Security control method for multi-mode power system under denial of service attack

Abstract

The invention relates to the technical field of power system safety control, in particular to a safety control method for a multi-mode power system under denial of service attack, which comprises the following steps: introducing a discrete time segmentation homogeneous semi-Markov chain based on parameters of the power system, and constructing a discrete time segmentation homogeneous semi-Markov jump system; according to the modal switching information of the discrete time segmented homogeneous semi-Markov jump system and the information of the two upper layer homogeneous Markov chains, the denial of service attack is introduced to obtain a denial of service attack model, and an output feedback controller is designed based on the denial of service attack model; and performing stability analysis on the denial of service attack model based on a set system stability target condition to obtain a controller gain meeting the system stability target condition, thereby improving the security and stability of the multi-mode power system under the denial of service attack.

Description

Technical Field

[0001] The present invention relates to the technical field of power system security control, and in particular to a security control method for a multi-modal power system under a denial of service attack. Background Art

[0002] As global energy demand grows, the fundamental role of the power system in ensuring social operation and economic development is becoming increasingly apparent. However, with the deep integration of information technology in the power sector, while improving the efficiency and intelligence level of the power system, it inevitably increases the risk of cyber attacks.

[0003] Among the many forms of network attacks, denial of service attacks are extremely harmful and can cause delays or even interruptions in information transmission in the power system, resulting in the inability to accurately feedback the real-time monitoring data of the power system and the inability to issue control instructions in a timely manner, posing a huge threat to the stable operation of the power system. Therefore, in-depth research on the power system under denial of service attacks is of great significance to ensuring the reliable power supply and safe operation of the entire power grid.

[0004] Among them, the Markov jump system has become an important research direction in the field of control due to its unique modeling advantages. For the Markov jump system, the probability distribution function of its residence time follows an exponential distribution or a geometric distribution. According to the memoryless characteristic, the transition probability is independent of the residence time. However, in practical applications in many industrial processes, this strict restriction is difficult to meet. More commonly, the residence time obeys some non-exponential or non-geometric distribution. In this case, the corresponding random jump system is called a semi-Markov jump system. Due to the characteristics of the non-exponential or non-geometric distribution, there is a correlation between the transition probability and the residence time of the semi-Markov jump system. Obviously, the semi-Markov jump system has lower conservatism and can therefore be applied to a wider range of practical systems.

[0005] Due to the complexity of the system, the system's residence time probability density function and transition probability will change in the actual process due to external factors, so it may not be reasonable to only consider the homogeneous characteristics of the system. In addition, in the actual power system, some important internal states are unobservable, resulting in some state information cannot be directly obtained.

[0006] Therefore, it is an urgent problem to study the security control method of multimodal power systems under denial of service attacks and establish a dynamic output feedback security controller under piecewise homogeneous semi-Markov switching theory in the discrete time domain. Summary of the invention

[0007] In order to solve the above problems raised by the background technology, the present invention provides a security control method for a multi-modal power system under a denial of service attack.

[0008] The technical solution of the present invention is as follows:

[0009] A method for securely controlling a multi-modal power system under a denial of service attack comprises the following steps:

[0010] S1. Based on the parameters of the power system, a discrete-time piecewise homogeneous semi-Markov chain is introduced to construct a discrete-time piecewise homogeneous semi-Markov jump system.

[0011] The switching of different modes in the discrete-time piecewise homogeneous semi-Markov jump system is described by a discrete-time piecewise homogeneous semi-Markov kernel that introduces two upper homogeneous Markov chains;

[0012] S2. According to the mode switching information of the discrete-time piecewise homogeneous semi-Markov jump system and the information of the two upper homogeneous Markov chains, a denial of service attack is introduced to obtain a denial of service attack model, and an output feedback controller is designed based on the denial of service attack model;

[0013] S3. Perform stability analysis on the denial of service attack model based on the set system stability target conditions to obtain the controller gain that meets the system stability target conditions.

[0014] Specifically, the description of the discrete-time piecewise homogeneous semi-Markov kernel F(t) of the two upper homogeneous Markov chains introduced in S1 is expressed as follows:

[0015] definition is the dwell time between the ath transition and the (a+1)th transition, and k0=0; κ a is the time of the ath jump, and κ0=0, κ a+1 is the time of the a+1th jump;

[0016]

[0017] Where f is the discrete-time piecewise homogeneous semi-Markov kernel, Pr is the probability, t is the dwell time, is the probability density function of the dwell time depending on the current mode and the next mode, is the transition probability of a discrete-time piecewise homogeneous embedded Markov chain.

[0018] Furthermore, the residence time probability density function Transition Probabilities of Discrete-Time Piecewise Homogeneous Embedded Markov Chains The expressions are as follows:

[0019] in, is the mode at the ath jump, and its value is γ; is the mode at the a+1th jump, and its value is Satisfy at the same time and

[0020] Furthermore, the two upper homogeneous Markov chains introduced They are described as follows:

[0021]

[0022] Among them, θ mn is the upper homogeneous Markov chain The transition probability, θ mn ∈[0,1], Take values ​​from the set Θ={1,2,...m,n,...}, where m is In kappa a+1 -1 moment value, n is In kappa a+1 The value of the moment; π cd is the upper homogeneous Markov chain The transition probability, π cd ∈[0,1], The value is taken from the set Π={1,2,...c,d,...}, where c is In kappa a+1 -1 moment value, d is In kappa a+1 The value of the moment;.

[0023] Specifically, the discrete-time piecewise homogeneous semi-Markov jump system constructed in S1 is expressed as follows:

[0024] s(κ+1)=A φ(κ) s(κ)+B φ(κ) u(κ),

[0025] y(κ)=C φ(κ) s(κ),

[0026] Among them, s(κ), u(κ) and y(κ) are the system state, control input and measurement output respectively, A φ(κ) , B φ(κ) and C φ(κ) are all system parameters, {φ(κ),κ≥0} is a discrete-time piecewise homogeneous semi-Markov chain. The value of γ, For different switching modes.

[0027] Specifically, the output feedback controller designed in S2 Specifically expressed as:

[0028]

[0029] in, is the controller state, u(κ) is the control input, and are controller gains, y act (κ) is the actual transmission signal under the influence of DoS attack.

[0030] Furthermore, the denial of service attack model obtained in S2 The specific description is as follows:

[0031]

[0032] in, is the matrix parameter of the closed-loop power system, and the error term is defined as Augmentation System and is a matrix variable, defined as

[0033]

[0034] Among them, A γ =A φ(κ) , B γ =B φ(κ) , C γ =C φ(κ) is the parameter matrix of the system when the mode is γ.

[0035] Specifically, in S3, the stability analysis of the denial of service attack model is performed based on the set system stability target conditions, and the set system stability target conditions are specifically:

[0036] Existence Parameters Upper limit of stay time is a set of integers, a symmetric matrix X γmc (τ,i)>0, Where τ, i, j are all constant variables, and the matrix Z, for when When:

[0037]

[0038] Among them, ξ is a constant variable, H γmc , All are matrix variables.

[0039] Furthermore, the actual transmission signal y under the influence of the denial of service attack act(κ) is expressed as:

[0040] y act (κ)=η(κ)y(κ)+ω(1-η(κ))y(κ),

[0041] Among them, η(κ) is the control variable of the denial of service attack, which is used to simulate whether the attack occurs. When η(κ)=1, the system is attacked, otherwise, the system is not attacked. ω is a constant, y(κ) is the measurement output; η(κ) is a random variable and conforms to the following Bernoulli distribution: That is, the probability that η(κ)=1 is the expected value of η(κ) And there is ω∈[0,1].

[0042] The controller gain in S3 that meets the system stability target condition is expressed as follows:

[0043]

[0044] The beneficial effects of the present invention are:

[0045] 1. The present invention provides a security control method for a multimodal power system under a denial of service attack. Based on the parameters of the power system, a discrete-time piecewise homogeneous semi-Markov chain is introduced to construct a discrete-time piecewise homogeneous semi-Markov jump system. The system has strong heterogeneity and randomness, can better describe the dynamic characteristics of the multimodal power system, and enhances the robustness of the system in a complex environment.

[0046] 2. The present invention introduces a denial of service attack based on the mode switching information of the discrete-time piecewise homogeneous semi-Markov jump system and the information of the two upper homogeneous Markov chains, obtains a denial of service attack model, and designs an output feedback controller to ensure the stability and reliability of the system under the influence of the denial of service attack; at the same time, it can accurately describe the dynamic characteristics of the multimodal power system under the denial of service attack, effectively suppress the impact of the denial of service attack on the system, and solve the problem of safety control of the multimodal power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In the attached picture:

[0048] Figure 1 A schematic flow chart of a method for securely controlling a multi-modal power system under a denial of service attack in an embodiment;

[0049] Figure 2 Schematic diagram of open-loop state trajectory of the power system in the embodiment;

[0050] Figure 3 A schematic diagram of control input of a denial of service attack model in an embodiment;

[0051] Figure 4 Schematic diagram of the state trajectory of the denial of service attack model in the embodiment. DETAILED DESCRIPTION

[0052] Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings.

[0053] Example

[0054] This embodiment provides a method for securely controlling a multi-modal power system under a denial of service attack. Figure 1 , including the following steps:

[0055] S1. Based on the parameters of the power system, a discrete-time piecewise homogeneous semi-Markov chain is introduced to construct a discrete-time piecewise homogeneous semi-Markov jump system.

[0056] The switching of different modes in a discrete-time piecewise homogeneous semi-Markov jump system is described by a discrete-time piecewise homogeneous semi-Markov kernel with two upper homogeneous Markov chains.

[0057] In this embodiment, a single machine connected to an infinite bus is considered, where the infinite bus shows the Thevenin equivalent circuit of a large interconnected power system. The dynamic model of the infinite bus single machine power system is described as follows:

[0058]

[0059] The variable description is shown in the following table:

[0060]

[0061] Set up the state-space equations:

[0062]

[0063] in,

[0064]

[0065] C = [0 1 0 0],

[0066] The parameter values ​​are as follows: d =0.32pu,χ d =1.6pu,χ q =1.55pu,T′ do =6s,χ e =0.4pu, T E =0.05s, L1=L2=0.8, k1, k2, ..., k6 are the linearization model constants of the synchronous motor.

[0067] Then, based on the parameters of the power system, a discrete-time piecewise homogeneous semi-Markov chain is introduced to construct a discrete-time piecewise homogeneous semi-Markov jump system. The constructed discrete-time piecewise homogeneous semi-Markov jump system is expressed as follows:

[0068] s(κ+1)=A φ(κ) s(κ)+B φ(κ) u(κ),

[0069] y(κ)=C φ(κ) s(κ),

[0070] Among them, s(κ), u(κ) and y(κ) are the system state, control input and measurement output respectively, A φ(κ) , B φ(κ) and C φ(κ) are all system parameters, {φ(κ),κ≥0} is a discrete-time piecewise homogeneous semi-Markov chain. The value of γ, For different switching modes.

[0071] Specifically, in this embodiment The system parameters are shown as follows:

[0072]

[0073] B1=[-0.0001417 -5.836×10 -5 0.06133 22.27] T ,

[0074] B2=[-9.692×10 -5 -3.99×10 -5 0.06123 22.15] T ,

[0075] C1=[0 1 0 0],

[0076] C2=[0 1 0 0].

[0077] Description of the two upper-level homogeneous Markov chains introduced The discrete-time piecewise homogeneous semi-Markov kernel F(t) is expressed as follows:

[0078] definition is the dwell time between the ath transition and the (a+1)th transition, and k0=0; κ a is the time of the ath jump, and κ0=0, κ a+1 is the time of the a+1th jump;

[0079]

[0080] Where f is the discrete-time piecewise homogeneous semi-Markov kernel, Pr is the probability, t is the dwell time, is the probability density function of the dwell time depending on the current mode and the next mode, is the transition probability of a discrete-time piecewise homogeneous embedded Markov chain.

[0081] The residence time probability density function is used to describe the system jumps to the mode under mode γ The probability distribution of the residence time when ; the transition probability of the discrete time piecewise homogeneous embedded Markov chain is used to describe the system jump from mode γ to mode probability.

[0082] Dwell time probability density function Transition Probabilities of Discrete-Time Piecewise Homogeneous Embedded Markov Chains The expressions are as follows:

[0083]

[0084] in, is the mode at the ath jump, and its value is γ; is the mode at the a+1th jump, and its value is Satisfy at the same time and

[0085] For the two upper homogeneous Markov chains introduced They are described as follows:

[0086]

[0087] Among them, θ mn is the upper homogeneous Markov chain The transition probability, θ mn ∈[0,1], Take values ​​from the set Θ={1,2,...m,n,...}, where m is In kappa a+1 -1 moment value, n is In kappa a+1 The value of the moment; π cd is the upper homogeneous Markov chain The transition probability, π cd ∈[0,1], The value is taken from the set Π={1,2,...c,d,...}, where c is In kappa a+1 -1 moment value, d is In kappa a+1 The value of the moment.

[0088] In this example, two upper homogeneous Markov chains are considered and The value set of is {1,2}, and the transition probability matrix between the two upper homogeneous Markov chains is

[0089] The two transition probabilities TP1 and TP2 of the system, namely the upper homogeneous Markov chain The transition probability, the upper homogeneous Markov chain The transition probability is:

[0090] The two probability density functions of the system, RT-PMF1 and RT-PMF2, are:

[0091]

[0092]

[0093] The upper limit of the residence time is

[0094] S2. According to the mode switching information of the discrete-time piecewise homogeneous semi-Markov jump system and the information of the two upper homogeneous Markov chains, a denial of service attack is introduced to obtain a denial of service attack model, and an output feedback controller is designed based on the denial of service attack model.

[0095] Design of output feedback controller Specifically expressed as:

[0096]

[0097] in, is the controller state, u(κ) is the control input, and are controller gains, y act (κ) is the actual transmission signal under the influence of DoS attack.

[0098] Actual transmission signal y under the influence of denial of service attack act (κ) is expressed as:

[0099] y act (κ)=η(κ)y(κ)+ω(1-η(κ))y(κ),

[0100] Among them, η(κ) is the control variable of the denial of service attack, which is used to simulate whether the attack occurs. When η(κ)=1, the system is attacked, otherwise, the system is not attacked. ω is a constant, y(κ) is the measurement output; η(κ) is a random variable and conforms to the following Bernoulli distribution: That is, the probability that η(κ)=1 is the expected value of η(κ) And there is ω∈[0,1].

[0101] The resulting denial of service attack model The specific description is as follows:

[0102]

[0103] in, is the matrix parameter of the closed-loop power system, and the error term is defined as Augmentation System and All are matrix variables;

[0104]

[0105]

[0106] Among them, A γ =A φ(κ) , B γ =B φ(κ) , C γ =C φ(κ) are the parameter matrices of the system when the mode is γ.

[0107] S3. Perform stability analysis on the denial of service attack model based on the set system stability target conditions to obtain the controller gain that meets the system stability target conditions.

[0108] The stability analysis of the denial of service attack model is performed based on the set system stability target conditions. The set system stability target conditions are specifically:

[0109] Existence Parameters Upper limit of stay time is a set of integers, a symmetric matrix X γmc (τ,i)>0, Where τ, i, j are all constant variables, and the matrix Z, for when When:

[0110]

[0111] Among them, ξ is a constant variable, H γmc , All are matrix variables.

[0112]

[0113]

[0114] H γmc (τ,i)=X γmc (τ,i)-ZZ T ,

[0115]

[0116] The controller gain that meets the system stability target condition is expressed as:

[0117]

[0118]

[0119] In this embodiment, different expressions of controller gains that meet the system stability target condition are as follows:

[0120]

[0121] In order to intuitively show the feasibility of the stability analysis of the power system in step S3, some data simulation results are plotted on Figure 2-4 middle, Figure 2 is the open-loop state trajectory of the power system, where the horizontal axis is time and the vertical axis is the power system state value. The initial state is selected as s(0) = [0.1 -0.3 0.15 -0.1] T , Figure 3 It describes the control input of the closed-loop system, i.e., the denial of service attack model. The horizontal axis is time, and the vertical axis is the power system input, which converges to the origin under the denial of service attack. Figure 4 It describes the state trajectory of the closed-loop system, i.e. the denial of service attack model, with the horizontal axis being time and the vertical axis being the power system state value, and reaches the equilibrium point under the output feedback control. Figures 2 to 4 It can be seen that the method of the present invention can effectively suppress the impact of denial of service attacks on the power system, solve the output feedback control problem under the non-homogeneous characteristics of the power system, and improve the security of the power system.

Claims

1. A method for securely controlling a multi-modal power system under a denial of service attack, characterized in that: The following steps are involved: S1. Based on the parameters of the power system, a discrete-time piecewise homogeneous semi-Markov chain is introduced to construct a discrete-time piecewise homogeneous semi-Markov jump system. The switching of different modes in the discrete-time piecewise homogeneous semi-Markov jump system is described by a discrete-time piecewise homogeneous semi-Markov kernel that introduces two upper homogeneous Markov chains; S2. According to the mode switching information of the discrete-time piecewise homogeneous semi-Markov jump system and the information of the two upper homogeneous Markov chains, a denial of service attack is introduced to obtain a denial of service attack model, and an output feedback controller is designed based on the denial of service attack model; S3. Perform stability analysis on the denial of service attack model based on the set system stability target conditions to obtain the controller gain that meets the system stability target conditions.

2. The method for securely controlling a multi-modal power system under a denial of service attack according to claim 1, characterized in that: The description of the two upper homogeneous Markov chains introduced in S1 The discrete time piecewise homogeneous semi-Markov kernel F(t) is expressed as follows: definition is the dwell time between the ath transition and the (a+1)th transition, and k0=0; κ a is the time of the ath jump, and κ0=0, κ a+1 is the time of the a+1th jump; Where f is the discrete-time piecewise homogeneous semi-Markov kernel, Pr is the probability, t is the dwell time, is the probability density function of the dwell time depending on the current mode and the next mode, is the transition probability of a discrete-time piecewise homogeneous embedded Markov chain.

3. According to a method for secure control of a multi-modal power system under a denial of service attack according to claim 2, it is characterized in that: The residence time probability density function Transition Probabilities of Discrete-Time Piecewise Homogeneous Embedded Markov Chains The expressions are as follows: in, is the mode at the ath jump, and its value is γ; is the mode at the a+1th jump, and its value is Satisfy at the same time and 4. The method for securely controlling a multi-modal power system under a denial of service attack according to claim 2 is characterized in that: For the two upper homogeneous Markov chains introduced They are described as follows: Among them, θ mn is the upper homogeneous Markov chain The transition probability, θ mn ∈[0,1], Take values ​​from the set Θ={1,2,...m,n,...}, where m is In kappa a+1 -1 moment value, n is In kappa a+1 The value of the moment; π cd is the upper homogeneous Markov chain The transition probability, π cd ∈[0,1], The value is taken from the set Π={1,2,...c,d,...}, where c is In kappa a+1 -1 moment value, d is In kappa a+1 The value of the moment;.

5. The method for securely controlling a multi-modal power system under a denial of service attack according to claim 1, characterized in that: The discrete-time piecewise homogeneous semi-Markov jump system constructed in S1 is expressed as follows: s(κ+1)=A φ(κ) s(k)+B φ(κ) u(k), y(κ)=C φ(κ) s(k), Among them, s(κ), u(κ) and y(κ) are the system state, control input and measurement output respectively, A φ(κ) , B φ(κ) and C φ(κ) are all system parameters, {φ(κ),κ≥0} is a discrete-time piecewise homogeneous semi-Markov chain. The value of γ, For different switching modes.

6. The method for securely controlling a multi-modal power system under a denial of service attack according to claim 1, characterized in that: The output feedback controller designed in S2 Specifically expressed as: in, is the controller state, u(κ) is the control input, and are controller gains, y act (κ) is the actual transmission signal under the influence of DoS attack.

7. The method for securely controlling a multi-modal power system under a denial of service attack according to claim 1, characterized in that: The denial of service attack model obtained in S2 The specific description is as follows: in, is the matrix parameter of the closed-loop power system, and the error term is defined as Augmentation System and is a matrix variable, defined as Among them, A γ =A φ(κ) , B γ =B φ(κ) , C γ =C φ(κ) is the parameter matrix of the system when the mode is γ.

8. The method for securely controlling a multi-modal power system under a denial of service attack according to claim 1, characterized in that: In S3, the stability analysis of the denial of service attack model is performed based on the set system stability target conditions, and the set system stability target conditions are specifically: Existence Parameters Upper limit of stay time is a set of integers, a symmetric matrix X γmc (τ,i)>0, Where τ, i, j are all constant variables, and the matrix Z, for when When: Among them, ξ is a constant variable, H γmc , All are matrix variables.

9. The method for securely controlling a multi-modal power system under a denial of service attack according to claim 6, characterized in that: The actual transmission signal y under the influence of the denial of service attack act (κ) is expressed as: y act (κ)=η(κ)y(κ)+ω(1-η(κ))y(κ), Among them, η(κ) is the control variable of the denial of service attack, which is used to simulate whether the attack occurs. When η(κ)=1, the system is attacked, otherwise, the system is not attacked. ω is a constant, y(κ) is the measurement output; η(κ) is a random variable and conforms to the following Bernoulli distribution: That is, the probability that η(κ)=1 is the expected value of η(κ) And there is ω∈[0,1].

10. The method for securely controlling a multi-modal power system under a denial of service attack according to claim 1, characterized in that: The controller gain in S3 that meets the system stability target condition is expressed as follows:

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