An adaptive fault-tolerant control method for power cyber-physical systems

Abstract

The application discloses an adaptive fault-tolerant control method for a power cyber-physical system, and since deep integration between system devices, the risk of information attacks on the power system is increasing, which leads to unpredictable security vulnerabilities of the system. Once the attack occurs, the system operation will be unstable. Meanwhile, actuator failure can also cause serious deterioration of the performance of the control system, and even the stability of the system cannot be guaranteed, thus causing a disaster accident. The application proposes an adaptive fault-tolerant control method for the power cyber-physical system with network attacks and actuator failures, so that the power system can quickly and accurately recover to a stable operation state when subjected to attack signals. By using the method, the voltage phase angle and the generator frequency deviation of the generator node in the power cyber-physical system can be accurately controlled, the safety and reliability of the power cyber-physical system are ensured, and greater economic losses are avoided.

Description

Technical Field

[0001] This invention belongs to the field of power system security control technology, and designs an adaptive fault-tolerant control method for power cyber-physical systems. By adaptively controlling power cyber-physical systems susceptible to network attacks and actuator failures, the reliability and security of the system are improved. Background Technology

[0002] As traditional network control systems are gradually replaced by cyber-physical systems (CPS), new intelligent components and network technologies are being used to improve the efficiency and security of power cyber-physical systems. However, the use of communication networks and information technology also increases the risk of malicious attacks on power systems. Therefore, designing an effective control method for power cyber-physical systems to improve their reliability and security is crucial.

[0003] Recent studies have shown that with the development of cyber-physical systems (CPS), the deep integration of system devices has increased the risk of cyberattacks on power systems, leading to unpredictable security vulnerabilities. Once an attack occurs, system operation will become unstable. Simultaneously, actuator failures can severely degrade control system performance, even jeopardizing system stability and potentially causing catastrophic accidents. Therefore, designing an effective method to ensure the stability of power CPS systems susceptible to cyberattacks and actuator failures is crucial. Summary of the Invention

[0004] This invention addresses the technical problems of network attacks and actuator failures in power cyber-physical systems by proposing an adaptive fault-tolerant control method to achieve effective security control of power cyber-physical systems. Specifically, it is an adaptive fault-tolerant control method for power cyber-physical systems.

[0005] This invention takes into account the impact of network security and actuator failures in power cyber-physical systems. It establishes a state-space model of the power cyber-physical system, introduces sensor attack signals and actuator failure models, and designs an adaptive fault-tolerant controller to achieve secure control of the power cyber-physical system and ensure its safe and stable operation.

[0006] The specific steps of this invention are as follows:

[0007] Step 1: Establish the state-space model of the power information physical system

[0008] First, consider a power cyber-physical system containing m generators and n load buses. Based on the interconnection structure of the power system, it is encoded as an admittance-weighted graph, yielding a Laplace symmetric matrix. Where L ggL is the admittance matrix between generator nodes in a power system. gl L is the admittance matrix between generator nodes and load nodes in a power system. lg L is the admittance matrix between load nodes and generator nodes in a power system. ll This is the admittance matrix between load nodes in the power system; further simplified, it is shown in the following equation:

[0009]

[0010] Where, χ(t)=[δ T Δω T θ T ], δ T It is the transpose of the generator node voltage phase angle, Δω T It is the transpose of the generator frequency deviation, θ T It is the transpose of the phase angle of the non-generator node voltage; It is the differential of χ(t); It is the transpose of mechanically injected power. It is the transpose of the power consumed by the load at the node; I is the identity matrix, M is the identity matrix g It is the inertia of the generator; D g It is the damping factor of the generator.

[0011] Then, substituting matrices E, N, and P(t) into the above equation, we obtain the expressions for the various physical quantities and system parameters of the power information physical system, as shown in the following equation:

[0012]

[0013] By selecting the state vector

[0014] x=[δ Δω] T

[0015] Obtain the state-space model

[0016]

[0017] Among them is The derivative of the system state signal, symbol Let n represent the Euclidean space, and n be the order of the state vector. It is a controlled input signal of the power information physical system. m is the order of the control input vector. Matrix A and matrix B are shown below:

[0018]

[0019]

[0020] Step 2: Introduce attack signals from the power information physical system sensors.

[0021] Establish a sensor attack model, assuming the system state of a sensor attack is as follows:

[0022]

[0023] in This represents the system state after being attacked by a sensor. The sensor attack can be described as δ. s (t,x(t))=w(t)x(t), where It is an unknown time-varying parameter that satisfies symbol Let ||w(t)|| represent the Euclidean space, and ||w(t)|| represent the Euclidean norm of w(t). It is an unknown upper bound, w(t) ≠ -1. Let Then achievable It is an unknown constant.

[0024] Step 3: Establish a fault model for actuators in the power information physical system.

[0025] When actuator failures exist in the system, an actuator failure model of the following form is established:

[0026] u i F (t)=ρ i (t)u i (t)+σ i (t)u si (t)

[0027] Where u i F (t) represents the output signal of the i-th actuator channel, u i (t) represents the input signal of the i-th actuator channel, i = 1, ..., m, where m is the order of the control input vector; ρ i (t) is an unknown time-varying function; u si (t) is a non-parameterizable bounded time-varying function, represented as the jamming fault parameter in the i-th actuator; σ i (t) is defined as follows:

[0028]

[0029] Actuator failure models can be described as failure, jamming, and interruption. For ease of expression, a unified failure model can be written as follows:

[0030] u F (t)=ρ(t)u(t)+σ(t)u s (t)

[0031] Step 4: Controller Design

[0032] Design an adaptive fault-tolerant controller as shown below:

[0033]

[0034] The adaptive fault-tolerant controller consists of three parts, among which It is an estimate of K1(t), with the sign... Represents an n1×n2 dimensional vector or matrix. K2(t) and K3(t) are two auxiliary control functions. Part 1 This is to compensate for the loss caused by the failure to achieve the desired effectiveness. yes The i-th row is updated with the following adaptive law:

[0035]

[0036] Where b i It is the i-th column of B, where k and Γ i It is a positive constant, a positive definite matrix. and constant matrix The inequality (A+BK) is satisfied. T P+P(A+BK)<0. Part Two To compensate for the impact of sensor attacks on the power cyber-physical system, the expression for K2(t) is as follows:

[0037]

[0038] Where ||·|| denotes the Euclidean norm of a vector or matrix, and σ0(t) is any uniformly continuous bounded positive function satisfying This is an estimate of k1, which is updated according to the following adaptive law:

[0039]

[0040] γ1 is a positive constant, and k1 is an unknown positive number satisfying: Part Three To compensate for the impact of actuator failure on the power cyber-physical system, the expression for K3(t) is as follows:

[0041]

[0042] in This is an estimate of k2, which is updated according to the following adaptive law:

[0043]

[0044] γ² is a positive constant, and k² is an unknown positive number satisfying:

[0045] Step 5: Establish the state-space model of the closed-loop system.

[0046] Combining the introduced sensor attack signal and the established actuator fault model, based on the state-space model of the power cyber-physical system, the following closed-loop system state-space model is obtained:

[0047]

[0048] Substituting the designed adaptive fault-tolerant controller into the state-space model, we further obtain the following closed-loop system state-space model:

[0049]

[0050] As a preferred option, stability analysis of the closed-loop system is also included; specifically:

[0051] Establish the following class of Lyapunov functions

[0052]

[0053] in Γ is a positive constant; by taking the derivative get This ensures the safe and stable operation of the power information physical system.

[0054] This invention proposes an adaptive fault-tolerant control method for power cyber-physical systems (PCS) that are susceptible to network attacks and actuator failures, enabling the power system to quickly and accurately recover to a stable operating state when subjected to attack signals.

[0055] The method of this invention can accurately control the phase angle of generator node voltage and the generator frequency deviation in a power cyber-physical system, thus ensuring the safety and reliability of the power cyber-physical system and avoiding greater economic losses. Detailed Implementation

[0056] Step 1: Establish the state-space model of the power information physical system

[0057] First, consider a power cyber-physical system containing m generators and n load buses. Based on the interconnection structure of the power system, it is encoded as an admittance-weighted graph, yielding a Laplace symmetric matrix. Where L gg L is the admittance matrix between generator nodes in a power system. gl L is the admittance matrix between generator nodes and load nodes in a power system. lg L is the admittance matrix between load nodes and generator nodes in a power system. ll This is the admittance matrix between load nodes in the power system; further simplified, it is shown in the following equation:

[0058]

[0059] Where, χ(t)=[δ T Δω T θ T ], δ T It is the transpose of the generator node voltage phase angle, Δω T It is the transpose of the generator frequency deviation, θ T It is the transpose of the phase angle of the non-generator node voltage; It is the differential of χ(t); It is the transpose of mechanically injected power. It is the transpose of the power consumed by the load at the node; I is the identity matrix, M is the identity matrix g It is the inertia of the generator; D g It is the damping factor of the generator.

[0060] Then, substituting matrices E, N, and P(t) into the above equation, we obtain the expressions for the various physical quantities and system parameters of the power information physical system, as shown in the following equation:

[0061]

[0062] By selecting the state vector

[0063] x=[δ Δω] T

[0064] Obtain the state-space model

[0065]

[0066] Among them is The derivative of the system state signal, symbol Let n represent the Euclidean space, and n be the order of the state vector. It is a controlled input signal of the power information physical system. m is the order of the control input vector. Matrix A and matrix B are shown below:

[0067]

[0068]

[0069] Step 2: Introduce attack signals from the power information physical system sensors.

[0070] Establish a sensor attack model, assuming the system state of a sensor attack is as follows:

[0071]

[0072] in This represents the system state after being attacked by a sensor. The sensor attack can be described as δ. s (t,x(t))=w(t)x(t), where It is an unknown time-varying parameter that satisfies symbol Let ||w(t)|| represent the Euclidean space, and ||w(t)|| represent the Euclidean norm of w(t). It is an unknown upper bound, w(t) ≠ -1. Let Then achievable It is an unknown constant.

[0073] Step 3: Establish a fault model for actuators in the power information physical system.

[0074] When actuator failures exist in the system, an actuator failure model of the following form is established:

[0075] u i F (t)=ρ i (t)u i (t)+σ i (t)u si (t)

[0076] Where u i F (t) represents the output signal of the i-th actuator channel, u i (t) represents the input signal of the i-th actuator channel, i = 1, ..., m, where m is the order of the control input vector; ρ i (t) is an unknown time-varying function; u si (t) is a non-parameterizable bounded time-varying function, represented as the jamming fault parameter in the i-th actuator; σ i (t) is defined as follows:

[0077]

[0078] Actuator failure models can be described as failure, jamming, and interruption. For ease of expression, a unified failure model can be written as follows:

[0079] u F (t)=ρ(t)u(t)+σ(t)u s (t)

[0080] Step 4: Controller Design

[0081] Design an adaptive fault-tolerant controller as shown below:

[0082]

[0083] The adaptive fault-tolerant controller consists of three parts, among which It is an estimate of K1(t), with the sign... Represents an n1×n2 dimensional vector or matrix. K2(t) and K3(t) are two auxiliary control functions. Part 1 This is to compensate for the loss caused by the failure to achieve the desired effectiveness. yes The i-th row is updated with the following adaptive law:

[0084]

[0085] Where b i It is the i-th column of B, where k and Γ i It is a positive constant, a positive definite matrix. and constant matrix The inequality (A+BK) is satisfied. T P+P(A+BK)<0. Part Two To compensate for the impact of sensor attacks on the power cyber-physical system, the expression for K2(t) is as follows:

[0086]

[0087] Where ||·|| denotes the Euclidean norm of a vector or matrix, and σ0(t) is any uniformly continuous bounded positive function satisfying This is an estimate of k1, which is updated according to the following adaptive law:

[0088]

[0089] γ1 is a positive constant, and k1 is an unknown positive number satisfying: Part Three To compensate for the impact of actuator failure on the power cyber-physical system, the expression for K3(t) is as follows:

[0090]

[0091] in This is an estimate of k2, which is updated according to the following adaptive law:

[0092]

[0093] γ² is a positive constant, and k² is an unknown positive number satisfying:

[0094] Step 5: Establish the state-space model of the closed-loop system.

[0095] Combining the introduced sensor attack signal and the established actuator fault model, based on the state-space model of the power cyber-physical system, the following closed-loop system state-space model is obtained:

[0096]

[0097] Substituting the designed adaptive fault-tolerant controller into the state-space model, we further obtain the following closed-loop system state-space model:

[0098]

[0099] Step 6: Stability analysis of the closed-loop system

[0100] Establish the following class of Lyapunov functions

[0101]

[0102] in Γ is a positive constant; by taking the derivative get This ensures the safe and stable operation of the power information physical system.

Claims

1. An adaptive fault-tolerant control method for a power cyber-physical system, characterized in that: The method specifically includes the following steps: Step 1: Consider a containing generator and For a power cyber-physical system with a single load bus, establish a state-space model of the power cyber-physical system. ,symbol Represents Euclidean space. To control the order of the input vector, the matrix sum matrix As shown below: ; This represents the admittance matrix between generator nodes in a power system. This is the admittance matrix between generator nodes and load nodes in a power system. This is the admittance matrix between load nodes and generator nodes in a power system. It is the identity matrix. It's the generator's inertia. It is the damping factor of the generator; Step 2: Introduce attack signals from the sensors of the power information physical system; Establish a sensor attack model, assuming the system state of a sensor attack is as follows: in This indicates the system state after being attacked by a sensor; the sensor attack section is described as follows: ,in It is an unknown time-varying parameter that satisfies ,symbol Represents Euclidean space. express The Euclidean norm, It is an unknown upper realm. ;make ,Then , can be obtained , It is an unknown constant; Step 3: Establish a fault model for the actuators of the power information physical system; When actuator failures exist in the system, an actuator failure model of the following form is established: in Indicates the first The output signal of each actuator channel Indicates the first The input signal of each actuator channel, , To control the order of the input vector; It is an unknown time-varying function; It is a non-parameterizable bounded time-varying function, denoted as the... Stuck fault parameters in each actuator; The definition is as follows: The actuator fault model is described as failure fault, jamming fault, and interruption fault. For ease of expression, a unified fault model is written as follows: Step 4: Controller Design; Design an adaptive fault-tolerant controller as shown below: The adaptive fault-tolerant controller consists of three parts, among which yes The estimated value, sign express A vector or matrix of dimension 1; and There are two auxiliary control functions; the first part This is to compensate for the loss caused by the failure to achieve the desired effectiveness. yes The Okay, update with the following adaptive law: in yes The Column, in which , and It is a positive constant, a positive definite matrix. and constant matrix Satisfying inequalities ; It's the generator's inertia. This represents the admittance matrix between generator nodes in a power system. This is the admittance matrix between generator nodes and load nodes in a power system. This is the admittance matrix between load nodes and generator nodes in a power system. It is the damping factor of the generator, Part Two This is to compensate for the impact of sensor attacks on power cyber-physical systems. The expression is as follows: in Describes the Euclidean norm of a vector or matrix. It is any uniformly continuous bounded positive function that satisfies , yes The estimated value is updated according to the following law: It is a positive constant. An unknown positive number satisfies: Part Three This is to compensate for the impact of actuator failure on the power cyber-physical system. The expression is as follows: in yes The estimated value is updated according to the following law: It is a positive constant. An unknown positive number satisfies: ; Step 5: Establish the state-space model of the closed-loop system; Combining the introduced sensor attack signal and the established actuator fault model, based on the state-space model of the power cyber-physical system, the following closed-loop system state-space model is obtained: Substituting the designed adaptive fault-tolerant controller into the state-space model, we further obtain the following closed-loop system state-space model: 。 2. The adaptive fault-tolerant control method for a power cyber-physical system according to claim 1, characterized in that: Consider a containing generator and For a power cyber-physical system with a load bus, a state-space model of the power cyber-physical system is established, specifically as follows: Based on the interconnection structure of the power system, it is encoded as an admittance-weighted graph, yielding a Laplace symmetric matrix. ,in This is the admittance matrix between load nodes in the power system; further simplified, it is shown in the following equation: in, , It is the transpose of the generator node voltage phase angle. It is the transpose of the generator frequency deviation. It is the transpose of the phase angle of the non-generator node voltage; yes The differential; , It is the transpose of mechanically injected power. It is the transpose of the power consumed by the load at the node; , It is the identity matrix. It is the inertia of the generator; , It is the damping factor of the generator; Then, the matrix ,matrix and Substituting into the above equation, we obtain the expressions for the relationships between various physical quantities and system parameters of the power information physical system, as shown in the following equation: By selecting the state vector Obtain the state-space model Among them is The derivative of the system state signal, ,symbol Represents Euclidean space. Let be the order of the state vector. It is a controlled input signal of the power information physical system. , This controls the order of the input vector.

3. The adaptive fault-tolerant control method for a power cyber-physical system according to claim 1, characterized in that: The method also includes stability analysis of the closed-loop system, specifically: Establish the following class of Lyapunov functions in , , , It is a positive constant; by taking the derivative ,get This ensures the safe and stable operation of the power information physical system.

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