An asynchronous control method and device of a multi-modal power system and a storage medium

Abstract

The application relates to the technical field of electric power automation, in particular to an asynchronous control method and device of a multi-modal power system and a storage medium, wherein the method comprises the following steps: a discrete-time hidden semi-Markov jump system of the multi-modal power system is established; a mode transition probability depending on a residence time is designed according to the discrete-time hidden semi-Markov jump system; a transmission probability of an observation mode is determined according to the designed mode transition probability; a deception attack model is established according to the influence of the multi-modal power system under a deception attack; an observation mode-dependent asynchronous controller is designed based on the discrete-time hidden semi-Markov jump system and the deception attack model; and asynchronous controller parameters are determined according to the designed observation mode-dependent asynchronous controller. The method establishes a dynamic model of the multi-modal power system under an asynchronous mechanism, designs an asynchronous control strategy of the power system, and guarantees the stability of the power system.

Description

Technical Field

[0001] This invention relates to the field of power automation technology, specifically to an asynchronous control method, device, and storage medium for a multimodal power system. Background Technology

[0002] A power system is a highly nonlinear, high-dimensional, and hierarchically distributed dynamic system. Its grid structure, line count parameters, and load distribution have a significant impact on its operation. Any disturbance can cause system oscillations, instability, or even collapse. Therefore, ensuring the stable operation of the power system is its most important task, guaranteeing that the system can recover to an acceptable equilibrium state after being subjected to disturbances.

[0003] With the rapid development of power system-related fields, delays, collisions, and congestion are inevitable phenomena in power systems. Furthermore, the system is susceptible to nonlinear disturbances, which may prevent it from processing massive amounts of data in real time, leading to performance degradation. Power systems connect spatially distributed components through shared networks, bringing convenience but also security risks. Because the network links between components in a power system are open, they are vulnerable to network attacks. Network attacks are mainly divided into three categories: denial-of-service attacks, spoofing attacks, and replay attacks. Among these, spoofing attacks are a significant type of network attack, also known as fake data injection attacks. A typical spoofing attacker can capture sensor nodes and use unauthorized privileges to inject malicious code or modify programs, thereby reducing or even degrading system performance. Due to its superior modeling capabilities in structurally abrupt physical systems, applying Markov jump system theory to power systems has become an important research topic in the field of control.

[0004] The transition probability matrix of a stochastic jump system is primarily constrained by the probability distribution function of the dwell time. For Markov jump systems, the probability distribution function of dwell time follows an exponential / geometric distribution, and due to the memoryless property, the transition probability is independent of the dwell time. However, many industrial processes struggle to satisfy this strict constraint, and the dwell time follows other non-exponential / geometric distributions. In such cases, the corresponding stochastic jump system is called a semi-Markov jump system. Due to the non-exponential / geometric distribution, the transition probability of a semi-Markov jump system is related to the dwell time. This makes semi-Markov jump systems less conservative and applicable to a wider range of practical systems.

[0005] When using traditional Markov chains to analyze control systems, it is often assumed that the system modes are completely known; however, this ideal assumption is difficult to achieve in practice. Therefore, the concept of Hidden Markov Chains (HMCs) is proposed. An HMC can be viewed as a two-layer parametric process: the upper layer is a traditional homogeneous Markov chain; the lower layer is a sequence of observed modes, where the modes of the upper Markov chain cannot be directly observed. The sequence of observed modes consists of observed modes, and this sequence can be used to estimate the modes in the upper Markov chain. Based on its unique two-layer structure, HMCs have been applied to many practical systems as an important class of statistical models. Combining the advantages of semi-Markov chains and HMCs, the upper-layer stochastic process of the HMC is replaced by a semi-Markov chain, thus introducing the concept of Hidden Semi-Markov Chains (HSCs). Stability analysis and controller design are then performed on HSC jump systems.

[0006] In summary, researching asynchronous control methods for power systems under deception attacks and establishing an observation mode-dependent controller to ensure stable operation of the power system under deception attacks is an urgent problem to be solved. Summary of the Invention

[0007] To address the aforementioned problems, the present invention provides, in a first aspect, an asynchronous control method for a multimodal power system, the steps of which are as follows:

[0008] Establish a discrete-time hidden semi-Markov jump system for multimodal power systems;

[0009] Based on discrete-time hidden semi-Markov jump systems, design mode transition probabilities that depend on dwell time;

[0010] Based on the designed mode transition probabilities, determine the emission probability of the observed mode;

[0011] Based on the impact of deception attacks on multimodal power systems, a deception attack model is established;

[0012] Based on discrete-time hidden semi-Markov jump system and spoofing attack model, an asynchronous controller that depends on observation mode is designed.

[0013] Determine the asynchronous controller parameters based on the designed asynchronous controller that depends on the observation mode.

[0014] The proposed method addresses random deception attacks on power systems by establishing a dynamic model of a multimodal power system under an asynchronous mechanism and designing an asynchronous control strategy for the power system to ensure its stability.

[0015] In some implementations of the first aspect, the discrete-time hidden semi-Markov jump system for establishing the multimodal power system is as follows:

[0016]

[0017] Where z(k)∈R n Representing the system state, u(k)∈R m Indicates control input, Let {q(k), k≥0} be the matrix coefficients, and let {q(k), k≥0} be a discrete-time semi-Markov chain. Take the value from the middle.

[0018] In some implementations of the first aspect, the design of dwell-time-dependent mode transition probabilities based on the discrete-time hidden semi-Markov transition system includes:

[0019] definition In the first The second jump and the first The dwell time between the transitions, and It is the first At the moment of the next jump, and k0 = 0, It is the first The system mode at the time of the next transition;

[0020] Given a matrix Given a discrete-time semi-Markov kernel, the mode transition probability... And depends on the length of stay and meets the requirements.

[0021]

[0022] Where, δ ην It is the residence time probability density function.

[0023] In some implementations of the first aspect, determining the emission probability of the observation mode based on the designed mode transition probability includes:

[0024] Define the transition probability density function that depends on the dwell time of the current mode and the next mode as follows:

[0025]

[0026] Introduction This indicates the system's dwell time in the current mode, and Observation mode In finite sets Take the value from;

[0027] For any system mode Suppose there exists a finite set and Where H η ≥1 indicates that in the subset The number of elements in the middle.

[0028] The emission probability of the observed mode is determined as follows:

[0029]

[0030]

[0031] in, This is expressed as the system mode q(k) = η when the th... Secondary observation mode, Let be the emission probability matrix.

[0032] In some implementations of the first aspect, the establishment of a deception attack model based on the impact of deception attacks on multimodal power systems is as follows:

[0033] z ζ (k)=z(k)+ζ(k)(-z(k)+θ(k)),

[0034] Among them, z ζ (k) represents the actual signal under the influence of the deception attack, z(k) represents the system state, and θ(k) represents the deception attack signal, and given the known positive constants... Under the condition of satisfying The random variable ζ(k) follows a Bernoulli distribution.

[0035]

[0036]

[0037] When ζ(k) = 0, the actual control input signal is successfully transmitted in the system; when ζ(k) = 1, the deception attack signal replaces the actual control input signal.

[0038] In some implementations of the first aspect, the asynchronous controller designed based on the discrete-time hidden semi-Markov transition system and the spoofing attack model, which depends on the observation mode, is as follows:

[0039]

[0040] in, Let z be the gain matrix of the asynchronous controller, making the discrete-time hidden semi-Markov jump system stable; ζ (k) represents the actual signal under the influence of a deception attack; u(k)∈R m This indicates a control input.

[0041] In some implementations of the first aspect, the closed-loop system of the discrete-time hidden semi-Markov transition system under a deception attack is as follows:

[0042]

[0043] Where z(k)∈R n Representing the system state, u(k)∈R m Indicates control input, z ζ θ(k) represents the actual signal under the influence of the deception attack, and θ(k) represents the deception attack signal. The gain matrix of the asynchronous controller. For matrix coefficients, when q(k) = η, ζ(k) is a random variable that follows a Bernoulli distribution.

[0044] Furthermore, determining the asynchronous controller parameters based on the designed observation mode-dependent asynchronous controller includes:

[0045] There exists a scalar Symmetric matrix matrix when When, the inequality equation is satisfied

[0046]

[0047]

[0048] in,

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059] Based on the obtained matrix Determine the gain matrix of the asynchronous controller

[0060] The second aspect provides an asynchronous control device for a multimodal power system, including a processor and a memory, wherein the processor executes program data stored in the memory to implement an asynchronous control method for the multimodal power system.

[0061] The third aspect provides a readable medium for storing control program data, wherein the control program data, when executed by a processor, implements an asynchronous control method for a multimodal power system.

[0062] The beneficial effects of this invention are as follows:

[0063] Using a hidden semi-Markov model to describe a multimodal power system model under asynchronous mechanism has strong hybridity, randomness and modal nonsynchronicity, and can describe its dynamic characteristics well.

[0064] By utilizing available information about system transition modes and the probability of spoofing attacks, an asynchronous control law related to the observation mode is designed to ensure the stability of the power system and accurately describe the dynamic characteristics of the multimodal power system under the asynchronous mechanism. This effectively suppresses the impact of spoofing attacks on the power system, solves the asynchronous control problem of multimodal power systems, and improves the security performance of the power system. Attached Figure Description

[0065] Figure 1 A flowchart of an asynchronous control method for a multimodal power system;

[0066] Figure 2 Control input graph under deception attack;

[0067] Figure 3 This is a state trajectory diagram of the power system. Detailed Implementation

[0068] Exemplary embodiments of this disclosure will now be described in more detail with reference to the accompanying drawings.

[0069] Example

[0070] See Figure 1 This invention provides an asynchronous control method for a multimodal power system, the specific implementation steps of which are as follows:

[0071] Step 1: Establish a discrete-time hidden semi-Markov jump system for a multimodal power system;

[0072] The multimodal power system mainly considers single units connected to an infinite bus, which is represented by the Thevenin equivalent circuit of a large interconnected power system. Based on the single-unit power system of the infinite bus, the dynamic model is established as follows:

[0073]

[0074]

[0075]

[0076]

[0077] The variables are described in the table below:

[0078]

[0079]

[0080] The state-space equations of the multimodal power system, based on the dynamic model, are as follows:

[0081]

[0082]

[0083]

[0084]

[0085] Where z(t) represents the system state and u(t) represents the control input. Let Δδ and Δω be the matrix coefficients, respectively, and let ΔE' be the deviation of the rotor angle and the deviation of the rotor relative speed. q ΔE fd K1, K2, K3…K6 are the deviations of the transient electromotive force on the q-axis and the generator excitation voltage, respectively, and are the linearization model constants of the synchronous motor.

[0086] Furthermore, the parameter values ​​of the system under study are as follows:

[0087] 1) Synchronous motor parameters: x' d =0.32pu, x d =1.6pu, x q =1.55pu,T' do =6s,x e =0.4pu, M=10s, ω0=π×50rad / s;

[0088] 2) Exciter amplifier parameters: k E =50,T E =0.05s;

[0089] 3) Line reactance: L1 = L2 = 0.8.

[0090] Based on the state-space equations, the stochastic topology changes of the power system are represented by a semi-Markov chain, and a discrete-time hidden semi-Markov transition system of the multimodal power system is established:

[0091]

[0092] Where z(k)∈R n Representing the system state, u(k)∈R m Indicates control input, Let {q(k), k≥0} be the matrix coefficients, and let {q(k), k≥0} be a discrete-time semi-Markov chain. Take the value from the middle.

[0093] Based on the above parameter values, we obtain and The fitted data are as follows:

[0094]

[0095]

[0096]

[0097]

[0098] Step 2: Design mode transition probabilities that depend on dwell time, based on the discrete-time hidden semi-Markov jump system.

[0099] definition In the first The second jump and the first The dwell time between the transitions, and It is the first At the moment of the next jump, and k0 = 0, It is the first The mode of the system at the time of the next transition;

[0100] Given a matrix Given a discrete-time semi-Markov kernel, the mode transition probability... And depends on the length of stay and meets the requirements.

[0101]

[0102] Where, δ ηv It is the residence time probability density function.

[0103] Step 3: Determine the emission probability of the observed mode based on the designed mode transition probability;

[0104] Define the transition probability density function that depends on the dwell time of the current mode and the next mode as follows:

[0105]

[0106] consider Where the mode transition probability ξ 12 =1,ξ 21 =1, probability density function The upper limit of the length of stay is

[0107] Introduction This indicates the system's dwell time in the current mode, and The dwell time of the current mode Independent of the number of transitions Depends on sampling time k; observation mode In finite sets Take the value from;

[0108] For any system mode Suppose there exists a finite set and Where H η ≥1 indicates that in the subset The number of elements in the middle.

[0109] The emission probability of the observed mode is determined as follows:

[0110]

[0111]

[0112] in, This is expressed as the system mode q(k) = η when the th... Secondary observation mode, Let be the emission probability matrix.

[0113] Furthermore, the emission probability matrix is ​​fitted with data based on the dwell time as follows:

[0114]

[0115] Step 4: Based on the impact of deception attacks on multimodal power systems, establish a deception attack model as follows:

[0116] z ζ (k)=z(k)+ζ(k)(-z(k)+θ(k))

[0117] Among them, z ζ θ(k) represents the actual signal under the influence of the deception attack, θ(k) represents the deception attack signal, and θ(k) is a known positive constant. Under the condition of satisfying

[0118] ζ(k) is a random variable and follows a Bernoulli distribution: When ζ(k) = 0, the actual control input signal is successfully transmitted in the system; when ζ(k) = 1, the deception attack signal replaces the actual control input signal.

[0119] Further, the parameters of the deception attack model are obtained as follows:

[0120] Based on the deception attack model, the closed-loop system of the discrete-time hidden semi-Markov transition system under the deception attack is obtained as follows:

[0121]

[0122] Where z(k)∈R n Representing the system state, u(k)∈R m Indicates control input, z ζ θ(k) represents the actual signal under the influence of the deception attack, and θ(k) represents the deception attack signal. The gain matrix of the asynchronous controller. For matrix coefficients, when q(k) = η, ζ(k) is a random variable that follows a Bernoulli distribution.

[0123] Step 5: Based on the discrete-time hidden semi-Markov jump system and the spoofing attack model, design an asynchronous controller that depends on the observation mode;

[0124] The formula for the asynchronous controller that depends on the observation mode is as follows:

[0125]

[0126] in, Let z be the gain matrix of the asynchronous controller, making the discrete-time hidden semi-Markov jump system stable; ζ (k) represents the actual signal under the influence of a deception attack; u(k)∈R m This indicates a control input.

[0127] Step 6: Determine the asynchronous controller parameters based on the designed asynchronous controller that depends on the observation mode;

[0128] For any multimodal power system modes and observation mode There exists a scalar Symmetric matrix matrix when When, the inequality equation is satisfied

[0129]

[0130]

[0131] in,

[0132]

[0133]

[0134]

[0135]

[0136]

[0137]

[0138]

[0139]

[0140]

[0141]

[0142] Based on the determined discrete-time semi-Markov kernel, emission probability matrix, and deception attack model parameters, the matrix can be obtained. Determine the gain matrix of the asynchronous controller that satisfies the system stability objective.

[0143]

[0144]

[0145] like Figure 2 , Figure 3 As shown, Figure 2 This demonstrates that the control input of the asynchronous controller proposed in this invention converges to the origin under a deception attack; Figure 3 This demonstrates that the state trajectory of the power system reaches an equilibrium point under asynchronous control, which can effectively suppress the impact of deception attacks on the power system and improve the security of the power system.

[0146] Furthermore, the present invention provides an asynchronous control device for a multimodal power system, including a processor and a memory, wherein the processor executes program data stored in the memory to implement the aforementioned asynchronous control method for a multimodal power system.

[0147] Finally, the present invention provides a readable medium for storing control program data, wherein the control program data, when executed by a processor, implements the asynchronous control method for a multimodal power system.

Claims

1. An asynchronous control method for a multimodal power system, characterized in that, Includes the following steps: The discrete-time hidden semi-Markov jump system of a multimodal power system is established as follows: ， in, Indicates the system status. Indicates control input, , It is a discrete-time semi-Markov chain, in Take the value from; Based on discrete-time hidden semi-Markov transition systems, design mode transition probabilities that depend on dwell time, including: definition In the first The second jump and the first The dwell time between the transitions, and ; It is the first The moment of the next jump, and , It is the first The system mode at the time of the next transition; Given a matrix For discrete-time semi-Markov kernels, the mode transition probabilities And depends on the length of stay and meets the requirements ， in, It is the residence time probability density function; Based on the designed mode transition probabilities, determine the emission probabilities of the observed modes, including: Define the transition probability density function that depends on the dwell time of the current mode and the next mode as follows: ， Introduction This indicates the system's dwell time in the current mode, and ; Observation mode In finite sets Take the value from; For any system mode There exists a finite set and ,in Indicates in The number of elements in the middle. The emission probability of the observed mode is determined as follows: ， ， in, This is expressed as when the system mode is Time Secondary observation mode, Here is the emission probability matrix; Based on the impact of deception attacks on multimodal power systems, a deception attack model is established; Based on discrete-time hidden semi-Markov jump system and spoofing attack model, an asynchronous controller that depends on observation mode is designed. Based on the designed asynchronous controller that depends on the observation mode, determine the asynchronous controller parameters, including: There exists a scalar symmetric matrix ,matrix , , , ,when When, the inequality equation is satisfied ， in, , , , , , , , , , ， ,when hour, ; Based on the obtained matrix Determine the gain matrix of the asynchronous controller. .

2. The asynchronous control method for a multimodal power system according to claim 1, characterized in that, The deception attack model established based on the impact of deception attacks on multimodal power systems is as follows: ， in, The actual signal under the influence of a deception attack. z ( k ) indicates the system state. To deceive the attack signal, and in the case of known normal numbers Under the condition of satisfying ;random variable Follows Bernoulli distribution ， ， when At that time, the actual control input signal was successfully transmitted in the system; when At that time, the deceptive attack signal replaces the actual control input signal.

3. The asynchronous control method for a multimodal power system according to claim 1, characterized in that, The asynchronous controller designed based on the discrete-time hidden semi-Markov transition system and the spoofing attack model is as follows: ， in, Let be the gain matrix of the asynchronous controller, which makes the discrete-time hidden semi-Markov jump system stable; The actual signal under the influence of a deception attack; This indicates a control input.

4. The asynchronous control method for a multimodal power system according to claim 3, characterized in that, The closed-loop system of the discrete-time hidden semi-Markov transition system under deception attack is as follows: ， in, Indicates the system status. Indicates control input, The actual signal under the influence of a deception attack. To deceive the attack signal, The gain matrix of the asynchronous controller. ,when hour, ; For random variables that follow a Bernoulli distribution , .

5. An asynchronous control device for a multimodal power system, characterized in that, It includes a processor and a memory, wherein the processor executes program data stored in the memory to implement an asynchronous control method for a multimodal power system as described in any one of claims 1-4.

6. A readable medium, characterized in that, Used to store control program data, wherein the control program data, when executed by a processor, implements an asynchronous control method for a multimodal power system as described in any one of claims 1-4.

Images