Safety control method for random sudden change power system

Abstract

The invention discloses a safety control method for a random mutation power system, which belongs to the technical field of power system control, and comprises the following steps: introducing a hidden Markov process with unknown partial information to solve the switching problem of a circuit breaker in the power system and the condition that the mode information of the power system is limited; the influence of hybrid network attack on the stability of the power system is considered; constructing a controller model to obtain a closed-loop system model of the system under the hybrid network attack; giving a linear matrix inequality condition that the system is random and stable under disturbance and meets the H infinity performance index sigma; proving that the inequality condition is effective by utilizing a Lyapunov function and a performance index function; solving a gain matrix of the controller; according to the gain matrix of the controller and given system parameters, safety control over the discrete time Markov jump power system with the mode detection information is achieved. According to the invention, based on the combination of controller control and H-infinity performance index control, security control of the system can be realized under hybrid network attacks.

Description

Technical Field

[0001] The present invention relates to the technical field of power system control, and in particular to a safety control method for a random mutation power system. Background Art

[0002] Electricity is one of the fundamental driving forces for the development of modern society, so the reliability and stability of power systems are of vital importance. As the proportion of sustainable energy in the power grid continues to increase, power systems exhibit highly nonlinear and complex transient responses. In power systems, automatic voltage regulators are key components of the excitation system, and insufficient damping performance can lead to small low-frequency oscillations. These oscillations pose a major challenge to power systems because they gradually deteriorate, eventually leading to system separation and significant economic losses. To meet these challenges, experts have focused on using control strategies to improve the performance of power system stabilizers. For example, hierarchical controllers are used to enhance the stability of power systems. Similarly, some experts have proposed a sliding mode controller that can reduce oscillations.

[0003] Power systems are often affected by information interruptions, random disturbances, component failures, etc., which lead to sudden changes in system parameters or structures. In this case, the power system can be regarded as a system with finite modes, which can be represented as a Markov jump power system through Markov jump theory. This model can more accurately describe the transition process of the power system between different states and provide an effective method for dealing with uncertainties within the system. For example, some researchers have studied the load frequency control of power systems using Markov models, showing how this method can better cope with dynamic changes under different modes. Similarly, some researchers have also used Markov theory to describe the load frequency control model, providing valuable insights for the stable control of power systems.

[0004] At present, most of the research on Markov models assumes complete knowledge of the model information, which is inconsistent with the actual situation. Therefore, some experts introduced hidden Markov models, aiming to design observers to detect the operating mode of Markov jump power systems. The introduction of hidden Markov models effectively solves the challenge of limited mode information. Subsequently, hidden Markov models have attracted widespread attention and have been further studied. However, previous work has ignored the difficulty of obtaining complete information of the probability matrix. Therefore, some scholars have established a hidden Markov model based on a partially unknown transition probability matrix to characterize asynchronous phenomena. In contrast, other experts use hidden Markov models with partially unknown observation probability matrices to represent system and controller asynchronous. Although the research on hidden Markov models is quite extensive, the situation where both the transition probability matrix and the observation probability matrix are incomplete is still rarely explored, let alone in power systems with hidden Markov models. In view of the above discussion, how to deal with the situation where the transfer probability matrix and the observation probability matrix are partially unknown in hidden Markov jump power systems is one of the main research motivations of this invention.

[0005] On the other hand, as a networked control system, the power system faces a major challenge to its stable operation due to cyber security threats. The openness of communication equipment makes the power system vulnerable to false deception attacks and denial of service (DoS) attacks. DoS attacks mainly involve blocking the transmission channel, resulting in packet loss. Deception attacks involve injecting false information into the communication link, thereby compromising data integrity. At present, important research results have been achieved in the field of power system security control. For example, some researchers have studied the impact of deception and DoS attacks on the stability of power systems respectively. Although researchers have made significant progress in solving a single form of network attack type in power systems, they rarely consider the possibility of multiple forms of attacks such as deception attacks and DoS attacks occurring simultaneously (hybrid network attacks). Based on the above discussion, how to ensure the stable operation of hidden Markov jump power systems under hybrid network attacks is one of the main research motivations of this invention.

[0006] The above problems need to be solved urgently. Therefore, a safety control method for random mutation power system is proposed. Summary of the invention

[0007] The technical problem to be solved by the present invention is: how to deal with the situation where the transfer probability matrix and the observation probability matrix are partially unknown in the hidden Markov jump power system and how to ensure the stable operation of the hidden Markov jump power system under hybrid network attacks. A safety control method for a random mutation power system is provided. By controlling the controller based on H ∞ The combination of performance indicator control can achieve security control of the system under hybrid network attacks.

[0008] like Figure 7 As shown, the present invention solves the above technical problems through the following technical solutions, and the present invention comprises the following steps:

[0009] Step S1: Introduce a partially unknown hidden Markov process to solve the switching problem of circuit breakers in the power system and the situation where the power system mode information is limited;

[0010] Step S2: Consider the impact of hybrid network attacks on power system stability;

[0011] Step S3: construct a controller model to obtain a closed-loop system model of a discrete-time Markov jump power system with pattern detection information under a hybrid network attack;

[0012] Step S4: Give the system in step S3 that is stochastically stable under disturbance and satisfies H ∞ Linear matrix inequality conditions for performance index σ;

[0013] Step S5: Using the Lyapunov function and the performance index function to prove that the inequality condition in step S4 is valid;

[0014] Step S6: Solve the gain matrix of the controller;

[0015] Step S7: Implementing safety control of the discrete-time Markov jump power system with mode detection information according to the gain matrix of the controller in step S6 and given system parameters.

[0016] Furthermore, in step S1, the specific processing process is as follows:

[0017] S11: Establish the power system dynamic model as follows:

[0018]

[0019] Where δ is the rotor angle, x d is the synchronous reactance along the d-axis, x' d is the transient reactance along the d-axis, T e is the electrical torque, V is the infinite bus voltage, E fd is the generator field voltage, u is the stable signal, T do ' is the d-axis open-circuit transient time constant, V t is the terminal voltage, E q ' is the q-axis voltage after the transient reactance, x e is the external line reactance, M is the inertia coefficient, k E ,T E is the actuator gain and time constant, T m is the mechanical torque;

[0020] S12: The fourth-order state space model of the above power system is expressed as:

[0021]

[0022] in:

[0023] x T (α)=[Δδ Δω ΔE′ q ΔE fd ];

[0024]

[0025] Among them, x(β) and u(β) represent the state variable and control input of the βth node respectively, and y(β) is the measured output. is the internal coupling matrix between nodes, w(β) is the interval Additional interference on is the sensor’s measurement matrix, is the output matrix of the system, k 1 ,k 2 ...k 6 is the linearized model constant of the synchronous motor, Δω is the speed deviation;

[0026] S13: Introduce a hidden Markov process with unknown partial information and establish the following hidden Markov jump power system:

[0027]

[0028] in, It is a discrete-time Markov chain, i.e., the pattern information of the power system.

[0029] Furthermore, in step S13, in the hidden Markov jump power system, the transition probability matrix

[0030]

[0031] in,

[0032] Furthermore, in step S13, in the hidden Markov jump power system, the hidden Markov model is used for observation, and the information of r(β) is detected by ξ(β), ​​wherein, Observation probability matrix

[0033]

[0034] Furthermore, in step S2, a hybrid network attack means that DoS and spoofing attacks occur simultaneously. represents the probability of DoS attack, η(β)∈{0,1} represents the probability of deception attack, and the mathematical expectations of the two attacks are The probabilities of the two attacks occurring satisfy the following constraints:

[0035]

[0036] The nonlinear function f(·) is used to suppress the spoofing attack, which is specifically expressed as follows:

[0037] ||f(y(β))|| 2 ≤||Fy(β)|| 2

[0038] Among them, F represents the nonlinear upper limit and is a constant matrix.

[0039] Furthermore, in step S3, the specific processing process is as follows:

[0040] S31: Design the following controller:

[0041]

[0042] in, represents the controller gain matrix;

[0043] S32: Bring the controller into the hidden Markov jump power system in step S13 to obtain a closed-loop system model of a discrete-time Markov jump power system with pattern detection information under a hybrid network attack:

[0044]

[0045] Among them, x(β+1) represents the state variable of the β+1th node, y(β) is the measured output, is a given system parameter matrix, w(β) is a matrix in the interval Additional interference on is the sensor’s measurement matrix, is the output matrix of the system.

[0046] Furthermore, in step S4, given a scalar η∈[0,1], σ>0, diagonal nonlinear upper bound F matrix; if there exists a symmetric matrix And the matrix K λ , then when the system in step S32 meets the following conditions, it can ∞ Achieve random stability under performance index σ:

[0047]

[0048] The conditions are as follows:

[0049] In case 1: and case 2: When the condition is:

[0050]

[0051] In case 3: When the condition is:

[0052]

[0053] in:

[0054]

[0055] Φ 6 =[Φ 2 Φ 3 Φ 4 Φ 5 ],f=1,2,

[0056]

[0057] Furthermore, in step S5, the specific processing process is as follows:

[0058] S51: For w(β)≡0 and any initial value, when the condition When established, the system in step S32 is stochastically stable;

[0059] When all non-zero w(β)∈L[0,∞) and the zero initial state satisfy the following inequality: ∞ Performance index σ:

[0060]

[0061] S52: Select the following Lyapunov functional:

[0062]

[0063] make get:

[0064]

[0065] in,

[0066] Through the inequality in step S51 and the above formula, we can obtain:

[0067]

[0068] in:

[0069]

[0070] S53: Through the inequality condition in step S4, we get:

[0071]

[0072] S54: Analysis of the attack shows that:

[0073]

[0074] Then we get:

[0075]

[0076] From the Schur complement and the inequality condition in step S4, we can know that According to the above formula, we can know

[0077]

[0078] If w(β)≡0, then The system is stochastically stable;

[0079] Under zero initial conditions, w(β)≠0, we get Therefore, the system is stochastically stable and satisfies the specified H ∞ Performance index σ.

[0080] Furthermore, in step S6, the specific processing process is as follows:

[0081] S61: Order

[0082] S62: Perform equivalent transformation on some inequality conditions of step S4 as follows:

[0083] In case 1: and case 2: When , the equivalent transformation is as follows:

[0084]

[0085] In case 3: When , the equivalent transformation is as follows:

[0086]

[0087] in:

[0088]

[0089] S63: Then, the simulation software is used to calculate the value of the controller gain matrix by giving the matrix parameters.

[0090] Compared with the prior art, the present invention has the following advantages: the safety control method of the random mutation power system proposes a hidden Markov model containing partial information of the power system, which may exist in the transfer probability matrix, or in the observation probability matrix, or even in both; the safety control problem of the hidden Markov jump power system under hybrid network attacks is considered, and the impact of network attacks and transfer probabilities on the power system is deeply analyzed. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 It is a control system structure block diagram of a safety control method for a random mutation power system with pattern detection information in an embodiment of the present invention;

[0092] Figure 2 is a system mode and controller mode diagram in an embodiment of the present invention;

[0093] Figure 3 is a sequence diagram of different attacks in an embodiment of the present invention;

[0094] Figure 4 is a trajectory diagram of a controller in an embodiment of the present invention;

[0095] Figure 5 is a state trajectory diagram when the system does not include a controller in an embodiment of the present invention;

[0096] Figure 6 is a system trajectory diagram including a controller in an embodiment of the present invention;

[0097] Figure 7 It is a flow chart of a safety control method for a random mutation power system with pattern detection information according to the present invention. DETAILED DESCRIPTION

[0098] The following is a detailed description of an embodiment of the present invention. This embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation method and a specific operation process are given, but the protection scope of the present invention is not limited to the following embodiment.

[0099] This embodiment provides a technical solution: a safety control method for a random mutation power system with pattern detection information, comprising the following steps:

[0100] like Figure 1 As shown, a safety control method for a random mutation power system with pattern detection information provided by an embodiment of the present invention includes the following steps:

[0101] Step S1: Introduce a partially unknown hidden Markov process to effectively solve the switching problem of circuit breakers in the power system and the situation where the power system mode information is limited;

[0102]

[0103] Where δ is the rotor angle, x d is the synchronous reactance along the d-axis, x' d is the transient reactance along the d-axis, T e is the electrical torque, V is the infinite bus voltage, E fd is the generator field voltage, u is the stable signal, T do ' is the d-axis open-circuit transient time constant, V t is the terminal voltage, E q ' is the q-axis voltage after the transient reactance, x e is the external line reactance, M is the inertia coefficient, k E ,T E is the actuator gain and time constant, T m is the mechanical torque;

[0104] The fourth-order state space model of the SMIB system (1) is expressed as:

[0105]

[0106] in:

[0107] x T (α)=[Δδ Δω ΔE′ q ΔE fd ];

[0108]

[0109] x(β), u(β) represent the state variable and control input of the βth node respectively, y(β) is the measured output, is the internal coupling matrix between nodes, w(β) is the interval Additional interference on is the sensor’s measurement matrix, is the output matrix of the system, k 1 ,k 2 ...k 6 is the linearized model constant of the synchronous motor, and Δω is the speed deviation.

[0110] Consider the following hidden Markov jump power system:

[0111]

[0112] in, It is a discrete-time Markov chain, i.e., the pattern information of the power system.

[0113] Transition probability matrix

[0114]

[0115] in, m∈G, as well as

[0116] Since the modal information r(β) of the power system cannot be directly measured in practical applications, the hidden Markov model is used for observation. Specifically, the information of r(β) is detected by ξ(β), ​​where Observation probability matrix

[0117]

[0118] Step S2: Consider the impact of hybrid cyber attacks on power system stability

[0119] In actual power systems, remote access to devices may cause the system to suffer from DoS and spoofing attacks. Specifically, when a DoS attack occurs, the output of the controller y(β) = 0. On the other hand, when a spoofing attack occurs, the nonlinear function f(·) is used in this embodiment to represent the potential nonlinearity to suppress the spoofing attack. In addition, when the two attacks occur at the same time, this situation is equivalent to a DoS attack.

[0120] represents the probability of DoS attack, η(β)∈{0,1} represents the probability of spoofing attack, They represent the mathematical expectations of the two attacks respectively. Probability, the probability of the two attacks occurring respectively satisfies the following constraints:

[0121] The specific expression of using f(·) to suppress spoofing attacks is:

[0122] ||f(y(β))|| 2 ≤||Fy(β)|| 2 (5)

[0123] Among them, the nonlinear upper limit F is a constant matrix.

[0124] Step S3: construct a controller model to obtain a closed-loop system model of a discrete-time Markov jump power system with pattern detection information under a hybrid network attack.

[0125] Design the following controller form:

[0126]

[0127] in represents the controller gain matrix, the two subscripts of K represent the system mode and the observed mode respectively. Substituting (6) into (3), we can obtain the following hidden Markov jump power system with partially unknown information (i.e., the closed-loop system model of discrete-time Markov jump power system with mode detection information under hybrid network attack):

[0128]

[0129] Step S4: Give the system a random stability under disturbance and satisfy H ∞ Linear matrix inequality conditions for performance indicators.

[0130] Given a scalar η∈[0,1],σ>0, the diagonal nonlinear upper bound F matrix; if there exists a symmetric matrix λ∈M, and the matrix K λ , then when the system (7) satisfies the following conditions, it can be given by H ∞ Achieve random stability under performance index σ:

[0131]

[0132] Case 1: and case 2:

[0133]

[0134] Case 3:

[0135]

[0136] in:

[0137]

[0138] Φ 6 =[Φ 2 Φ 3 Φ 4 Φ 5 ],f=1,2,

[0139]

[0140] Step S5: Use the Lyapunov function and the performance index function to prove that the conditions in step S4 are valid.

[0141] When system (7) holds under given conditions, it not only behaves stochastically stable but also satisfies H ∞ Performance index σ.

[0142] For w(β)≡0 and any initial value, when the condition When it holds, the system (7) is stochastically stable.

[0143] When all non-zero w(β)∈L[0,∞) and the zero initial state satisfy the following inequality, the system (7) can reach the specified H ∞ Performance index σ.

[0144]

[0145] Consider the following Lyapunov functionals:

[0146]

[0147] make We can get:

[0148]

[0149] in,

[0150] Through formula (11) and the above formula, we can get:

[0151]

[0152] in:

[0153]

[0154] Through formula (8), we get:

[0155]

[0156] Analysis of the attack shows that:

[0157]

[0158] Combining equations (12) and (13), we obtain:

[0159]

[0160] From Schur complement and equations (9) and (10), we know that Further according to formula (14), we can get

[0161]

[0162] If w(β)≡0, we know The system is stochastically stable.

[0163] Under zero initial conditions, w(β)≠0, we can get The system is stochastically stable and satisfies the specified H ∞ Performance indicators.

[0164] Step S6: Solve the controller gain matrix:

[0165] make

[0166] It should be noted that λ is the observed pattern information, and ξ ( β ) is the observed information;

[0167] The equivalent transformation of some conditions of step S4 is as follows

[0168] Case 1: and case 2:

[0169]

[0170] Case 3:

[0171]

[0172] in:

[0173]

[0174] At this point, simulation software can be used to calculate the gain matrix K by giving matrix parameters. λ The value of .

[0175] Step S7: Verify the feasibility of safe and stable operation of the system through numerical example simulation.

[0176] When a line fails, the hidden Markov jump power system (7) controls the on / off state of the circuit breaker. There are two states, and the specific parameters are as follows:

[0177] Mode 1:

[0178]

[0179] Mode 2:

[0180]

[0181] The remaining parameters in this embodiment are assumed as follows:

[0182] F=diag{0.13,0.22,0.21,0.31},σ=30, η=0.5,ψ=1.21,w(β)=0.2cos(0.3β)e -0.56β , S 1 =[0.52 0.61 0.82 0.22] T , S 2 =[0.41 0.51 0.61 0.32] T .

[0183] Then, the controller gain matrix is ​​as follows:

[0184] K 1 =[-0.1665 -0.0151 0.0011 -0.0483],

[0185] K 2 =[-0.1532 -0.0115 0.0017 -0.0436].

[0186] According to equations (8)-(10), we can get Figure 4 The controller response diagram is shown in Figure 2. Under the action of the controller, the system still tends to be stable in the 10 simulation results, as shown in Figure 2. Figure 6 On the contrary, without the intervention of the controller, the system is in an unstable state, as shown in Figure 5 On the other hand, the modal diagram of the system and the controller is shown in Figure 2 The two modes are asynchronous, and the two types of attack sequences during this period are as follows: Figure 3 shown.

[0187] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A safety control method for a random mutation power system, characterized in that: The following steps are involved: Step S1: Introduce a partially unknown hidden Markov process to solve the switching problem of circuit breakers in the power system and the situation where the power system mode information is limited; Step S2: Consider the impact of hybrid network attacks on power system stability; Step S3: construct a controller model to obtain a closed-loop system model of a discrete-time Markov jump power system with pattern detection information under a hybrid network attack; Step S4: Give the system in step S3 that is stochastically stable under disturbance and satisfies H ∞ Linear matrix inequality conditions for performance index σ; Step S5: Using the Lyapunov function and the performance index function to prove that the inequality condition in step S4 is valid; Step S6: Solve the gain matrix of the controller; Step S7: Implementing safety control of the discrete-time Markov jump power system with mode detection information according to the gain matrix of the controller in step S6 and given system parameters.

2. The safety control method for a random mutation power system according to claim 1 is characterized in that: In step S1, the specific processing process is as follows: S11: Establish the power system dynamic model as follows: Where δ is the rotor angle, x d is the synchronous reactance along the d-axis, x' d is the transient reactance along the d-axis, T e is the electrical torque, V is the infinite bus voltage, E fd is the generator field voltage, u is the stable signal, T do ' is the d-axis open-circuit transient time constant, V t is the terminal voltage, E q ' is the q-axis voltage after the transient reactance, x e is the external line reactance, M is the inertia coefficient, k E ,T E is the actuator gain and time constant, T m is the mechanical torque; S12: The fourth-order state space model of the above power system is expressed as: in: x T (a)=[Δδ Δω ΔE′ q DE fd ]; Among them, x(β) and u(β) represent the state variable and control input of the βth node respectively, and y(β) is the measured output. is the internal coupling matrix between nodes, w(β) is the interval The additional interference on the sensor, C is the measurement matrix of the sensor, is the output matrix of the system, k1, k2...k6 are the linearization model constants of the synchronous motor, and Δω is the speed deviation; S13: Introduce a hidden Markov process with unknown partial information and establish the following hidden Markov jump power system: in, is a discrete-time Markov chain, i.e., the pattern information of the power system.

3. The safety control method for a random mutation power system according to claim 2 is characterized in that: In step S13, in the hidden Markov jump power system, the transition probability matrix in, 4. The safety control method for a random mutation power system according to claim 3 is characterized in that: In step S13, in the hidden Markov jump power system, the hidden Markov model is used for observation, and the information of r(β) is detected by ξ(β), ​​wherein, Observation probability matrix 5. A safety control method for a random mutation power system according to claim 4, characterized in that: In step S2, a hybrid network attack means that DoS and spoofing attacks occur simultaneously. represents the probability of DoS attack, η(β)∈{0,1} represents the probability of deception attack, and the mathematical expectations of the two attacks are The probabilities of the two attacks satisfy the following constraints: The nonlinear function f(·) is used to suppress the spoofing attack, which is specifically expressed as follows: ||f(y(β))|| 2 ≤||Fy(β)|| 2 Among them, F represents the nonlinear upper limit and is a constant matrix.

6. A safety control method for a random mutation power system according to claim 5, characterized in that: In step S3, the specific processing process is as follows: S31: Design the following controller: in, represents the controller gain matrix; S32: Bring the controller into the hidden Markov jump power system in step S13 to obtain a closed-loop system model of a discrete-time Markov jump power system with pattern detection information under a hybrid network attack: Among them, x(β+1) represents the state variable of the β+1th node, y(β) is the measured output, is a given system parameter matrix, w(β) is a matrix in the interval Additional interference on is the sensor’s measurement matrix, is the output matrix of the system.

7. A safety control method for a random mutation power system according to claim 6, characterized in that: In step S4, a scalar η∈[0,1],σ>0, diagonal nonlinear upper bound F matrix; if there exists a symmetric matrix And the matrix K λ , then when the system in step S32 meets the following conditions, it can ∞ Achieve random stability under performance index σ: The conditions are as follows: In case 1: and case 2: When the condition is: In case 3: When the condition is: in: Φ6=[Φ2 Φ3 Φ4 Φ5],f=1,2, 8. The safety control method for a random mutation power system according to claim 7 is characterized in that: In step S5, the specific processing process is as follows: S51: For w(β)≡0 and any initial value, when the condition When established, the system in step S32 is stochastically stable; When all non-zero w(β)∈L[0,∞) and the zero initial state satisfy the following inequality: ∞ Performance index σ: S52: Select the following Lyapunov functional: make get: in, Through the inequality in step S51 and the above formula, we can obtain: in: S53: Through the inequality condition in step S4, we get: S54: Analysis of the attack shows that: Then we get: From the Schur complement and the inequality condition in step S4, we can know that According to the above formula, we can know If w(β)≡0, then The system is stochastically stable; Under zero initial conditions, w(β)≠0, we get Therefore, the system is stochastically stable and satisfies the specified H ∞ Performance index σ.

9. A safety control method for a random mutation power system according to claim 8, characterized in that: In step S6, the specific processing process is as follows: S61: Order S62: Perform equivalent transformation on some inequality conditions of step S4 as follows: In case 1: and case 2: When , the equivalent transformation is as follows: In case 3: When , the equivalent transformation is as follows: in: S63: Then, the simulation software is used to calculate the value of the controller gain matrix by giving the matrix parameters.

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