structural block diagram of the interconnected power system of the present invention;

[0061] Figure 3 is the data transmission situation and switching process when a DoS attack occurs in the present invention;

[0062] Figure 4 is a schematic diagram of the random DoS attack switching signal of the present invention;

[0063] Figure 5 is a schematic diagram of the frequency deviation of different control schemes of the present invention. Among them, (a) is the frequency deviation of this embodiment of the application example of the present invention; (b) is the frequency deviation when adopting a static event-triggered control scheme with a fixed triggering threshold; (c) is the frequency deviation when adopting an event-triggered control scheme with a unidirectional adaptive adjustment triggering threshold;

[0064] Figure 6 is a schematic diagram of the triggering moment and triggering interval of different control schemes of the present invention. Among them, (a) is the application example of the present invention; (b) is a static event-triggered control scheme with a fixed triggering threshold; (c) is an event-triggered control scheme with a unidirectional adaptive adjustment triggering threshold;

[0065] Figure 7Schematic diagram of the control performance corresponding to different event-triggered control schemes of the present invention. Among them, (a) is the corresponding maximum frequency deviation; (b) is the integral of the absolute error (IAE) of the corresponding area control error (ACE); (c) is the corresponding variance of ACE; (d) is the corresponding number of event triggers. Specific implementation mode

[0066] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and gives the detailed implementation mode and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0067] The present invention provides a load frequency event-triggered control method for a power system considering a denial-of-service attack to solve the problem of system instability caused by a DoS attack. The flowchart of the method is as Figure 1 shown.

[0068] The method includes the following steps:

[0069] Step S1: Construct the first state-space equation of the load frequency control system corresponding to the interconnected power system.

[0070] Among them, the structure block diagram of the interconnected power system is as Figure 2 shown.

[0071] The first state-space equation includes the active power output of new energy, the active output of energy storage devices, the power grid load demand, etc., specifically as follows:

[0072]

[0073] Among them, x n (t) is the state space of area n, x n (t) = [Δf n , ΔP tie_n , ΔP mn , ΔP vn , ∫ACE n T , Δf n is the frequency deviation of area n, ΔP mn is the mechanical power output of the generator in area n, and the generator is generally a synchronous generator, ΔP vn is the governor valve opening, ΔP tie_n is the power fluctuation of the tie line in area n, ACE n is the control error of area n, ACE n = β n Δf​n +ΔP tie_n ,β n is the frequency offset factor of region n;

[0074] u(t) = [u 1 (t), u 2 (t), …, u N (t)] T , where u n (t) is the control command of region n;

[0075] w(t) = [ΔP d1 , ΔP d2 , …, ΔP dN T , where ΔP dn is the load fluctuation of region n;

[0076] A = [A nj N×N , where

[0077]

[0078] D n and M n are the generator damping coefficient and moment of inertia in region n respectively, T tn and T gn are the steam turbine and governor time constants in region n respectively, R n is the droop coefficient, and L nj is the tie-line synchronization coefficient between regions n and j;

[0079] B = diag{B n}, where

[0080]

[0081] C = diag{C n}, where

[0082]

[0083] F = diag{F n}, where

[0084]

[0085] where H n = [h n , h n + l n ), L n = [h n + l n , h​​n+1 ) respectively correspond to the sleep interval and the active interval of the DoS attack.

[0086] Assume that the system switches k times within the time interval [t 1 , t 2 . According to the average dwell time technique, we have: k ≤ 1 + (t 1 - t 0 ) / T d , then the attack frequency:

[0087]

[0088] Total time under attack: T ↑ = α(t 2 - t 1 ), where α is the attack time proportion coefficient.

[0089] It should be understood that among the above physical quantities, β n , D n , M n , T tn , T gn , R n , L nl are intrinsic quantities, and Δf n , ΔP mn , ΔP vn , ACE n are acquisition quantities.

[0090] Step S2: Design an adaptive event-triggered control scheme that bidirectionally adjusts the trigger threshold for the output performance of a new type of following system.

[0091] Among them, the control instruction of the adaptive event-triggered control scheme includes:

[0092] u(t) = Kx(t k h),

[0093] where K is the controller gain when working normally without DoS attack, h is the sampling period, t k h and t k+1 h are respectively two adjacent trigger times, t k h, t k+1 h ∈ N, are respectively the transmission delays of two adjacent trigger times, and the upper bound of the transmission delay is x(t k h) is the state quantity of the load frequency control system at the trigger time t k h.

[0094] Among them, the event-triggered communication mechanism of the adaptive event-triggered control scheme includes:

[0095]

[0096] wherein, the sampling time is i k h = t k h + lh, where lh is the time period between two adjacent trigger times, and δ(t k h) is a bounded adaptive trigger threshold, and e(i k h) is the difference between the state quantity of the load frequency control system at the sampling time i k h and the state quantity of the load frequency control system at the previous trigger time t k h. Both Φ and Ξ are performance weight matrices, and Φ, Ξ > 0.

[0097] In the existing event-triggered load frequency control scheme with an adaptive trigger threshold adjusted according to control performance, the trigger threshold generally adopts a unidirectional exponential growth update method. When the system deviation starts to damp, the exponential increase of the trigger threshold will cause the power control center to quickly lose the monitoring sensitivity to the load frequency control system, resulting in a slow recovery of the frequency deviation. Therefore, the two-way bounded adaptive trigger threshold adjustment mechanism of the embodiments of the present invention includes:

[0098] δ(t k h) = min{δ M , max{δ m , λδ(t k-1 h)}};

[0099]

[0100] wherein,

[0101]

[0102] y(t k h) and y(t k-1 h) are the output quantities of the load frequency control system at the trigger times t k h and t k+1 h respectively, δ m ≤δ(t k h)≤δ M , δ m and δ M are the upper and lower bounds of the bounded adaptive trigger threshold respectively, 0≤δ m ≤δ M< 1. When the output performance of the system deteriorates, the trigger threshold δ decreases, and the output performance of the system is restored by increasing the trigger times; conversely, when the output performance of the system improves, the trigger threshold δ increases, and the trigger times are reduced to save communication resources. The trigger threshold adjustment scheme at this time can complete two-way dynamic adaptive adjustment according to the output performance of the system, and can better balance system performance and saving communication network resources.

[0103] Obviously, compared with the existing adaptive update mechanism with no upper bound on the trigger threshold, the embodiment of the present invention ensures that after the frequency deviation of the interconnected power grid is effectively controlled, the control center still has a certain sensitivity to the monitoring of the operating state of the load frequency control system.

[0104] Step S3: Based on the first state-space equation and the adaptive event-triggered control scheme, establish a second state-space equation of the frequency control system corresponding to the interconnected power grid considering transmission delay.

[0105] Specifically, considering the delay problem in the adjustment process of the event-triggered control parameters, when the load frequency control system operates in a scenario without DoS attacks, based on the class sampling interval subset description method, the dynamic characteristics of the closed-loop load frequency control system within any two event trigger intervals can be described by the second state-space equation, specifically including:

[0106]

[0107] where τ(t) = t - i k h, is the sampling time i k h of the transmission delay, i k = t k , t k + 1, …, t k+1 .

[0108] Step S4: Determine the scenario switching process under random DoS attacks according to the second state-space equation.

[0109] Since the event trigger and the controller are located on both sides of the network, the occurrence of DoS attacks will cause the controller to be unable to receive the signals uploaded by the event trigger, resulting in a decline in the system control performance. Assume that [h n , h n+1 is a complete DoS attack signal, where t ∈ [h n , h n + l n ) the DoS signal is in the sleep interval and does not act on the system, and when t ∈ [h n + l n , h n+1 ) the DoS attack is in the active interval and acts on the system. Based on this, asFigure 3 As shown in the figure, the update process of the second state-space equation of the system under random DoS attacks is as follows:

[0110] Step 1, the normal operating phase without DoS attacks in the time period t ∈ [h n , h n +l n ):

[0111] The system is not under DoS attacks, the parameters of the event trigger and the controller gain remain unchanged, and the event trigger threshold changes with the system output performance.

[0112] The second state-space equation of the frequency control system in this normal operating phase without DoS attacks includes:

[0113]

[0114] The event-triggered communication mechanism of the frequency control system in this normal operating phase without DoS attacks includes:

[0115]

[0116] δ(t k h) = min{δ M , max{δ m , λδ(t k-1 h)}}

[0117]

[0118] Step2, the phase of being under DoS attacks in the time period t ∈ [h n +l n , h n+1 ):

[0119] t = h n +l n After the system is under DoS attacks at time t = h + l, the controller cannot receive the signal uploaded by the event trigger, and at this time u(t) = 0.

[0120] The second state-space equation of the frequency control system in this phase of being under DoS attacks includes:

[0121]

[0122] The event-triggered communication mechanism of the adaptive event-triggered control scheme in this phase of being under DoS attacks includes:

[0123]

[0124] Step S5: Establish the design criterion for the event-triggered control parameters of the scenario switching process under random DoS attacks according to the Lyapunov stability theory, and update the event-triggered control parameters according to the event-triggered control parameter update criterion to control the load frequency.

[0125] Among them, the event-triggered control parameter is the event-triggered threshold of the adaptive event-triggered control scheme.

[0126] Specifically, the design criterion for the event-triggered control parameters includes:

[0127] Given scalars λ, γ, ρ > 0, if there exist appropriate-dimensional matrices that satisfy the linear matrix inequality and symmetric positive definite matrices Λ, then the load frequency control system is output stable when suffering from DoS attacks;

[0128] The control gain and the positive definite matrix satisfy: K = YΛ -1 、

[0129] Among them, the linear matrix inequality includes:

[0130]

[0131] And,

[0132]

[0133] Among them,

[0134]

[0135] It should be understood that I is the identity matrix, and the asterisk "*" indicates that the matrix at this position is the transpose of the matrix symmetric to the matrix on the diagonal at this position.

[0136] Through the above design criterion for the event-triggered control parameters, the frequency stability of the interconnected power system under switching and random power fluctuations during DoS attacks can be guaranteed.

[0137] Specifically, considering that the DoS attack causes the system output performance to decline, the event-triggered control parameter update criterion for the scenario switching process under random DoS attacks determined according to the dwell time technique includes:

[0138] Let the load frequency control system suffer from DoS attacks and switch k times during the operation period [t 0 , t 1 , and the switching times are T 1 , T 2 , …, T k, the average dwell time T d The number of switches satisfies k ≤ 1 + (t 1 -t 0 ) / T d ;

[0139] Given scalars λ, σ, γ, ρ > 0, if there exists a DoS attack time proportion coefficient α ∈ [0, 1), and the appropriate-dimensional matrices K, X and symmetric positive definite matrices Λ that satisfy the event-triggered control parameter design criterion and the inequality Then the load frequency control system satisfies convergence and stability under random DoS attacks;

[0140] Among them, the inequality includes:

[0141]

[0142] Among them, is the minimum required average dwell time.

[0143] Through the above method, the switched system under DoS attacks can achieve convergent and stable operation.

[0144] In addition, the present invention also discloses a computer-readable storage medium, on which computer program instructions are stored; when the computer program instructions are executed by a processor, the method for event-triggered switched load frequency control under DoS attacks as described in the above embodiments is implemented.

[0145] In addition, the present invention also discloses an event-triggered switched load frequency control system under DoS attacks, including: the computer-readable storage medium as described in the above embodiments.

[0146] The technical solution of the embodiments of the present invention will be further described below with a specific application example.

[0147] In order to verify the feasibility of the method for event-triggered switched load frequency control of interconnected power systems under random DoS attacks proposed by the present invention, the application example of the present invention tests a two-area interconnected power grid load frequency control system as shown in Table 1. The comparison methods are selected as: 1) an event-triggered control scheme with a fixed trigger threshold; 2) an event-triggered control scheme with a unidirectional adaptive adjustment trigger threshold;

[0148] Table 1 Parameter values of the frequency control system of the interconnected power system

[0149]

[0150]

[0151] Figure 4Shows the random DoS attack handover signal. Figure 5 Shows the frequency deviation of different control schemes. Figure 6 Shows the trigger time and trigger interval of different control schemes. Figure 7 Shows the control performance corresponding to different event-triggered control schemes.

[0152] According to Figure 7 In (a)-(d) above, compared with the unidirectional adaptive threshold adjustment control scheme and the static trigger threshold control scheme, for the scheme involved in the embodiments of the present invention, although the maximum value of the frequency deviation under the scheme of the embodiments of the present invention has increased by 0.15% and 0.19%; the integral of the absolute error IAE of the area control error ACE under the scheme of the embodiments of the present invention has increased by 0.53% and 0.9%, and the variance of ACE under the scheme of the embodiments of the present invention has increased by 0.1% and 0.16%; however, the number of triggers has decreased significantly by 2.8% and 43.1%. It can be seen that compared with other event-triggered control schemes, the scheme of the embodiments of the present invention has a bounded adaptive update mechanism for the trigger threshold. Although the control performance has decreased slightly, the change is very small, and the number of triggers has decreased significantly, which is conducive to saving communication resources and ensuring the monitoring sensitivity of the control center to the load frequency control system.

[0153] In summary, the present invention establishes a 0-1 model for whether a DoS attack occurs. For the case where a DoS attack does not occur, a controller and an event-triggered strategy for adjusting the trigger threshold according to the following output performance are designed to stabilize the load frequency control system at a low communication frequency. At the same time, considering the consequence that the control signal cannot be transmitted when the system is under a DoS attack, resulting in unstable system output at this time, the system convergence stability under a DoS attack is deduced based on the average dwell time technique to solve the problem that the existing interconnected power grid frequency control process is vulnerable to network attacks, thus causing system instability.

[0154] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative work. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field of the present invention based on the concept of the present invention through logical analysis, reasoning or limited experiments on the basis of the prior art should be within the protection scope determined by the claims.

Claims

1. An event-triggered control method for load frequency in a power system considering denial-of-service attacks, characterized in that, the method comprises the following steps: S1. Construct the first state-space equation of the load frequency control system corresponding to the power system; S2. An adaptive event-triggered control scheme that follows the two-way adjustment trigger threshold of the system output performance, where the time period between two adjacent trigger moments of the control instruction of the adaptive event-triggered control scheme satisfies the bounded adaptive trigger threshold of δ(t k h) = min{δ M , max{δ m , λδ(t k-1 h)}}, where is the bounded adaptive trigger threshold, δ m , δ M are the upper and lower bounds of the bounded adaptive trigger threshold respectively, t k h, t k+1 h are two adjacent trigger moments, and λ is a control parameter. The control parameter is specifically: Among them, y(t k h), y(t k-1 h) are the output quantities of the load frequency control system at the trigger moments t k h, t k+1 h respectively, and the difference Δy(t k h) of the output quantities is: S3. Based on the first state-space equation and the adaptive event-triggered control scheme, establish the second state-space equation of the frequency control system corresponding to the interconnected power grid considering transmission delay; S4. Determine the scenario switching process under random DoS attacks according to the second state-space equation; S5. Establish a design criterion for the event-triggered control parameters of the switching process under random DoS attacks according to the Lyapunov stability theory, and update the event-triggered control parameters according to the event-triggered control parameter update criterion to control the load frequency.

2. The event-triggered control method for load frequency in a power system considering denial-of-service attacks according to claim 1, characterized in that, the control instruction of the adaptive event-triggered control scheme is: where \(u(t)\) is the control command, \(K\) is the controller gain when working properly without DoS attacks, \(h\) is the sampling period, and \(t\) k \(h\) and \(t\) k+1 \(h\) are two adjacent triggering moments respectively, and are the transmission delays at two adjacent triggering moments respectively. The upper bound of the transmission delay is \(x(t\) k \(h)\) is the state variable of the load frequency control system at the triggering moment \(t\) k \(h\).

3. The event-triggered control method for load frequency in a power system considering denial-of-service attacks according to claim 2, characterized in that, for the event-triggered communication mechanism of the adaptive event-triggered control scheme, the relationship between two adjacent trigger times is: where the sampling time is \(i\) k \(h = t\) k \(h + l_h\), where \(l_h\) is the time period between two adjacent triggering times, \(\delta(t\) k \(h)\) is a bounded adaptive triggering threshold, \(e(i\) k \(h)\) is the difference between the state quantity of the load frequency control system at the sampling time \(i\) k \(h\) and the state quantity of the load frequency control system at the previous triggering time \(t\) k \(h\), \(\varPhi\) and \(\varXi\) are both performance weight matrices, \(x(t\) k \(h)\) is the state quantity of the load frequency control system at the triggering time \(t\) k \(h)\).

4. The event-triggered control method for load frequency in a power system considering denial-of-service attacks according to claim 1, characterized in that, the second state-space equation of S4 is: Among them, , where x n (t) is the state space of area n, x n (t) = [Δf n , ΔP tie_n , ΔP mn , ΔP vn , ∫ACE n T , Δf n is the frequency deviation of area n, ΔP mn is the mechanical power output of the generator in area n, ΔP vn is the governor valve opening, ΔP tie_n is the tie-line power fluctuation in area n, ACE n is the control error of area n, ACE n = β n Δf n + ΔP tie_n , β n is the frequency deviation factor of area n,​ A = [A nj N×N , where​ Among them, D n and M n are the generator damping coefficient and moment of inertia in area n respectively, T tn and T gn are the time constants of the steam turbine and governor in area n respectively, R n is the droop coefficient, and L nj is the tie-line synchronizing coefficient between areas n and j; B = diag{B n} where, K is the controller gain that works normally without DoS attacks; For sampling time i k Transmission delay of h, i k Is t k , t k +1, …, t k+1 , ; w(t) = [ΔP d1 , ΔP d2 , L, ΔP dN T , where ΔP dn is the load fluctuation in region n​ F is F = diag{F n}, where, M n is the moment of inertia of the generator in area n; e(i k h) is the sampling time i k h, and is the difference between the state quantity of the load frequency control system at the sampling time i k h and the state quantity of the load frequency control system at the previous trigger time t y(t) is the observable quantity, C = diag{C n} Among them, β n is the frequency offset factor of region n.

5. The event-triggered control method for load frequency in a power system considering denial-of-service attacks according to claim 4, characterized in that, In S4, assume that [h n , h n+1 is a complete DoS attack signal, where when t ∈ [h n , h n +l n ), the DoS signal is in the sleep interval and does not act on the system. When t ∈ [h n +l n , h n+1 ), the DoS attack is in the active interval and acts on the system. The second state-space equation determines the scenario switching process under random DoS attacks as follows: During the normal operation phase without DoS attacks in the time period \(t\in[h n ,h n +l n ), the second state space equation does not change; Time period \(t\in[h n +l n ,h n+1 ), during the stage of suffering from a DoS attack, the controller cannot receive the signal uploaded by the event trigger, and the control instruction \(u(t) = 0\) of the adaptive event-triggered control scheme. At this time, the second state-space equation is updated as follows: 。 6. The event-triggered control method for load frequency in a power system considering denial-of-service attacks according to claim 5, characterized in that, the first state-space equation is: where u(t) is the control command and S DoS (t) is the DoS attack signal.

7. The event-triggered control method for load frequency in a power system considering denial-of-service attacks according to claim 6, characterized in that, the DoS attack signal is: Among them, H n = [h n , h n + l n ), L n = [h n + l n , h n+1 ) respectively correspond to the sleep interval and the active interval of the DoS attack.

8. The event-triggered control method for load frequency in a power system considering denial-of-service attacks according to claim 1, characterized in that, the event-triggered control parameter update criterion is: Suppose during the operation period [t 0 , t 1 , the load frequency control system has been switched k times due to DoS attacks, and the switching times are T 1 , T 2 , …, T k , and the average dwell time T d and the number of switches satisfy k ≤ 1 + (t 1 - t 0 ) / T d ; Meanwhile, given scalars λ, σ, γ, ρ > 0, if there exists a DoS attack time proportion coefficient α ∈ [0, 1), and the appropriate-dimensional matrices K, X that satisfy the event-triggered control parameter design criterion and the inequality, as well as the symmetric positive definite matrix Λ, .

9. The event-triggered control method for load frequency in a power system considering denial-of-service attacks according to claim 8, characterized in that, the inequality satisfied is: where, T d is the average dwell time, λ and σ are given scalars, is the minimum required average dwell time, α is the DoS attack time proportion coefficient, is the upper bound of the transmission delay.

10. The event-triggered control method for load frequency in a power system considering denial-of-service attacks according to claim 8, characterized in that, the design criterion for the event-triggered control parameters is: Given scalars λ, γ, ρ > 0, if there exist appropriate - dimensional matrices X% that satisfy linear matrix inequalities, and symmetric positive - definite matrices Λ, , then the design criteria for event - triggered control parameters are satisfied.

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