A method and system for h∞ intermittent event-triggered load frequency safety control of a multi-region interconnected power system under DoS attack

Abstract

The application provides a kind of H ∞ Intermittent event triggered load frequency safety control method and system, the method comprises: establishing the model of multi-region interconnected power system based on switching system;Based on DoS attack, obtain H ∞ Intermittent event triggering mechanism;Based on the H ∞ Intermittent event triggering mechanism, obtain load frequency safety controller;Based on the H ∞ Intermittent event triggering mechanism, combined with the model of multi-region interconnected power system based on switching system, obtain the closed-loop multi-region interconnected power system model with interference and DoS attack;The load frequency safety controller is used for the closed-loop multi-region interconnected power system model, realize H ∞ Intermittent event triggered load frequency safety control under DoS attack.The application can design a reasonable event triggered transmission strategy in a multi-node competitive environment with limited resources, effectively improve the performance of multi-region interconnected power system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power system safety control, and particularly relates to a multi-region interconnected power system H ∞ Intermittent event triggered load frequency safety control method and system. BACKGROUND

[0002] The operation of a new power system relies on a stable network space, and an open communication environment in the network space can make the system more vulnerable to network attacks. During the initial stage of design, construction and operation of the new power system, the importance of network security is generally insufficient, which undoubtedly significantly increases the risk of network attacks on the new power system and then causes power outage accidents. Compared with traditional physical attack means, network attacks such as denial-of-service (DoS) attacks exhibit high concealment and flexibility in the new power system. Such security incidents can not only affect the daily life of the public and cause different degrees of economic and property losses, but also directly threaten the safety of people's lives and even endanger the stability of the entire country and society. In order to resist network attacks, researchers have designed a series of network defense mechanisms such as firewalls, intrusion detection, and security scanning. However, once the network attacks break through these defense measures, not only can they interfere with and damage the data transmission process of the network layer, but also can indirectly control and even damage the underlying physical facilities, and then trigger various serious new power system safety accidents. Therefore, it is of great significance to study the safety control problem of the new power system.

[0003] DoS attacks can destroy the real-time communication of a multi-region interconnected power system, and then cause redundant communication, so it is necessary to consider the event triggering mechanism, how to design a reasonable event triggered transmission strategy in a resource-limited multi-node competitive environment, and effectively improve the performance of the multi-region interconnected power system is a technical problem to be solved at present. SUMMARY

[0004] To solve the problems in the prior art, the application provides a multi-region interconnected power system H ∞ Intermittent event triggered load frequency safety control method and system, which aims to design a reasonable event triggered transmission strategy in a resource-limited multi-node competitive environment, and effectively improve the performance of the multi-region interconnected power system.

[0005] To achieve the above object, the application provides the following scheme:

[0006] A multi-region interconnected power system H ∞ Intermittent event triggered load frequency safety control method under DoS attack, the method comprises:

[0007] S1, a multi-region interconnected power system model based on a switching system is established;

[0008] S2, obtaining H ∞ based on the DoS attack, based on an intermittent event triggering mechanism;

[0009] S3, obtaining the load frequency safety controller based on the H ∞ based on an intermittent event triggering mechanism;

[0010] S4, obtaining the closed-loop multi-regional interconnected power system model with interference and DoS attack based on the H ∞ based on an intermittent event triggering mechanism, combined with the multi-regional interconnected power system model based on the switching system;

[0011] S5, using the load frequency safety controller for the closed-loop multi-regional interconnected power system model to realize the H ∞ based on an intermittent event triggering mechanism.

[0012] Preferably, the multi-regional interconnected power system model in S1 is:

[0013]

[0014] wherein,

[0015]

[0016] B = diag{B1, B2, …, B n}, u(t) = [u1(t), u2(t), …, u n (t)] T

[0017] F = diag{F1, F2, …, F n}, w(t) = [w1(t), w2(t), …, w n (t)] T ,w p (t) = ΔP dp (t)

[0018] C = diag{C1, C2, …, C n}, y(t) = [y1(t), y2(t), …, y n (t)] T ,y p (t) = ACE p , T pj = T jp

[0019]

[0020] wherein, is the derivative of x(t) with respect to time t, x(t) is the multi-area power system state vector, x p (t) is the pth area power system state vector, u(t) is the multi-area power system input vector, u p (t) is the pth area power system input vector, w(t) is the multi-area power system disturbance vector, w p (t) is the pth area power system disturbance vector, y(t) is the multi-area power system output vector, y p (t) is the pth area power system output vector; A, B, C, F, A pp , A pj , B p , C p , F p are matrices with appropriate dimensions; is the number of areas of the multi-area interconnected power system, the index variable p = 1, 2,..., n, j = 1, 2,..., n, and p ≠ j; Δf p , ΔP vp , ΔP mp , ΔP dp are the frequency deviation, the valve position deviation, the generator mechanical output deviation, and the load deviation, respectively; M p , T chp , D p , T gp , R p are the generator moment of inertia, the hydro-turbine time constant, the generator damping coefficient, the governor time constant, and the speed droop parameter, respectively; T pj is the tie-line synchronizing coefficient between the pth and jth control areas, T jp is the tie-line synchronizing coefficient between the jth and pth control areas; the ACE p signal of each area is defined as the linear combination of the tie-line power exchange and the frequency deviation, i.e., ACE p = β p Δf p + ΔP tie-p , where β p is the frequency deviation coefficient of the pth control area, ΔP tie-p is the tie-line power exchange of the pth control area, and the ACE signal combines the area frequency deviation and the grid tie-line power exchange as the input of the controller; for the multi-area interconnected power system, the grid tie-line power exchange between the control areas satisfies the following formula:

[0021]

[0022] Preferably, the H ∞ intermittent event triggering mechanism in S2 is:

[0023] t k,i,η h={e T (t)Ωe(t)≤σy T (t k，i h+jh)Ωy(t k，i h+jh)|t k，i h+jh∈[t k，η ,S k，η )}∪{t k，η}

[0024] where the intermittent strategy is to divide the total time interval into a series of k disjoint time intervals h is the sampling period, Ω is a matrix with appropriate dimensions, e(t) = y(t k，i )- y(t k，i h+jh) is the event-triggered output error, is the sensor output trigger value of the lth event trigger, and represents the jth sampling data in the trigger interval [t k,i h, t k,i+1 h), the event-triggered weight value σ ∈ [0, 1), s k,η represents the middle time of the active interval and the sleep interval set [t k,η , t k,η+1 ] of the ηth disturbance signal.

[0025] Preferably, the load frequency safety controller in S3 is:

[0026]

[0027] where K is the controller gain matrix, d k,i,η (t) represents the event-triggered transmission delay, e k,i,η (t) represents the event-triggered output error, Φ 1,k,η represents the sleep interval of the ηth disturbance signal in the kth working interval, Φ 2,k,η represents the active interval of the ηth disturbance signal in the kth working interval, N k,i,η represents the sampling interval of the i th event trigger in the sleep interval of the ηth disturbance signal in the kth working interval.

[0028] Preferably, the closed-loop multi-region interconnected power system model in S4 is:

[0029]

[0030] where e(t) and d(t) represent e k,i,η (t) and d k,i,η (t), respectively.

[0031] Preferably, the method further comprises: giving a sufficient condition for existence of the load frequency safety controller under the LMI framework through a Lyapunov functional:

[0032] The closed-loop multi-area interconnected power system with DoS attack is exponentially stable when there is no disturbance;

[0033] Under zero initial condition, the inequality For a given scalar γ>0 and any non-zero disturbance Holds, E[X] represents an expected operator, The space of square-integrable vector functions on [0,∞) is described.

[0034] Preferably, the Lyapunov functional is as follows:

[0035]

[0036] Wherein, i represents a variable, P i , U i , M i , X i are positive definite matrices, δ i is a scalar, Γ i is an exponential function, and θ is a time auxiliary parameter.

[0037] The application also provides a H ∞ intermittent event-triggered load frequency safety control system for realizing the method, the system comprising: an initial power system module, a trigger mechanism module, a controller module, a closed-loop power system module and a safety control module.

[0038] The initial power system module is configured to establish a multi-area interconnected power system model based on a switched system.

[0039] The trigger mechanism module is configured to obtain an H ∞ intermittent event trigger mechanism based on a DoS attack.

[0040] The controller module is configured to obtain a load frequency safety controller based on the H ∞ intermittent event trigger mechanism.

[0041] The closed-loop power system module is configured to obtain a closed-loop multi-area interconnected power system model with disturbance and DoS attack based on the H ∞ intermittent event trigger mechanism and the multi-area interconnected power system model based on a switched system.

[0042] The safety control module is used for the closed-loop multi-region interconnected power system model to realize H ∞ The intermittent event triggers the load frequency safety control.

[0043] Compared with the prior art, the present application has the following beneficial effects:

[0044] The present application is directed to a multi-region interconnected power system with interference and DoS attack, and proposes a H ∞ The intermittent event triggers the load frequency safety control method and system. The intermittent event triggered control only triggers the control action when the working interval and the system state deviate from the preset threshold or meet the specific event condition, which can greatly reduce the communication burden of the multi-region power system and reduce the redundant operation. At the same time, the control strategy adopts output feedback, and the implementation only needs a small amount of sensors and actuators, which can effectively reduce the control cost and is easy to implement. The present application models the system as a switching system model, designs a H ∞ The intermittent event triggers the load frequency safety control method and system. The intermittent event triggered control only triggers the control action when the working interval and the system state deviate from the preset threshold or meet the specific event condition, which can greatly reduce the communication burden of the multi-region power system and reduce the redundant operation. At the same time, the control strategy adopts output feedback, and the implementation only needs a small amount of sensors and actuators, which can effectively reduce the control cost and is easy to implement. The present application models the system as a switching system model, designs a H ∞ The present application can design a reasonable event triggered transmission strategy in a multi-node competitive environment with limited resources, and effectively improve the performance of the multi-region interconnected power system. BRIEF DESCRIPTION OF DRAWINGS

[0045] In order to more clearly illustrate the technical solutions of the present application, the following briefly introduces the drawings needed in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0046] Figure 1 The present application is directed to a multi-region interconnected power system with interference and DoS attack, and proposes a H ∞ The intermittent event triggers the load frequency safety control method and system. The intermittent event triggered control only triggers the control action when the working interval and the system state deviate from the preset threshold or meet the specific event condition, which can greatly reduce the communication burden of the multi-region power system and reduce the redundant operation. At the same time, the control strategy adopts output feedback, and the implementation only needs a small amount of sensors and actuators, which can effectively reduce the control cost and is easy to implement. The present application models the system as a switching system model, designs a H

[0047] Figure 2 The present application is directed to a multi-region interconnected power system with interference and DoS attack, and proposes a H

[0048] Figure 3 The present application is directed to a multi-region interconnected power system with interference and DoS attack, and proposes a H

[0049] Figure 4 The present application is directed to a multi-region interconnected power system with interference and DoS attack, and proposes a H ∞Intermittent event triggered load frequency safety control signal schematic diagram;

[0050] Figure 5 H ∞ Intermittent event triggered load frequency safety control system module schematic diagram. DETAILED DESCRIPTION

[0051] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0052] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0053] Embodiment one

[0054] As Figure 1 shown, the present application provides a H ∞ Intermittent event triggered load frequency safety control method, comprising:

[0055] S1, establishing a multi-region interconnected power system model based on a switched system;

[0056] S2, based on a DoS attack, obtaining a H ∞ Intermittent event triggering mechanism;

[0057] S3, based on the H ∞ Intermittent event triggering mechanism, obtaining a load frequency safety controller;

[0058] S4, based on the H ∞ Intermittent event triggering mechanism, combining the multi-region interconnected power system model based on the switched system, obtaining a closed-loop multi-region interconnected power system model with interference and DoS attack;

[0059] S5, using the load frequency safety controller for the closed-loop multi-region interconnected power system model, realizing H ∞ Intermittent event triggered load frequency safety control of the multi-region interconnected power system under DoS attack.

[0060] Further, the specific implementation process of the present application is as follows:

[0061] Consider a multi-region interconnected power system as follows:

[0062]

[0063] wherein,

[0064]

[0065] B = diag{B1, B2,..., B n}, u(t) = [u1(t), u2(t),..., u n (t)] T

[0066] F = diag{F1, F2,..., F n}, w(t) = [w1(t), w2(t),..., w n (t)] T ,w p (t) = ΔP dp (t)

[0067] C = diag{C1, C2,..., C n}, y(t) = [y1(t), y2(t),..., y n (t)] T ,y p (t) = ACE p , T pj = T jp

[0068]

[0069] wherein, is the derivative of x(t) with respect to time t, x(t) is the state vector of the multi-area power system, x p (t) is the state vector of the pth area power system, u(t) is the input vector of the multi-area power system, u p (t) is the input vector of the pth area power system, w(t) is the disturbance vector of the multi-area power system, w p (t) is the disturbance vector of the pth area power system, y(t) is the output vector of the multi-area power system, y p (t) is the output vector of the pth area power system. A, B, C, F, A pp , A pj , B p , C p , F p are matrices with appropriate dimensions. is the number of areas of the multi-area interconnected power system, the index variable p = 1, 2,..., n, j = 1, 2,..., n, and p ≠ j; Δf p , ΔP vp , ΔP mp , ΔPdp respectively, are frequency deviation, valve position deviation, generator mechanical output deviation, load deviation; M p , T chp , D p , T gp , R p respectively, are generator moment of inertia, hydro-turbine time constant, generator damping coefficient, governor time constant, speed droop parameter; T pj is the tie-line synchronization coefficient between the pth and jth control area, T jp is the tie-line synchronization coefficient between the jth and pth control area; the ACE p signal of each area is defined as the linear combination of the tie-line power exchange and the frequency deviation between areas, i.e., ACE p = β p Δf p + ΔP tie-p , where β p is the frequency deviation coefficient of the pth control area, ΔP tie-p is the tie-line power exchange of the pth control area, the ACE signal combines the area frequency deviation and the grid tie-line power exchange as the input of the controller; for a multi-area interconnected power system, the grid tie-line power exchange between control areas satisfies the following formula:

[0070]

[0071] Subsequently, the system input variables based on the output feedback load frequency proportional integral controller can be expressed as:

[0072] u(t) = Ky(t) = KCx(t)

[0073] where K = diag{K1, K2, …, K n} and K p = [K Pp K Ip ] represent the controller gain of the pth control area. K P represents the controller gain proportional element gain, K I represents the controller gain integral element gain. K Pp represents the proportional element gain of the pth control area, K Ip represents the integral element gain of the pth control area.

[0074] The intermittent strategy is to divide the total time interval into a series of k disjoint time intervals where 0 = t0< t1< t2…< t k-1 < t k … satisfy Each control period [t k , tk+1 ) by the working interval [t k ,m k ) and the rest interval [m k ,t k+1 ), where m k denotes the middle time of the kth control period [t k ,t k+1 ). Note that [t k ,m k ) and [m k ,t k+1 ) have fixed period length.

[0075] According to the characteristics of intermittent control (the controller only runs in the working interval), DoS attacks can only attack the controller in the working interval. The following definitions are given:

[0076]

[0077] The kth working interval [t k ,m k ) is divided into a series of η disjoint time intervals and t k,0 < t k,1 < t k,2 < ··· < t k,η-1 < t k,η ··· satisfy Each control period [t k,n ,t k,η+1 ) is composed of an active interval [s k,η ,t k,η+1 ) and a sleep interval [t k,η ,s k,η ). Among them, the interval [s k,η ,t k,η+1 ) represents the active interval of the kth working interval under the ηth disturbance signal, and the interval [t k,η ,s k,η ) represents the sleep interval of the kth working interval under the ηth disturbance signal, where s k,η denotes the middle time of the active interval and sleep interval set [t k,η ,t k,η+1 ) under the ηth disturbance signal.

[0078] Consider the intermittent controller, the system input variable is as follows:

[0079]

[0080] Assume that all control areas are measured and outputted synchronously with the same sampling period h (h > 0). Let the sensor output trigger value for the i-th event trigger number, denotes the trigger interval [t k,i h, t k,i+1 h) of the j-th sampling data. The next transmission time can be determined by the following way:

[0081] e T (t)Ωe(t)≤σy T (t k，i h+jh)Ωy(t k， ih+jh) (4)

[0082] where Ω is a matrix with appropriate dimensions, e(t) = v(t k，i h) - y(t k，i h+jh) is the event-triggered output error, and the event-triggered weight value σ ∈ [0, 1).

[0083] When considering DoS attacks, the transmission time under the event-triggered mechanism can be modified as t k,i,η h = {e T (t)Ωe(t)≤σy T (t k，i h+jh)Ωy(t k，i h+jh)|t k，i h+jh∈[t k，η , s k，η )}∪{t k，η} (5)

[0084] where i + 1 denotes the next event trigger number occurring in the η-th jamming signal time period. Under the event-triggered mechanism (5), the actual transmitted data packet is

[0085] y(t k，i，η h) = Cx(t k，i，η h) (6)

[0086] where i ∈ {0, 1,..., i(η)} and the upper bound value In particular,

[0087] In order to simplify the representation of each time interval and trigger number, define:

[0088]

[0089] where r(η) denotes the event trigger number set, Φ 1,k,η denotes the sleep interval of the η-th jamming signal in the k-th working interval, Φ 2,k,η denotes the active interval of the η-th jamming signal in the k-th working interval, and N k,l,ηdenotes the sampling interval of the ith event-triggered number of the kth working interval of the ηth interference signal dormant interval. Note that the sampling interval of the ith event-triggered number is in the form as follows:

[0090]

[0091] wherein and the upper bound value λ of j k,i,η satisfies the following condition:

[0092]

[0093] For the convenience of representation, define two event-triggered sampling intervals and as follows:

[0094]

[0095] Then, the ηth interference signal dormant interval Φ of the kth working interval can be derived as 1,k,η as follows:

[0096]

[0097] For the convenience of representation, set the interval denotes the event-triggered sampling interval and the dormant interval Φ 1,k,η is the intersection as follows:

[0098]

[0099] Then for define the following two piecewise functions:

[0100]

[0101] wherein d k,i,η (t) denotes the event-triggered transmission delay, e k,i,η (t) denotes the event-triggered output error, which means d k,i,η (t)∈[0, h), t ∈ N k,i,η ∩ Φ 1,k,η , i ∈ r(η).

[0102] In combination with equation (11) and equation (12), the actually transmitted data (6) can be rewritten as:

[0103] y(t k,i,η h) = e k,i,η (t) + Cx(t - d k,i,η ), t ∈ N k,i,η ∩ Φ k,i,ηi e r(η). (13)

[0104] Based on the event-triggered strategy, the controller is designed as:

[0105]

[0106] For convenience of description, e k,i,η (t) and d k,i,η (t) can be denoted by e(t) and d(t), respectively. Then, the multi-area interconnected power system can be described by the following switched system:

[0107]

[0108] where e(t) satisfies the following constraints:

[0109] e T (t)Ωe(t)≤σx T (t-d(t))C T ΩCx(t-d(t)). (16)

[0110] The present application designs a H ∞ intermittent event-triggered load frequency safety controller (14) to ensure that the closed-loop multi-area interconnected power system (15) with disturbances and DoS attacks is exponentially stable, while meeting the H ∞ performance. Specifically, the design of the controller meets the following requirements:

[0111] (i) When there is no disturbance, the closed-loop multi-area interconnected power system with DoS attacks is exponentially stable.

[0112] (ii) Under zero initial condition, the inequality holds for a given scalar γ > 0 and any non-zero disturbance , denotes the expectation operator, describes the space of square-integrable vector functions on [0, ∞).

[0113] Lemma 1 considers a matrix R = R T > 0, then for all continuously differentiable functions defined on the interval the following inequality holds:

[0114]

[0115] where

[0116]

[0117] Lemma 2 assumes that there is a matrix such that for a given symmetric positive definite matrix satisfies then for any scalar θ∈(0,1), the following inequality holds:

[0118]

[0119] Lemma 3 assumes that matrix is a full column rank matrix, whose singular value decomposition is W = UW0V, where U and V are orthogonal matrices, is a rectangular diagonal matrix, whose positive real numbers on the diagonal are arranged in descending order. Assume is a symmetric matrix, then there exists a matrix X such that PW = WX if and only if P has the following form: where and

[0120] Further, before analyzing the H ∞ performance stability of system (15) and designing the controller (14), in order to facilitate expression, a variable is introduced, and i in the present application all has the effect of representing the corresponding time interval:

[0121]

[0122] In addition, for i = 1, 2 and are defined as:

[0123]

[0124] where l 1,k,0 = t k , l 1,k+1,0 = t k+1 and and η v represents the maximum number of DoS interference signals in the vth working interval.

[0125] Theorem 1: For a given interference signal DoS(t) with known parameters T and and controller gain matrix K, system (15) is exponentially stable at H ∞ performance level γ. If there exist known positive parameters δ i , h, μ i and σ, and matrices P i > 0, U 1i > 0, U 2i > 0, M i > 0, X i > 0 (i = 1, 2) and N ij with appropriate dimensions (i, j = 1, 2, 3, 4), then the following LMIs are satisfied:

[0126]

[0127]

[0128] where

[0129]

[0130] Ξ i1 = -2M i -N i1 -N i2 -N i3 -N i4 ,Ξ i2 = -8M i + sym(N i1 -N i2 +N i3 -N i4 )

[0131] Ξ i3 = -4X i +N i1 +N i2 -N i3 -N i4 .Ξ i4 = -2M i -N i1 +N i2 +N i3 -N i4

[0132]

[0133] Ξ i7 = 2N i3 + 2N i4 ,Ξ i8 = 6M i - 2N i3 + 2N i4 ,Ξ i9 = -4N i4

[0134] Proof: Construct a Lyapunov functional V i (t) in the form

[0135]

[0136] where P i , U i , M i , X i are 5n x 5n positive definite matrices, scalar δ i > 0, and exponential function θ is a time auxiliary parameter.

[0137] Then, taking the derivative of V i (t), we have

[0138]

[0139] Applying Lemma 1 and Lemma 2, we have the following inequalities:

[0140]

[0141]

[0142] where

[0143] Π1= (e1- e3) ξ(t), Π2= (e1+ e3- 2e4) ξ(t)

[0144] Π3= (e1- e2) ξ(t), Π4= (e1+ e2- 2e5) ξ(t)

[0145] Π5= (e2- e3) ξ(t), Π2= (e2+ e3- 2e6) ξ(t)

[0146]

[0147] e z (z = 1, 2, 3, 4, 5, 6) is the row block matrix of the z-th block behavior identity matrix. And when , where (23) and (24) hold.

[0148] Definition:

[0149]

[0150] Further, define ξ1(t) = [ξ T (t), e(t), w(t)] T and ξ2(t) = [ξ(t), w(t)] T , and combining (21)-(24), we have

[0151]

[0152] When w(t) = 0 and i = 1, 2, we have

[0153]

[0154] According to conditions (16)-(18), the following inequalities hold at any switching time

[0155]

[0156] If t∈[l 1,m ,l 2,m ), from (23) and (24) we have:

[0157]

[0158] where Define T=t k,m -t k,m-1 and T off =s k,m-1 -t k,m-1 . And the lower bound of each jammer period and each rest period is Note that because From the definition of DoS jammer (2) we have Thus

[0159] V(t)≤e -ρm V1(0). (29)

[0160] In particular, from we have Thus

[0161]

[0162] Similarly, we can derive

[0163]

[0164] Define ε=(p / T), c1=min{λ max (P i )}, From (27) and (28) we have

[0165]

[0166] On the other hand, from the definition of V(t) we have

[0167] V(t)≥c1||x(t)|| 2 ,V1(0)≤c2||ψ|| 2 (33)

[0168] Thus, from (29) and (30) we have

[0169]

[0170] Therefore, we have proved that the system (15) has exponential stability with decay rate ε.

[0171] Let the function Λ(s) = y(s) T (s)y(s)-γ 2 w(s) T w(s), it is easy to see that for any have

[0172]

[0173] Similarly, for any Easy to obtain

[0174]

[0175] Note that for all And t∈[0,(m+1)T), derived from equations (26) and (27)

[0176]

[0177] Furthermore, by inequality (17) and constraints... It can be deduced

[0178]

[0179] Therefore, under zero initial conditions, by further combining equations (37) and (38), we can derive...

[0180]

[0181] Therefore, by integrating equations (35) and (36) from 0 to (m+1)T, and combining them with equation (39), we can obtain...

[0182]

[0183] As t→∞, we can obtain from equation (40)

[0184]

[0185] For all w(t) ∈ L2[0,+∞) that satisfy the zero initial condition, the proof is complete.

[0186] Based on Theorem 1, to solve H ∞ The design problem of a safety controller for intermittent event-triggered load frequency yielded the following results:

[0187] Theorem 2: For a given set of known parameters T and ... The interference signal DoS(t) causes the system (15) to be exponentially stable at the performance level γ of H∞. If there exists a known positive parameter ∈ 1i ,∈ 2i δ i ,h,μi and sigma, and matrix P i > 0, U 1i > 0, U 2i > 0, M i > 0, X i > 0 (i = 1, 2) and with appropriate dimension N ij (i,j = 1, 2, 3, 4), i = 1, 2, then formula (17)-(19) and the following LMIs are satisfied:

[0188]

[0189] where

[0190]

[0191] The remaining parameters are given in Theorem 1, and the controller gain can be calculated by K = (B T P1B) -1 B T BY.

[0192] Proof: Assume that the control input matrix B -1 has a singular value decomposition According to Lemma 3, there exists a 5n x 5n matrix G such that for P1B = BG. Further, define Y = GK, then P1BK = BGK = BY. Replace P1BK in Theorem 1 by BY, and use the inequalities and Theorem 2 can be obtained. The proof is completed.

[0193] In summary, the present application proposes a kind of H ∞ performance-based load frequency safety control method and system for multi-area interconnected power system under DoS attack for the multi-area interconnected power system existing interference and DoS attack. Intermittent event triggered control can greatly reduce the communication burden of multi-area power system and reduce redundant operation, and the control strategy adopts output feedback, and its implementation only needs a small amount of sensor and actuator, can effectively reduce control cost and be easy to implement. The present application models the system as a switching system model, designs H ∞ intermittent event triggered load frequency safety controller;By constructing switching Lyapunov functional, simultaneously in the framework of LMI, sufficient condition for the existence of controller is given, which can guarantee that the system is exponentially stable and meets H ∞ performance. The present application can design reasonable event triggered transmission strategy in the resource-limited multi-node competitive environment, effectively improve the performance of multi-area interconnected power system.

[0194] Example Two

[0195] Example Two verifies the feasibility of the method described in Example One by taking a three-area interconnected power system with disturbance and DoS attack as an example. Table 1 lists some parameters of each area of the system.

[0196] Table 1 Parameters of each area of the system

[0197] Name M β D R [CAT g ]]> [CAT ch ]]> Zone One 10 21.0 1.0 0.05 0.1 0.3 Zone Two 12 21.5 1.5 0.05 0.17 0.4 Zone Three 12 21.8 1.8 0.05 0.20 0.35

[0198] Assume the sleep time and rest time of the jammer T off Limited to T = 1 s and That is: 0.8≤T off ≤1.

[0199] Select μ1= 2.8, μ2= 0.6, δ1= 1.4, δ2= 0.7, h = 0.02 s, ∈ 11 = 1, ∈ 12 = 1, ∈ 21 = 1, ∈ 22 = 1, γ = 2 and σ = 0.4. According to Theorem 2, the weight matrix under the event-triggered condition (16) is obtained as

[0200] Ω = diag{Ω1, Ω2, Ω3}

[0201] Wherein

[0202]

[0203] Then use the LMI toolbox to solve Theorem 2, and the controller gain is obtained as follows:

[0204] K = diag{K1, K2, K3}

[0205] Wherein

[0206] K1= [-0.0083 0.0501], K2= [-0.0102 0.0608], K3= [-0.0108 0.0484].

[0207] And set the initial state as: x0= [x 10 x 20 x 30 ] T , wherein x 10 = [0.020.04-0.05-0.09] T , x 20 = [-0.020.05-0.05-0.04] T , x 30 = [0.040.04-0.015-0.05]T Then, we let ω(t) be:

[0208]

[0209] The controller with the above controller gain is applied to the three-region interconnected power system with disturbance and DoS attack, and simulation results can be obtained. The release time instant and interval of the event-triggered scheme under DoS attack are shown in Figure 2 , and Figure 3 is the state response of each region of the system, and H ∞ is the H Figure 4 of each region in the system.

[0210] Embodiment Three

[0211] As shown in Figure 5 , the application further provides a H ∞ intermittent event-triggered load frequency safety control system for a multi-region interconnected power system under DoS attack, which is used to implement the method of embodiment one, and the system comprises an initial power system module, a trigger mechanism module, a controller module, a closed-loop power system module and a safety control module.

[0212] The initial power system module is used to establish a multi-region interconnected power system model based on a switched system.

[0213] The trigger mechanism module is used to obtain H ∞ ∞ intermittent event-triggered mechanism based on DoS attack.

[0214] The controller module is used to obtain a load frequency safety controller based on the H

[0215] ∞ intermittent event-triggered mechanism. ∞ The closed-loop power system module is used to obtain a closed-loop multi-region interconnected power system model with disturbance and DoS attack based on the H ∞ intermittent event-triggered mechanism and in combination with the multi-region interconnected power system model based on a switched system.

[0216] The safety control module is used to apply the load frequency safety controller to the closed-loop multi-region interconnected power system model to implement H ∞ ∞ intermittent event-triggered load frequency safety control for the multi-region interconnected power system under DoS attack.

[0217] The above-described embodiments are only descriptions of the preferred modes of the application and do not limit the scope of the application. Without departing from the design spirit of the application, various modifications and improvements to the technical solutions of the application made by those skilled in the art shall fall within the protection scope of the claims of the application.

Claims

1. A multi-zone interconnected power system under DoS attack H ∞ An intermittent event triggered load frequency safety control method, characterized in that, The method comprises: S1, establishing a multi-area interconnected power system model based on a switching system; S2, based on DoS attack, obtaining H ∞ intermittent event triggering mechanism S3, based on the H ∞ intermittent event triggering mechanism, obtaining a load frequency safety controller; S4、 based on the H ∞ The intermittent event triggering mechanism, combined with the multi-region interconnected power system model based on the switching system, obtains the closed-loop multi-region interconnected power system model with interference and DoS attack. S5, the load frequency safety controller is used for the closed-loop multi-region interconnected power system model, realizing the multi-region interconnected power system under the DoS attack H ∞ intermittent event triggered load frequency safety control Said S2 in said H ∞ The intermittent event triggering mechanism is: ， The intermittent strategy involves dividing the total time interval. Divided into a series non-overlapping time intervals , h The sampling period is For a matrix with appropriate dimensions, The error is output as an event trigger. For the first The sensor outputs the trigger value based on the number of times an event is triggered. Indicates trigger interval The first Each sampled data point, event trigger weight value , Indicates the first Set of active and dormant regions under interference signals The middle moment; The load frequency safety controller in S3 is: ， in, K For the controller gain matrix, This indicates a transmission delay triggered by the event. This indicates that the event triggers an output error. Indicates the first k The first work interval The dormancy interval of each interference signal Indicates the first k The first work interval The active range of the interference signal, Indicates the first k The first work interval The dormant interval of the interference signal The sampling interval for the number of times each event is triggered.

2. The multi-zone interconnected power system under DoS attack according to claim 1 H ∞ The intermittent event triggered load frequency safety control method is characterized in that, The multi-area interconnected power system model in S1 is: ， Wherein, ， ， ， ， ， ， wherein is x ( t ) the derivative with respect to time t , x ( t ) is the multi-area power system state vector, is the state vector of the p th area power system, is the multi-area power system input vector, is the input vector of the p th area power system, is the multi-area power system disturbance vector, is the disturbance vector of the p th area power system, is the multi-area power system output vector, is the output vector of the p th area power system; , , , , , , , , is a matrix of appropriate dimension; is the number of areas of the multi-area interconnected power system, the index variable , , and ; , , , are the frequency deviation, the valve position deviation, the generator mechanical output deviation, and the load deviation, respectively; , , , , are the generator moment of inertia, the hydro-turbine time constant, the generator damping coefficient, the governor time constant, and the speed droop parameter, respectively; is the tie-line synchronizing coefficient between the p th and the j th control area, T jp is the tie-line synchronizing coefficient between the j th and the p th control area; the signal of each area is defined as a linear combination of the tie-line power exchange and the frequency deviation, i.e. where is the frequency deviation coefficient of the p th control area, is the p power exchange between control areas, ACE The signal combines the regional frequency deviation and the power exchange of the network tie-line as the input of the controller; for the multi-regional interconnected power system, the power exchange of the network tie-line between control areas satisfies the following formula: 。 3. The multi-zone interconnected power system under DoS attack according to claim 1 H ∞ The intermittent event triggered load frequency safety control method is characterized in that, The closed-loop multi-area interconnected power system model in S4 is: ， wherein and respectively represent and .

4. The multi-zone interconnected power system under DoS attack according to claim 3 H ∞ The intermittent event triggered load frequency safety control method is characterized in that, The method further comprises: through a Lyapunov functional, giving a sufficient condition for the existence of the load frequency safety controller under an LMI framework: When there is no interference, the closed-loop multi-area interconnected power system with DoS attack is exponentially stable; In the zero initial condition, the inequality holds for given scalar and arbitrary nonzero disturbance denotes the expectation operator, describes the space of square integrable vector functions on ​​ 5. The multi-zone interconnected power system under DoS attack according to claim 4 H ∞ The intermittent event triggered load frequency safety control method is characterized in that, The Lyapunov functional As follows: ， wherein, i denotes a variable, , , , are positive definite matrices, is a scalar, is an exponential function, is a time auxiliary parameter.

6. A multi-zone interconnected power system under DoS attack H ∞ Intermittent event triggered load frequency safety control system for implementing the method according to any one of claims 1-5, characterized in that, The system comprises: an initial power system module, a trigger mechanism module, a controller module, a closed-loop power system module and a safety control module; The initial power system module is used for establishing a multi-area interconnected power system model based on a switching system; The trigger mechanism module is configured to obtain, based on a DoS attack H ∞ intermittent event trigger mechanism The controller module is configured to obtain the load frequency safety controller based on the H ∞ An intermittent event triggering mechanism obtains a load frequency safety controller. The closed-loop power system module is configured to obtain a closed-loop multi-regional interconnected power system model with disturbance and DoS attack based on a multi-regional interconnected power system model of a switching system. H ∞ An intermittent event triggering mechanism is combined with a multi-regional interconnected power system model based on a switching system to obtain a closed-loop multi-regional interconnected power system model with disturbance and DoS attack. The security control module is configured to use the load frequency security controller for the closed-loop multi-region interconnected power system model to implement a multi-region interconnected power system under a DoS attack H ∞ Intermittent event triggered load frequency security control.

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