Load frequency sliding mode defense control method and device facing spoofing attack, computer equipment, readable storage medium and program product

Abstract

The invention relates to a spoofing attack-oriented load frequency sliding mode defense control method and device, computer equipment, a computer readable storage medium and a computer program product, relates to the technical field of power grid dispatching, and can improve the robustness of frequency regulation. The method comprises the following steps: determining a load frequency control model of a power system based on pre-acquired operation parameters, pulse interference characteristics and time-varying delay characteristics of the power system; the pulse interference characteristics are used for describing spoofing attack behaviors in the cross-domain communication network; based on a load frequency control model, constructing an integral type sliding mode surface containing a system state integral item; based on the load frequency control model and the integral sliding mode surface, determining a sliding mode control strategy aiming at the time lag influence corresponding to the historical state deviation and the time-varying time delay characteristic under the condition of meeting the constraint condition of the Lyapunov stability criterion; and based on the sliding mode control strategy, generating a frequency adjustment instruction for the power system.

Description

Technical Field

[0001] This application relates to the field of power grid dispatching technology, and in particular to a load frequency sliding mode defense control method, device, computer equipment, computer-readable storage medium and computer program product for deception attacks. Background Technology

[0002] With the advancement of multi-domain interconnection in power systems, load frequency control increasingly relies on networked communication. However, the open cross-domain communication environment exposes the system to severe deception attacks, where attackers often implement sudden, pulse-like interference by tampering with or falsifying measurement data.

[0003] Traditional load frequency control methods are typically based on the assumption that the measured signals are true and reliable, and are mainly designed for normal load disturbances, random noise, or communication delays. They are difficult to effectively deal with malicious data tampering. When subjected to spoofing attacks, existing control strategies often fail to maintain the dynamic consistency of the system, which can easily lead to drastic frequency fluctuations or even system instability. Summary of the Invention

[0004] Therefore, it is necessary to provide a load frequency sliding mode defense control method, device, computer equipment, computer-readable storage medium, and computer program product for addressing the above-mentioned technical problems.

[0005] Firstly, this application provides a load frequency sliding mode defense control method for deception attacks, including:

[0006] Based on the pre-acquired operating parameters, pulse interference characteristics, and time-varying delay characteristics of the power system, a load frequency control model for the power system is determined; the pulse interference characteristics are used to describe spoofing attack behavior in cross-domain communication networks.

[0007] Based on the load frequency control model, an integral sliding surface containing a system state integral term is constructed; the system state integral term is used to accumulate historical state deviations, which are determined based on the system state abrupt changes caused by the deception attack on the power system.

[0008] Based on the load frequency control model and the integral sliding surface, and under the constraint of the Lyapunov stability criterion, a sliding mode control strategy is determined to address the time delay effects corresponding to the historical state deviation and the time-varying time delay characteristics.

[0009] Based on the sliding mode control strategy, frequency regulation commands for the power system are generated.

[0010] In one embodiment, the power system includes a generator, a speed governor, a steam turbine, and an energy storage unit; determining the load frequency control model of the power system based on pre-acquired operating parameters, pulse interference characteristics, and time-varying delay characteristics includes:

[0011] Based on the operating parameters, the state vector of the power system is determined; the state vector includes frequency deviation, frequency preset value deviation, turbine valve position deviation, generator mechanical power deviation, and energy storage unit output power deviation.

[0012] Based on the control input to the power system, the state vector, and the time-varying delay characteristics, the continuous dynamic equation of the power system is determined;

[0013] The instantaneous switching process of the power system is determined based on the pulse frequency and pulse intensity indicated by the pulse interference characteristics; the pulse frequency and pulse intensity respectively satisfy preset pulse frequency conditions and pulse intensity conditions.

[0014] Based on the continuous dynamic equations and the instantaneous jump process, the load frequency control model is determined.

[0015] In one embodiment, constructing an integral sliding surface containing system state integral terms based on the load frequency control model includes:

[0016] Based on the state vector of the load frequency control model and the preset sliding mode control parameters, the linear transformation term is determined;

[0017] Based on the operating parameters, the system dynamic parameters and input coupling parameters of the power system are determined, and based on the system dynamic parameters, the input coupling parameters, and the state feedback gain, the target closed-loop dynamic characteristics are determined; the state feedback gain satisfies a preset state feedback gain condition.

[0018] Based on the target closed-loop dynamic characteristics and the state vector, the state integral term is determined;

[0019] The integral sliding surface is determined based on the linear transformation term and the state integral term.

[0020] In one embodiment, the sliding mode control strategy, based on the load frequency control model and the integral sliding surface, and under the constraint of the Lyapunov stability criterion, is determined to address the time delay effects corresponding to the historical state deviation and the time-varying delay characteristics, including:

[0021] Based on the historical state deviation, the instantaneous change trend of the integral sliding surface is determined;

[0022] Based on the instantaneous change trend and the preset sliding mode control conditions, the time delay deviation equation corresponding to the time delay effect is determined;

[0023] Obtain the first constraint condition of the Lyapunov stability criterion containing the state vector;

[0024] Based on the load frequency control model and the time delay deviation equation, and under the condition of satisfying the first constraint, a sliding mode control strategy is determined for the time delay effect corresponding to the time-varying time delay characteristics.

[0025] In one embodiment, the sliding mode control strategy, based on the load frequency control model and the integral sliding surface, and under the constraint of the Lyapunov stability criterion, is determined to address the time delay effects corresponding to the historical state deviation and the time-varying delay characteristics, including:

[0026] Obtain a finite time that meets the preset control time conditions;

[0027] Based on finite time, obtain the second constraint condition of the Lyapunov stability criterion involving the integral sliding surface;

[0028] Based on the load frequency control model and the integral sliding surface, and under the condition of satisfying the second constraint, a sliding mode control strategy is determined to address the time delay effects corresponding to the historical state deviation and the time-varying delay characteristics.

[0029] In one embodiment, based on the load frequency control model and the integral sliding surface, and under the condition of satisfying the second constraint, a sliding mode control strategy is determined for the time delay effects corresponding to the historical state deviation and the time-varying delay characteristics, including:

[0030] Based on the state vector and state feedback gain of the load frequency control model, the reference state feedback control quantity is determined.

[0031] Based on the energy amplitude of the state vector under the time-varying delay characteristics and the preset time delay boundary parameters, the time delay effect compensation gain is determined;

[0032] Based on the polarity direction of the historical state deviation and the time delay effect compensation gain, the adaptive sliding mode control quantity is determined;

[0033] Based on the baseline state feedback control quantity and the adaptive sliding mode control quantity, the sliding mode control strategy corresponding to the finite time is determined under the condition that the second constraint is satisfied.

[0034] Secondly, this application also provides a load frequency sliding mode defense control device for deception attacks, comprising:

[0035] The load frequency control model construction module is used to determine the load frequency control model of the power system based on the pre-acquired operating parameters, pulse interference characteristics, and time-varying delay characteristics of the power system; the pulse interference characteristics are used to describe spoofing attack behavior in cross-domain communication networks.

[0036] An integral sliding surface establishment module is used to construct an integral sliding surface containing system state integral terms based on the load frequency control model; the system state integral terms are used to accumulate historical state deviations, which are determined based on the system state abrupt changes caused by the deception attack on the power system.

[0037] The sliding mode control strategy determination module is used to determine the sliding mode control strategy for the time delay effects corresponding to the historical state deviation and the time-varying time delay characteristics based on the load frequency control model and the integral sliding surface, while satisfying the constraints of the Lyapunov stability criterion.

[0038] The frequency regulation command determination module is used to generate frequency regulation commands for the power system based on the sliding mode control strategy.

[0039] Thirdly, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps:

[0040] Based on the pre-acquired operating parameters, pulse interference characteristics, and time-varying delay characteristics of the power system, a load frequency control model for the power system is determined; the pulse interference characteristics are used to describe spoofing attack behavior in cross-domain communication networks.

[0041] Based on the load frequency control model, an integral sliding surface containing a system state integral term is constructed; the system state integral term is used to accumulate historical state deviations, which are determined based on the system state abrupt changes caused by the deception attack on the power system.

[0042] Based on the load frequency control model and the integral sliding surface, and under the constraint of the Lyapunov stability criterion, a sliding mode control strategy is determined to address the time delay effects corresponding to the historical state deviation and the time-varying time delay characteristics.

[0043] Based on the sliding mode control strategy, frequency regulation commands for the power system are generated.

[0044] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the following steps:

[0045] Based on the pre-acquired operating parameters, pulse interference characteristics, and time-varying delay characteristics of the power system, a load frequency control model for the power system is determined; the pulse interference characteristics are used to describe spoofing attack behavior in cross-domain communication networks.

[0046] Based on the load frequency control model, an integral sliding surface containing a system state integral term is constructed; the system state integral term is used to accumulate historical state deviations, which are determined based on the system state abrupt changes caused by the deception attack on the power system.

[0047] Based on the load frequency control model and the integral sliding surface, and under the constraint of the Lyapunov stability criterion, a sliding mode control strategy is determined to address the time delay effects corresponding to the historical state deviation and the time-varying time delay characteristics.

[0048] Based on the sliding mode control strategy, frequency regulation commands for the power system are generated.

[0049] Fifthly, this application also provides a computer program product, including a computer program that, when executed by a processor, performs the following steps:

[0050] Based on the pre-acquired operating parameters, pulse interference characteristics, and time-varying delay characteristics of the power system, a load frequency control model for the power system is determined; the pulse interference characteristics are used to describe spoofing attack behavior in cross-domain communication networks.

[0051] Based on the load frequency control model, an integral sliding surface containing a system state integral term is constructed; the system state integral term is used to accumulate historical state deviations, which are determined based on the system state abrupt changes caused by the deception attack on the power system.

[0052] Based on the load frequency control model and the integral sliding surface, and under the constraint of the Lyapunov stability criterion, a sliding mode control strategy is determined to address the time delay effects corresponding to the historical state deviation and the time-varying time delay characteristics.

[0053] Based on the sliding mode control strategy, frequency regulation commands for the power system are generated.

[0054] The aforementioned load frequency sliding mode defense control method, device, computer equipment, computer-readable storage medium, and computer program product for deception attacks determine the load frequency control model of the power system based on pre-acquired operating parameters, impulse interference characteristics, and time-varying delay characteristics of the power system. Impulse interference characteristics are used to describe deception attack behavior in cross-domain communication networks. Based on the load frequency control model, an integral sliding surface containing a system state integral term is constructed. The system state integral term is used to accumulate historical state deviations, which are determined based on the system state abrupt changes caused by the deception attack. Based on the load frequency control model and the integral sliding surface, and under the constraint of the Lyapunov stability criterion, a sliding mode control strategy is determined to address the time delay effects corresponding to historical state deviations and time-varying delay characteristics. Based on the sliding mode control strategy, frequency adjustment commands for the power system are generated. In this application, a high-fidelity load frequency control model is constructed by modeling spoofing attacks in cross-domain communication networks as pulse interference characteristics and incorporating time-varying delay features, effectively solving the problem of system model mismatch in complex network environments. By utilizing an integral sliding mode surface containing system state integral terms, historical state deviations caused by spoofing attacks are accumulated and dynamically compensated, eliminating steady-state errors caused by instantaneous state changes. Furthermore, the sliding mode control strategy is solved based on strict constraints of the Lyapunov stability criterion, theoretically guaranteeing the exponential stability of the closed-loop system in the face of both pulse attacks and time-varying delay disturbances, thereby achieving high robustness and dynamic security defense of power system frequency regulation. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the description of the embodiments of this application or related technologies will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 This is a flowchart illustrating a load frequency sliding mode defense control method against deception attacks in one embodiment.

[0057] Figure 2 This is a schematic diagram of the physical power system architecture in one embodiment;

[0058] Figure 3 This is a schematic diagram of the dynamic response of a power system containing energy storage units under non-sliding mode control in one embodiment;

[0059] Figure 4 This is a schematic diagram of the dynamic response of a power system containing an energy storage unit under sliding mode control in one embodiment;

[0060] Figure 5 This is a structural block diagram of a load frequency sliding mode defense control device against deception attacks in one embodiment.

[0061] Figure 6 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0062] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0063] It should be noted that the terms "first," "second," etc., used in this application can be used to describe various elements, but these elements are not limited by these terms. These terms are only used to distinguish the first element from the second element. The terms "comprising" and "having," and any variations thereof, used in this application, are intended to cover non-exclusive inclusion. The term "multiple" used in this application refers to two or more. The term "and / or" used in this application refers to one of the embodiments, or any combination of multiple embodiments.

[0064] The load frequency sliding mode defense control method against deception attacks provided in this application embodiment can be applied to power systems, which may include physical power systems, cross-domain communication networks, and load frequency control centers.

[0065] The physical power system can be any size interconnected power grid area or microgrid system requiring frequency regulation. It includes, but is not limited to, various power generation devices with frequency response capabilities (such as thermal power, hydropower, nuclear power, or new energy units such as wind and solar power) and energy storage and regulation resources. These physical components collect system operating status data (such as frequency deviation, power deviation, etc.) in real time through sensors (such as phasor measurement units). It should be noted that the embodiments of this application do not limit the specific power generation form, topology, or capacity of the power system.

[0066] Cross-domain communication networks are used to connect physical power systems and load frequency control centers, enabling information exchange through the uploading of measurement data and the issuance of control commands. Considering the wide-area distribution of modern power systems, these communication networks are typically open or semi-open cross-domain interconnection networks. Their physical media can be wired networks (such as fiber optics, power line carriers), wireless networks (such as 5G, 4G, WiFi, satellite communication), or combinations thereof; their communication protocols can be Modbus or general network protocols based on TCP / IP. Due to the characteristics of cross-domain transmission and network bandwidth limitations, data inevitably exhibits time-varying and delay characteristics during transmission. Simultaneously, the open network environment makes communication links easily exposed to malicious attackers, leading to data tampering or the injection of false information, i.e., deception attacks. In some embodiments, in this heterogeneous and complex communication environment, the security of power system frequency control faces new challenges. Specifically, during multi-domain interconnection and cross-gateway communication, attackers can forge, tamper with, or delay measurement data to impose misleading inputs on the control center, forming deception attacks with suddenness and stealth. Such attacks typically manifest as pulse interference, causing instantaneous deviations in system measurement signals, which in turn lead to erroneous responses in the frequency regulation circuit, and in severe cases, can cause system oscillations or even instability.

[0067] The load frequency control center can be an implementing entity for the defensive control method of this application. Specifically, it can be one or more servers or terminals deployed in the power grid dispatch center, or a dispatch system integrating servers and terminals. This control center receives system status data transmitted via a cross-domain communication network, which may contain attack interference and delays. Based on the load frequency control model and sliding mode control strategy of this application, it calculates and generates frequency adjustment commands, which are then fed back to the actuators (such as speed governors) of the physical power system via the communication network, thereby achieving robust control of the power system frequency.

[0068] In one exemplary embodiment, such as Figure 1 As shown, a load frequency sliding mode defense control method for deception attacks is provided, applied to a server deployed in a load frequency control center, including the following steps S102 to S108. Wherein:

[0069] Step S102: Based on the pre-acquired operating parameters, pulse interference characteristics, and time-varying delay characteristics of the power system, determine the load frequency control model of the power system; the pulse interference characteristics are used to describe spoofing attack behavior in cross-domain communication networks.

[0070] Among them, the operating parameters can be scalar or vector data that characterize the inherent physical properties and dynamic response capabilities of each physical component in the power system. When called by the server, they are used as the basic coefficients to construct the system state equations to reflect the frequency change rate and recovery speed of the system after being disturbed. Specifically, they can cover the rotational inertia of the generator set, the frequency sensitivity of the system load, the response time constant of the governor and turbine, and the charging and discharging characteristic parameters of the energy storage unit.

[0071] Impulse interference features can be characteristic data used to describe spoofing attacks that occur in cross-domain communication networks. They are usually modeled as pulse functions or sequences with specific intensity and occurrence time, used to characterize the instantaneous jump effect of the attacker's instantaneous, discontinuous tampering of measurement signals or control commands on the system state trajectory.

[0072] Time-varying delay characteristics can be used to characterize the time lag parameters that dynamically change over time when data is exchanged between different domains. They are usually determined based on the congestion level of the communication network or changes in the routing path, and are used to reflect the coupling effect of cross-domain transmission on the real-time performance of signals.

[0073] Determining a load frequency control model for a power system can specifically include constructing a state-space equation comprising state variables, control inputs, and disturbance terms. The state-space equation explicitly includes an impulse disturbance term characterized by impulse disturbance features, and a time-delay state term characterized by time-varying delay features. The impulse disturbance term is configured to describe the instantaneous abrupt change in the system state vector at the moment of an attack, while the time-delay state term is configured to describe the coupled influence of historical system states on the evolution of the current state. In this way, the model can comprehensively describe the frequency response behavior of the power system under normal operation and under cyberattacks.

[0074] Optionally, the load frequency control model can be constructed as a hybrid dynamic system model. In this model, the server divides the system behavior into two processes: continuous flow and discrete jumps. The continuous flow process describes the physical response of the generator and governor in a non-attack state, while the discrete jump process is specifically used to describe the instantaneous reset of the system state caused by pulse interference characteristics. This modeling approach can more accurately cover sparse network attack scenarios, treating attack behavior as a special dynamic mode of the system rather than simply external noise.

[0075] Step S104: Based on the load frequency control model, construct an integral sliding surface containing system state integral terms; the system state integral terms are used to accumulate historical state deviations, which are determined based on the system state changes caused by deception attack behavior.

[0076] The integral sliding surface can be a dynamic hyperplane function used to constrain the direction of the evolution of the power system state trajectory. It is configured as a combinational logic structure containing linear and integral terms to ensure that the system state can converge to the equilibrium point along a predetermined path after encountering a disturbance.

[0077] The system state integral term can be the cumulative result of the system state variables in the time dimension. It is calculated based on historical state data before the current moment and is used to introduce the memory feature of the system into the mathematical model, thereby eliminating steady-state errors caused by model uncertainty or persistent attack interference.

[0078] Historical state deviation can be a sequence of differences between the actual operating state of the system and the ideal reference state. It directly reflects the continuous impact of the instantaneous change in system state caused by deception attack behavior (i.e., impulse interference) on the time axis, and is smoothed under integral action to suppress high-frequency jitter.

[0079] Specifically, based on the aforementioned load frequency control model (such as the state-space equations), the server designs a sliding mode surface function. In this process, the server first determines a linear transformation matrix that allows the closed-loop system poles to be placed in the left half-plane, and multiplies this matrix by the current system state vector to obtain a linear transformation term. Subsequently, the server integrates the system state deviations at historical moments to generate a system state integral term. Finally, the server linearly combines the linear transformation term and the system state integral term (e.g., by subtraction or weighted summation) to construct an integral sliding mode surface. The set of zero levels on this sliding mode surface represents the ideal dynamic trajectory of the system.

[0080] Optionally, the construction process of the integral sliding surface can be non-static. The server can preset a set of dynamic weight coefficients associated with system performance indicators (such as damping ratio and natural oscillation frequency), and dynamically adjust the weight of the integral term according to the real-time monitored attack intensity (i.e., the amplitude of the pulse interference). When a large-amplitude pulse attack is detected, causing a strong change in system state, the server can automatically increase the weight of the integral term to enhance the system's "smoothing" and "memory" capabilities for sudden deviations, preventing the controller from overreacting to instantaneous jumps.

[0081] Optionally, the calculation interval for the system state integral term can be a finite time domain based on a sliding time window, rather than a full-time domain accumulation starting from the system startup time. The server can integrate only the historical state deviation within the most recent time window (e.g., the last 5 power frequency cycles) to reduce the lag effect of outdated data on the current control strategy, thereby improving the dynamic tracking speed of the sliding surface itself to changes in system state.

[0082] Step S106: Based on the load frequency control model and the integral sliding surface, and under the constraint of the Lyapunov stability criterion, determine the sliding mode control strategy for the time delay effects corresponding to the historical state deviation and time-varying time delay characteristics.

[0083] Among them, the sliding mode control (SMC) strategy can be a variable structure control law used to drive the state trajectory of the power system from any initial position to move towards and maintain the sliding on a preset integral sliding surface. It can be configured as a set of nonlinear control command generation rules containing switching logic, aiming to forcibly constrain the evolution direction of the system state by switching the control input at high frequency, so that it is invariant to parameter perturbations and external disturbances.

[0084] Lyapunov stability criteria can be used as a sufficient mathematical condition to determine whether a dynamic system can automatically recover to equilibrium after being disturbed. It can be constructed based on the positive definiteness of the energy function and the negative definiteness of its derivative, and is used to provide mathematical boundary constraints to ensure the asymptotic stability of the closed-loop system when designing control laws.

[0085] The control strategy for the effects of time delay specifically refers to introducing a compensation term into the control law to offset or compensate for the state lag effect caused by cross-domain communication transmission delay, so as to prevent the system from diverging due to phase lag caused by time delay.

[0086] Specifically, based on the aforementioned load frequency control model and integral sliding surface, the server first constructs a Lyapunov candidate function (e.g., a quadratic energy function) containing sliding surface variables. Then, the server differentiates this candidate function with respect to time and substitutes the state equations from the load frequency control model into the derivative expression. To meet the system stability requirement (i.e., derivative less than zero), the server parses the control input expression that can counteract the effects of uncertainties, impulse disturbances, and time delays in the model, thereby determining the sliding mode control strategy. This strategy can consist of two parts: an equivalent control component, used to maintain the system's motion on the sliding surface, primarily counteracting known nominal system dynamics and time delay effects; and a switching control component, used to overcome system uncertainties and historical state deviations caused by impulse disturbances, driving the system state to traverse phase space to reach the sliding surface.

[0087] Optionally, to address the jitter issues that may exist in traditional sliding mode control, the server can choose an exponential or power-law approaching law to design the control strategy. This allows the system state to approach the sliding surface at a faster speed when it is far from the sliding surface, and automatically decrease the approaching speed when it is close to the sliding surface. Furthermore, to address historical state deviations, the server can introduce an adaptive gain adjustment mechanism into the control strategy. This dynamically adjusts the switching gain based on the integral value of the historical deviation, ensuring that abrupt deviations caused by deception attacks are suppressed while minimizing the amplitude of the control input to avoid excessive mechanical shock to the actuators.

[0088] Step S108: Based on the sliding mode control strategy, generate frequency regulation commands for the power system.

[0089] The frequency regulation command can be a control signal used to drive the physical actuators of the power system. It is generated by the dimensionless control quantity calculated by the server based on the sliding mode control law, after digital-to-analog conversion or protocol encapsulation, and is configured to be transmitted to the edge controller (such as the governor controller of the generator set or the converter controller of the energy storage unit) through the cross-domain communication network to adjust the mechanical power output of the prime mover or the active power throughput of the energy storage device, thereby physically changing the frequency response trajectory of the power system.

[0090] Specifically, during its operating cycle, the server collects the current state vector of the power system in real time (including frequency deviation, power deviation, etc.) and substitutes it into the sliding mode control strategy (i.e., the mathematical expression of the sliding mode control law) determined in the previous steps for calculation, obtaining the target control quantity that can offset the effects of pulse interference and time delay. Subsequently, the server maps this target control quantity into specific physical operating parameters. For example, for generator sets, the server converts it into a governor valve opening adjustment command; for energy storage units, the server converts it into an inverter active power reference value command. Finally, the server packages and sends these commands through the communication interface, forming a closed-loop control.

[0091] In this embodiment, a high-fidelity load frequency control model is constructed by modeling spoofing attacks in cross-domain communication networks as pulse interference characteristics and incorporating time-varying delay features, effectively solving the problem of system model mismatch in complex network environments. By utilizing an integral sliding mode surface containing system state integral terms, historical state deviations caused by spoofing attacks are accumulated and dynamically compensated, eliminating steady-state errors caused by instantaneous state changes. Furthermore, the sliding mode control strategy is solved based on strict constraints of the Lyapunov stability criterion, theoretically ensuring the exponential stability of the closed-loop system when facing both pulse attacks and time-varying delay disturbances, thereby achieving high robustness and dynamic security defense of power system frequency regulation.

[0092] In one embodiment, the power system includes a generator, a speed governor, a steam turbine, and an energy storage unit; based on pre-acquired operating parameters, pulse interference characteristics, and time-varying delay characteristics of the power system, a load frequency control model for the power system is determined, including:

[0093] Based on operating parameters, the state vector of the power system is determined; the state vector includes frequency deviation, frequency preset value deviation, turbine valve position deviation, generator mechanical power deviation, and energy storage unit output power deviation. Based on the control inputs, state vector, and time-varying delay characteristics of the power system, the continuous dynamic equations of the power system are determined. Based on the pulse frequency and pulse intensity indicated by the pulse interference characteristics, the instantaneous jump process of the power system is determined; the pulse frequency and pulse intensity satisfy preset pulse frequency and pulse intensity conditions, respectively. Based on the continuous dynamic equations and the instantaneous jump process, the load frequency control model is determined.

[0094] Here, the state vector can be a minimal set of variables used to fully characterize the operating status of the power system at any given time. It is constructed by the server based on real-time monitoring data of each physical component within the system and is used to define the system's location in mathematical space. In one embodiment, as in... Figure 2 In the power system shown, the state vector may include frequency deviation reflecting the power grid supply and demand balance, frequency preset value deviation reflecting the control target error, turbine valve position deviation and generator mechanical power deviation reflecting the actuator action range, and energy storage unit output power deviation reflecting the flexibility resource status.

[0095] Continuous dynamic equations can be differential equations that describe the continuous evolution of the state of a power system over time in a period of time without instantaneous attack transitions. They are constructed based on the physical inertia, damping characteristics, and network transmission delay of the power system and are used to characterize the smooth motion trajectory of the system under the combined action of normal physical laws and communication delays.

[0096] A sudden change process can be a mathematical model that describes the discontinuous change in the system state within a very short time when a deception attack occurs. It originates from the attacker's malicious tampering or injection of data and is modeled by the server as a sudden increment of the state vector at the moment of the attack. This increment is limited by the attacker's capability boundary.

[0097] Specifically, in such Figure 2 In the power system shown, the server can identify key physical components, including generators that provide basic inertia, speed governors that regulate speed, steam turbines that convert energy, and energy storage units that handle rapid power throughput. The server then establishes the physical coupling relationships between these components and extracts the differences between each component's deviation from its rated operating point, combining them into a multi-dimensional column vector, which serves as the core variable of the control model.

[0098] In one embodiment, a state-space mathematical model of the power system is established. This model treats the main generator, governor, turbine, and energy storage unit as a unified dynamic object, and the power system model can be expressed as formula (1):

[0099] (1)

[0100] in , , , , and These are frequency deviation, frequency preset value deviation, turbine valve position deviation, generator mechanical power deviation, and energy storage unit output power deviation, respectively. , , , , , and These represent the equivalent inertial constant, damping coefficient, turbine time constant, governor time constant, droop coefficient, energy storage unit time constant, and unit adjustment factor, respectively. and These represent the participation ratios of the speed governor and the energy storage system, respectively, and their sum is 1.

[0101] Optionally, under this power system model, let State vector It can satisfy , , .in It is a regional control error signal. It is the frequency deviation factor.

[0102] Specifically, the server analyzes the generator rotor motion equations, the first-order inertial element of the speed governor, and the response characteristics of the energy storage unit based on Newton's second law and the transfer functions of each component. The server transforms these physical laws into a state-space form. In particular, the server introduces a time delay term into the equations. This term uses historical state data after subtracting the time-varying delay from the current moment to quantify the impact of signal lag caused by the communication network on the current system state derivative.

[0103] Alternatively, the continuous dynamic equation can be expressed as a functional differential equation of the following form, Equation (2):

[0104]

[0105] in, For system dynamic parameters, For the time-delay system matrix, Represents a time-varying transmission delay and satisfies , For input coupling parameters, To control the input.

[0106] Specifically, the server defines a series of discrete attack points in the model. At these specific moments, the system state no longer follows the evolutionary pattern of the aforementioned continuous dynamic equations, but instead is superimposed with an additional attack vector. The server sets constraints on the frequency of this attack and the energy magnitude of a single attack, that is, it limits the upper limit of the number of attacks per unit time and the maximum deviation modulus of a single attack on the system state, in order to conform to the objective law that attackers have limited resources in actual network attacks.

[0107] Alternatively, the instantaneous jump process and its constraints can be described by the following pulse system equations and inequalities: at the attack moment The system state satisfies formula (3):

[0108] (3)

[0109] in, Represents the pulse intensity (matrix) and satisfies the pulse intensity condition: and , This represents the upper bound of the attack intensity, indicating the maximum energy amplification factor of the attack. Simultaneously, it represents the pulse sequence of the attack. Pulse frequency condition (average dwell time constraint) must be met: .in, It is an interval The number of pulse (attack) points on the surface. It is a positive constant, and It is the average length of stay.

[0110] Specifically, the server determines the load frequency control model of formula (4) based on continuous dynamic equations and instantaneous jump processes:

[0111] (4)

[0112] In this embodiment, the load frequency control model including energy storage units established through the above steps explicitly considers the complex interference factors brought about by cross-domain communication networks. Specifically, the model accurately models unpredictable short-term spoofing injection behavior as a pulse-type disturbance term constrained by norm boundedness, and models signal lag caused by network congestion as a time-varying delay state term. Compared with traditional linear models that only consider Gaussian white noise or constant delay, the model constructed in this embodiment can more realistically reflect the dynamic response characteristics of modern power systems in a deeply integrated "cyber-physical" environment, providing a precise mathematical basis for the subsequent design of robust controllers that can tolerate data tampering and communication delays. This fundamentally solves the problem of system instability caused by model mismatch when facing network attacks using traditional control strategies.

[0113] In one embodiment, based on the load frequency control model, an integral sliding surface containing system state integral terms is constructed, including:

[0114] Based on the state vector of the load frequency control model and the preset sliding mode control parameters, the linear transformation term is determined; based on the operating parameters, the system dynamic parameters and input coupling parameters of the power system are determined, and based on the system dynamic parameters, input coupling parameters and state feedback gain, the target closed-loop dynamic characteristics are determined; the state feedback gain satisfies the preset state feedback gain condition; based on the target closed-loop dynamic characteristics and the state vector, the state integral term is determined; based on the linear transformation term and the state integral term, the integral sliding surface is determined.

[0115] The linear transformation term can be a fundamental geometric component used to project the system trajectory in the high-dimensional state space onto the low-dimensional sliding mode subspace. It can be obtained by performing matrix multiplication between the current system state vector and the pre-set sliding mode parameter matrix (i.e., sliding mode control parameters). It is used to define the slope or direction of the sliding surface in the state space, thereby determining the convergence speed of the system in the sliding mode.

[0116] The target closed-loop dynamic characteristics can be a matrix describing the expected dynamic behavior of the system during the ideal sliding mode motion phase, used to specify the equivalent dynamic characteristics (such as pole positions) of the system state when sliding on the sliding surface.

[0117] The state integral term can be a cumulative quantity reflecting the historical operating trajectory of the system. It is obtained by performing time integration on the weighted state vector at historical moments and is used to introduce a memory element in the control law to eliminate steady-state errors caused by model uncertainty or persistent deception attacks.

[0118] Specifically, the server reads a pre-configured sliding mode parameter matrix from the storage unit, the dimension of which matches the dimension of the system state vector. The server acquires the current system state data (such as frequency deviation, power deviation, etc.) in real time and multiplies it with the sliding mode parameter matrix to obtain a linear combination vector that reflects the degree of deviation of the current system state from the ideal equilibrium point.

[0119] Subsequently, the system dynamic parameters and input coupling parameters are extracted from the load frequency control model. Next, the server introduces a state feedback gain matrix that allows the system poles to be located in the left half-plane. The server multiplies the input matrix and the feedback gain matrix, then superimposes the result onto the system matrix to form a new composite matrix, which represents the ideal closed-loop dynamics of the system on the sliding surface. The server then uses this composite matrix to perform a weighted integration of all historical state vectors from the initial time step to the current time step, calculating the value of the integral term. Finally, based on the linear transformation term and the state integral term, the final integral sliding surface is determined through a combination of linear algebraic operations (such as subtraction).

[0120] Alternatively, the complete construction process of the integral sliding surface can be described by the following mathematical formula (5):

[0121] (5)

[0122] in, These are the sliding mode control parameters. For system dynamic parameters, For input coupling parameters, State feedback gain, For integration variables. State feedback gain. The selection must satisfy the following condition: The eigenvalues ​​all have negative real parts (i.e., they satisfy the Lyapunov stability requirement).

[0123] In some embodiments, state feedback gain The selection must satisfy the following constraints ,in, , , It is a boundary parameter matrix, which in some embodiments can be represented as , that is, the identity matrix.

[0124] In this embodiment, by constructing an integral sliding surface of the above form, this application introduces an integral action for the system state into the sliding mode control design. Compared with a traditional linear sliding surface, this integral term can effectively accumulate and eliminate steady-state deviations caused by cross-domain communication spoofing attacks or load disturbances, ensuring that the system frequency recovers to its rated value without steady-state error. Simultaneously, this design allows the system to enter the sliding mode motion state from the initial moment, eliminating the arrival phase in traditional sliding mode control, thereby significantly improving the system's dynamic response speed and robustness to sudden pulse interference.

[0125] In one embodiment, based on the load frequency control model and the integral sliding surface, and under the constraint of the Lyapunov stability criterion, a sliding mode control strategy is determined to address the time delay effects corresponding to historical state deviations and time-varying delay characteristics, including:

[0126] Based on historical state deviations, the instantaneous change trend of the integral sliding surface is determined; based on the instantaneous change trend and preset sliding mode control conditions, the time delay deviation equation corresponding to the time delay effect is determined; the first constraint condition of the Lyapunov stability criterion containing the state vector is obtained; based on the load frequency control model and the time delay deviation equation, under the condition of satisfying the first constraint condition, the sliding mode control strategy for the time delay effect corresponding to the time-varying time delay characteristics is determined.

[0127] The instantaneous change trend can be a dynamic variable that characterizes the rate of evolution of the integral sliding surface function value with time. It can be obtained by performing a first-order differential operation on the sliding surface function with respect to time, and is used to describe whether the system state trajectory is currently moving away from or approaching the ideal sliding hyperplane.

[0128] The time delay deviation equation can be a mathematical expression that quantifies the interference effect of the transmission delay of the communication network on the dynamic behavior of the sliding surface. In the differentiation process, the state terms containing the time delay parameters are retained and used as interference sources that need to be compensated or canceled when calculating the control law in the later stage.

[0129] The first constraint can be a set of algebraic inequalities (such as linear matrix inequalities) derived from Lyapunov's direct method that guarantee the monotonically decreasing energy function of the system. These inequalities specify the mathematical relationships that must be satisfied between the gain matrices of the control system in order for the system state to eventually converge to zero.

[0130] Specifically, the server first performs a first-order differential operation on the constructed integral sliding surface with respect to the time variable, thereby obtaining the rate of change function describing the dynamic behavior of the sliding surface. In this differential process, the server substitutes the continuous dynamic equations of the power system into the derivative expression of the sliding surface, thus replacing the time derivative of the system state vector with an algebraic expression containing the system matrix, input matrix, and disturbance matrix. Since the continuous dynamic equations contain time-delay terms describing the influence of historical states, this algebraic expression naturally retains the coupling effect of time-varying delay characteristics on the sliding surface dynamics, thus forming the time-delay deviation equation.

[0131] Next, to ensure the asymptotic stability of the closed-loop system, the server constructs a positive definite function based on the system error energy (i.e., a Lyapunov candidate function) and sets a stability criterion that the time derivative of this energy function must always be less than zero. Based on this stability criterion and the aforementioned time-delay deviation equation, the server uses the equivalent control principle to inversely calculate the target control input that can offset the system's inherent dynamics, communication delays, and external impulse interference. This control input is designed to include two parts: one part is an equivalent control component used to maintain the system's sliding on the sliding surface, which accurately offsets the known model dynamics and time-delay effects; the other part is a switching control component used to forcibly suppress uncertainties and attack interference, which applies a reverse force according to the sign of the sliding surface.

[0132] Optionally, the derivation of the sliding mode control strategy first involves calculating the derivative of the sliding surface using formula (6). :

[0133] (6)

[0134] Derivative Substituting into the system equations, we obtain formula (7):

[0135] (7)

[0136] make (Or, using the equivalent control principle), the equivalent sliding mode control law formula (8) can be obtained:

[0137] (8)

[0138] Furthermore, to handle uncertainties and impulse interference, the server adds a switching term to the equivalent control, ultimately determining the sliding mode control strategy. For formula (9):

[0139] (9)

[0140] Furthermore, the equivalent controller Substituting into the system state equation, we can obtain its sliding dynamic system model as formula (10):

[0141] (10)

[0142] Specifically, given that the pulse frequency and pulse intensity satisfy the preset pulse frequency condition and pulse intensity condition respectively, and the state feedback gain satisfies the preset state feedback gain condition, in order to verify that the system has achieved exponential stability, the following Lyapunov function condition is selected as the first constraint condition, as shown in formula (11):

[0143] (11)

[0144] Based on inequality techniques, we can obtain formula (12):

[0145] (12)

[0146] in , ,in and , Exponential decay coefficient, The overshoot coefficient reflects the range of amplitude jumps or overshoot of the system at the initial moment or the instant of being attacked by a pulse. Finite time upper bound.

[0147] Based on the above derivation, it can be seen that the sliding dynamic system achieves exponential synchronous stability, that is, under time-varying transmission delay and impulse disturbance, as long as the initial state of the system reaches the designed sliding surface and remains on it, it will eventually converge to the equilibrium point.

[0148] In this embodiment, the sliding mode control strategy determined in the above manner strictly follows the Lyapunov stability theorem in theory, thereby ensuring the exponential stability of the closed-loop power system. Specifically, this strategy utilizes the strong robustness of sliding mode control to completely compensate for the time-varying delay effects caused by cross-domain communication networks, so that the system performance is no longer constrained by the congestion level of the communication link. At the same time, by introducing integral action and high-frequency switching terms for historical state deviations into the control law, this strategy can effectively suppress pulsed state changes caused by deception attacks, ensuring that the system frequency can still quickly and smoothly recover to the rated value when encountering malicious network attacks, and has extremely strong anti-interference capabilities.

[0149] In one embodiment, based on the load frequency control model and the integral sliding surface, and under the constraint of the Lyapunov stability criterion, a sliding mode control strategy is determined to address the time delay effects corresponding to historical state deviations and time-varying delay characteristics, including:

[0150] Obtain a finite time that satisfies the preset control time conditions; based on the finite time, obtain the second constraint condition of the Lyapunov stability criterion containing the integral sliding surface; based on the load frequency control model and the integral sliding surface, determine the sliding mode control strategy for the time delay effects corresponding to the historical state deviation and time-varying time delay characteristics, under the condition of satisfying the second constraint condition.

[0151] Among them, the finite time can be a preset maximum time allowed for the system to recover to a steady state from the moment it is disturbed. It can be determined according to preset power system safety standards (such as the hard provisions on frequency recovery time in power grid dispatching regulations) and relay protection action time limit requirements. It is used to define the dynamic response speed boundary of the controller and ensure that frequency fluctuations are pulled back to a safe range before triggering tripping or load shedding protection.

[0152] The second constraint can be an enhanced mathematical criterion based on the finite-time stability theory. It differs from the ordinary stability condition (the first constraint) that only requires the system to converge asymptotically within an infinite time. It usually requires that the derivative of the system's energy function is not only negative, but that its decay rate must also satisfy a specific nonlinear differential inequality. This mathematically ensures that the system's state trajectory can reach the sliding surface and stabilize within a definite time limit, rather than at infinity.

[0153] Specifically, the server reads the maximum allowable adjustment time threshold from a pre-set control parameter library. This threshold is typically set in seconds (e.g., 5 or 10 seconds), depending on the current grid inertia level and tolerance for frequency deviation. The server inputs this time threshold as a core performance indicator in the control strategy design into subsequent calculations.

[0154] The server constructs a Lyapunov energy function containing the aforementioned integral sliding surface and establishes a time-dependent differential inequality for this energy function. To satisfy the requirement of finite-time convergence, the server introduces a negative term in this inequality that is proportional to a fractional power of the energy function itself. The server mandates that the derivative of the energy function must be less than or equal to the negative of the weighted sum of this fractional power term and a linear term. This constraint forces the system to converge faster away from the equilibrium point while maintaining a finite convergence rate near the equilibrium point, thus establishing the second constraint.

[0155] Optionally, the following pulse frequency estimation strategy can be introduced, as shown in formula (13):

[0156] (13)

[0157] in, This represents the maximum number of attacks before the pulse stops indexing / convergence. Indicates the first in the attack sequence The specific time point of a deception attack pulse injection system. Initial moment, It is a pulse intensity parameter, determined by the pulse intensity.

[0158] In the pulse sequence exist and At that time, and based on the above pulse frequency estimation strategy, it satisfies ,in, It can be known that the sliding system is driven to the designed sliding surface and maintained on the sliding surface within a finite time, thus obtaining the preset control time condition, as shown in formula (14):

[0159] (14)

[0160] Based on the aforementioned limited time, the following Lyapunov function condition is further selected as the first constraint condition, as shown in formula (15):

[0161] (15)

[0162] Based on the sliding surface, we have formula (16):

[0163] (16)

[0164] Subsequently, the derivative of the Lyapunov function with respect to time t can be expressed as formula (17):

[0165] (17)

[0166] Substituting the sliding mode load frequency control law into the equation, and using the inequality... Formula (18) can be obtained:

[0167] (18)

[0168] According to the conditions Formula (19) can be obtained:

[0169] (19)

[0170] make Multiply both sides of the derivative of the Lyapunov function with respect to time t by And in the interval Integrating, we get formula (20):

[0171] (20)

[0172] like We are able to obtain and In other words, the state vector of the power system Can be done in a limited time The inner reach design of the sliding surface And it is unaffected by impulse effects. If This means .because Similar to the method described above, formula (21) can be further derived:

[0173] (twenty one)

[0174] Finally, we can obtain formula (22):

[0175] (twenty two)

[0176] Obviously, for ,have And for have In other words, under a control law that satisfies the finite-time condition, the state of the system can be determined within a finite time. The system reaches the designed sliding surface, and simultaneously, under pulse interference, the system state will remain on the sliding surface. superior.

[0177] In this embodiment, by introducing finite-time control constraints, the dynamic response speed of the system is improved. After being subjected to deceptive attacks or load changes, the system can smooth out fluctuations more quickly, greatly enhancing the survivability and regulation efficiency of the power grid under extreme conditions.

[0178] In one embodiment, based on the load frequency control model and the integral sliding surface, and under the condition of satisfying the second constraint, a sliding mode control strategy is determined for the time delay effects corresponding to historical state deviations and time-varying delay characteristics, including:

[0179] Based on the state vector and state feedback gain of the load frequency control model, the reference state feedback control quantity is determined; based on the energy amplitude of the state vector under time-varying delay characteristics and the preset time delay boundary parameters, the time delay effect compensation gain is determined; based on the polarity direction of the historical state deviation and the time delay effect compensation gain, the adaptive sliding mode control quantity is determined; based on the reference state feedback control quantity and the adaptive sliding mode control quantity, the sliding mode control strategy corresponding to the finite time is determined under the condition of satisfying the second constraint.

[0180] The reference state feedback control quantity can be a linear control component used to maintain the basic linear dynamic characteristics of the power system. It is obtained by the server through linear algebraic operations between the real-time system state vector and the pre-designed state feedback matrix, and is used to configure the system poles at the desired stable positions under ideal conditions without external disturbances and time delays.

[0181] The time delay effect compensation gain can be a variable gain coefficient used to dynamically offset the state lag deviation caused by the transmission delay of the communication network. It can be estimated based on the modulus (i.e., energy amplitude) of the current system state and the upper bound of the norm of the time delay term. It is used to ensure that the amplitude of the control law is sufficient to cover the uncertainty disturbance boundary caused by the time delay effect. The time delay boundary parameter can be the maximum predictive coefficient describing the degree of influence of network delay on the system.

[0182] Adaptive sliding mode control can be a nonlinear control component used to drive the system state across phase space to reach and remain on the sliding surface. It is used to apply a high-frequency, variable-direction thrust to the system, forcing the system state trajectory to always point towards the sliding surface.

[0183] The polarity direction directly reflects whether the current system state is "above" or "below" the sliding surface.

[0184] Specifically, the server reads real-time status data such as the current frequency deviation and power deviation of the power grid. Then, the server retrieves the pre-stored state feedback gain matrix from the storage unit. The server multiplies this matrix by the state vector to calculate a basic control signal value. This value represents the required adjustment level when only considering the system's linear stability requirements.

[0185] Subsequently, the server performs norm calculations on the state vectors of the current moment and historical moments (moments affected by time delay) to assess the energy level of the system state. Considering the uncertainty of time-varying delay, the server uses inequality scaling techniques, combined with preset time delay boundary parameters, to calculate a scalar gain value. The magnitude of this gain value is positively correlated with the fluctuation amplitude of the current system state; that is, the more severe the system fluctuation, the larger the calculated compensation gain, to ensure sufficient control energy to suppress the divergence trend caused by time delay.

[0186] The server calculates the value of the current integral sliding surface function and extracts its sign (positive or negative). Then, the server multiplies the time delay compensation gain calculated in the previous step by this sign value. To suppress jitter, the server can also introduce smoothing logic, such as using a saturation function instead of the ideal sign function near the sliding surface zeros. The resulting control quantity is a nonlinear control component that can adaptively resist time delays and attack disturbances.

[0187] The server determines the adaptive sliding mode control quantity based on the adaptive switching gain and the polarity direction of the sliding mode surface, and then superimposes it with the reference state feedback control quantity to determine the sliding mode control strategy.

[0188] Optionally, the server first calculates the Euclidean norm (or other vector norm) of the system state vector at the current moment and multiplies it by a first weighting coefficient. Simultaneously, the server retrieves the state vector from a historical moment (after delay correction) stored in the cache, calculates its norm, and multiplies it by a second weighting coefficient. Furthermore, the server introduces a preset positive real constant as a robust basis value. The server performs scalar addition on the above three parts (constant term, current state term, and time-delay state term) to obtain the adaptive switching gain required at the current moment. This gain value automatically scales as the system state deviates from the equilibrium point, exhibiting an adaptive characteristic where the worse the state, the greater the gain, thus accelerating the convergence time to the sliding surface.

[0189] Optionally, the calculation logic of the adaptive switching gain and its correlation coefficient can be described by the following formula (23):

[0190] (twenty three)

[0191] in, , , , This is a preset constant; in some embodiments, it can be 1 / 2. It is the maximum value in the preset parameter set.

[0192] Alternatively, the final sliding mode control strategy can be described by the following formula (24):

[0193] (twenty four)

[0194] in, It is a symbolic function.

[0195] In this embodiment, the control strategy combines linear feedback and nonlinear adaptive compensation to achieve standardized optimization and enhanced robustness of control parameters. This design transforms controller tuning into a standard mathematical problem, eliminating reliance on manual experience for adjustment, and automatically finding the optimal control quantity for different operating conditions (especially complex conditions with time-varying delays and spoofing attacks).

[0196] To verify the effectiveness of the proposed load frequency sliding mode defense control method against spoofing attacks in spoofing attack and complex disturbance environments, a simulation experimental platform for a power system containing energy storage units was constructed. This platform comprehensively considers uncertainties such as cross-domain communication delays and spoofing attacks, and simulates the impact of network layer spoofing behavior on system frequency stability by injecting short-time spoofing pulses into the measurement signal channel.

[0197] In the simulation study, the defensive control method proposed in this application is compared and analyzed with the traditional proportional-integral control method that does not employ a sliding mode strategy. Corresponding to Figure 2 The main parameters of the power system simulation system are shown in Table 1, including the inertial constants of conventional generator sets and energy storage units, the time constant of the speed governor, the proportional coefficient and the frequency regulation coefficient, etc., all of which are typical parameter values ​​used in power system analysis.

[0198] Table 1 Simulation System Parameters

[0199]

[0200] Under the same load disturbance and spoofing pulse injection conditions, frequency regulation was performed using both a conventional controller and the SMC defense controller proposed in this application. Simulation results show that the proposed method can still maintain rapid frequency recovery and small overshoot when subjected to spoofing attacks, significantly improving the finite-time stability and dynamic response performance of the system, and verifying the effectiveness and robustness of the proposed sliding mode defense control strategy under complex network interference conditions.

[0201] In one specific embodiment, let the initial state of the power system containing the energy storage unit be... Moreover, the time delay satisfies The system is affected by deception attacks. , and Without employing a sliding mode control strategy, the dynamic response diagram of the power system containing energy storage units is as follows: Figure 3 As shown, the system is affected by the deception attack at 1s, 2s, 3s, and 4s, and the system state changes significantly and ultimately cannot reach a stable state.

[0202] Therefore, the parameter matrix of the proposed sliding surface function is selected. , And the parameters of the proposed sliding mode control strategy Based on the system parameters, it can be concluded that... and Then the pulse sequence When condition (22) is met , and when It also satisfies the preset pulse frequency condition. Furthermore, the state feedback gain condition and (22) are satisfied and... According to Theorems 1 and 2, the proposed SMC-based control strategy can ensure that the power system with energy storage units reaches a stable state under the influence of deception attacks and time-varying delays. Its simulation diagram is shown below. Figure 4 As shown, it can be seen that with the SMC strategy, the power system containing energy storage units can eventually reach a stable state, verifying the effectiveness of the SMC strategy designed in this paper.

[0203] To quantify and compare the dynamic performance of the system under different control strategies, three performance indicators were introduced: integral of absolute error (IAE), integral of time-weighted absolute error (ITAE), and integral of squared error (ISE). The results are shown in Table 2. Without the SMC strategy, IAE was 0.13249, ITAE was 15.5041, and ISE was 0.010427. However, after adopting the control strategy of this application, IAE decreased to 0.11516, ITAE significantly decreased to 12.5531, and ISE decreased to 0.0084975. This shows that all error indicators decreased during the dynamic adjustment process, especially ITAE, which decreased by approximately 19%, demonstrating the significant advantage of the sliding mode control strategy in improving the system's rapid response capability.

[0204] Table 2 Dynamic performance indicators under different conditions

[0205]

[0206] To enable those skilled in the art to better understand the above steps, the following example illustrates the embodiments of this application, but it should be understood that the embodiments of this application are not limited thereto.

[0207] In one embodiment, with the rapid development of power system communication networks and the deepening of multi-domain interconnection, the control and monitoring aspects of the system increasingly rely on networked information interaction. However, in this heterogeneous and complex communication environment, the security of power system frequency control faces new challenges. Especially during multi-domain interconnection and cross-gateway communication, attackers can forge, tamper with, or delay measurement data to impose misleading inputs on the control center, creating deceptive attacks that are both sudden and covert. Such attacks typically manifest as pulse interference, causing instantaneous deviations in system measurement signals, thereby inducing erroneous responses in the frequency regulation stage, and in severe cases, leading to system oscillations or even instability.

[0208] Traditional load frequency control methods are primarily designed to address load disturbances, random noise, or communication delays. They typically assume that measured signals are accurate and reliable, neglecting the impact of network-level data tampering. Under spoofing attacks, these control methods are susceptible to sudden interference, losing dynamic consistency and causing abrupt changes in control inputs and output spikes, ultimately disrupting system balance and stability. Meanwhile, existing defense mechanisms largely focus on intrusion detection, encrypted communication, or anomaly identification, failing to reflect the direct impact of attacks on system frequency stability and lacking quantitative evaluation mechanisms for defense effectiveness. This makes it difficult to verify the defensive performance of frequency control systems in complex network environments, and its security boundaries and defensive capabilities lack effective measurement.

[0209] Furthermore, modern power systems are characterized by cross-domain interconnection and multi-gateway communication. System nodes are widely distributed, and communication paths are complex. Attackers can launch cross-domain spoofing attacks through multi-hop links or routing nodes between different domains. Such attacks are discontinuous and random, making traditional defense models based on single-domain or fixed topologies inapplicable. When spoofing attacks are injected into measurement circuits in the form of short-duration pulses, conventional control models cannot capture their instantaneous dynamic characteristics, nor can they suppress and analyze such sudden disturbances in real time at the control level. Therefore, a comprehensive control strategy that can adapt to cross-domain communication environments and balance attack defense with evaluation and verification is urgently needed to ensure the system remains stable and controllable even when subjected to spoofing attacks.

[0210] Among existing control methods, sliding mode control (SMC) has been widely applied in load frequency control due to its simple structure, fast response speed, and strong robustness to model uncertainties. However, traditional SMC methods still have shortcomings in dealing with spoofing attacks: on the one hand, sudden changes in the measurement signal caused by the attack can lead to transient spikes in the controller output, affecting system stability; on the other hand, the lack of a unified modeling method for spoofing disturbances makes it impossible to optimize and adjust control parameters according to attack characteristics. Furthermore, existing SMC strategies focus primarily on control accuracy and dynamic performance, lacking corresponding attack detection and evaluation mechanisms, making it impossible to quantitatively verify and reproducibly test the defense effectiveness. These shortcomings make it difficult for control algorithms to achieve closed-loop defense and reliable evaluation in actual power systems.

[0211] To address the aforementioned issues, this application proposes a sliding mode defense control method against spoofing attacks for load frequency control (LFC) in power systems with energy storage units under cross-domain communication environments. This method models the load frequency control process as a hybrid dynamic system affected by cross-domain network spoofing attacks and measurement interference. By designing an integral sliding surface and a finite-time convergent control law, robust frequency stability control of the system under spoofing interference and uncertainties is achieved.

[0212] The load frequency control method of this application specifically includes the following steps:

[0213] System modeling is performed, and an LFC state-space model with energy storage units is established. A deception attack interference term under cross-domain communication is explicitly introduced to describe the transient tampering effect of the attack on the measurement signal in the form of pulses, providing a constraint object for controller design.

[0214] Sliding surface design is employed to construct an integral sliding surface function. The integral memory characteristic is used to counteract the dynamic deviation caused by deceptive interference, thereby enhancing the system's robustness against abnormal measurements and deceptive signals.

[0215] Sliding mode dynamic analysis is performed, and the equivalent sliding mode dynamic equation after the system reaches the sliding surface is derived. The Lyapunov method is used to give the stability criterion under the presence of deception attack, so as to ensure the stability of the system in the sliding mode stage.

[0216] Design a finite-time sliding mode control law to ensure that the system state reaches and remains on the sliding surface within a finite time, quickly suppressing frequency deviations caused by deception attacks and achieving stable recovery.

[0217] By coordinating sliding mode control and deception defense mechanisms, high-precision, rapid, and robust frequency regulation of the power system with energy storage participation is achieved, overcoming the instability of traditional control methods under network deception and external disturbances. This method has clear theoretical support, excellent dynamic performance, and good engineering feasibility, and can significantly improve the security and operational reliability of the power system under network attack environments, making it highly valuable for application and promotion.

[0218] It should be understood that although the steps in the flowcharts of the above embodiments are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the above embodiments may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages in other steps. It is understood that the steps in different embodiments can be freely combined as needed, and all non-contradictory solutions formed by such combinations are within the scope of protection of this application.

[0219] Based on the same concept, this application also provides a load frequency sliding mode defense control device for implementing the load frequency sliding mode defense control method for deception attacks described above. The solution provided by this device is similar to the implementation described in the above method. Therefore, the specific limitations of one or more embodiments of the load frequency sliding mode defense control device for deception attacks provided below can be found in the limitations of the load frequency sliding mode defense control method for deception attacks described above, and will not be repeated here.

[0220] In one exemplary embodiment, such as Figure 5 As shown, a load frequency sliding mode defense control device for deception attacks is provided, comprising: a load frequency control model construction module 510, an integral sliding surface establishment module 520, a sliding mode control strategy determination module 530, and a frequency adjustment command determination module 540, wherein:

[0221] The load frequency control model construction module 510 is used to determine the load frequency control model of the power system based on the pre-acquired operating parameters, pulse interference characteristics, and time-varying delay characteristics of the power system; the pulse interference characteristics are used to describe spoofing attack behavior in cross-domain communication networks.

[0222] The integral sliding surface establishment module 520 is used to construct an integral sliding surface containing system state integral terms based on the load frequency control model; the system state integral terms are used to accumulate historical state deviations, which are determined based on the system state abrupt changes caused by the deception attack behavior to the power system.

[0223] The sliding mode control strategy determination module 530 is used to determine the sliding mode control strategy for the time delay effects corresponding to the historical state deviation and the time-varying time delay characteristics based on the load frequency control model and the integral sliding surface, under the constraint conditions of satisfying the Lyapunov stability criterion.

[0224] The frequency adjustment command determination module 540 is used to generate frequency adjustment commands for the power system based on the sliding mode control strategy.

[0225] In one embodiment, the power system includes a generator, a speed governor, a steam turbine, and an energy storage unit; the load frequency control model construction module 510 is further configured to:

[0226] Based on the operating parameters, the state vector of the power system is determined; the state vector includes frequency deviation, frequency preset value deviation, turbine valve position deviation, generator mechanical power deviation, and energy storage unit output power deviation.

[0227] Based on the control input to the power system, the state vector, and the time-varying delay characteristics, the continuous dynamic equation of the power system is determined;

[0228] The instantaneous switching process of the power system is determined based on the pulse frequency and pulse intensity indicated by the pulse interference characteristics; the pulse frequency and pulse intensity respectively satisfy preset pulse frequency conditions and pulse intensity conditions.

[0229] Based on the continuous dynamic equations and the instantaneous jump process, the load frequency control model is determined.

[0230] In one embodiment, the integral sliding surface establishment module 520 is further configured to:

[0231] Based on the state vector of the load frequency control model and the preset sliding mode control parameters, the linear transformation term is determined;

[0232] Based on the operating parameters, the system dynamic parameters and input coupling parameters of the power system are determined, and based on the system dynamic parameters, the input coupling parameters, and the state feedback gain, the target closed-loop dynamic characteristics are determined; the state feedback gain satisfies a preset state feedback gain condition.

[0233] Based on the target closed-loop dynamic characteristics and the state vector, the state integral term is determined;

[0234] The integral sliding surface is determined based on the linear transformation term and the state integral term.

[0235] In one embodiment, the sliding mode control strategy determination module 530 is further configured to:

[0236] Based on the historical state deviation, the instantaneous change trend of the integral sliding surface is determined;

[0237] Based on the instantaneous change trend and the preset sliding mode control conditions, the time delay deviation equation corresponding to the time delay effect is determined;

[0238] Obtain the first constraint condition of the Lyapunov stability criterion containing the state vector;

[0239] Based on the load frequency control model and the time delay deviation equation, and under the condition of satisfying the first constraint, a sliding mode control strategy is determined for the time delay effect corresponding to the time-varying time delay characteristics.

[0240] In one embodiment, the sliding mode control strategy determination module 530 is further configured to:

[0241] Obtain a finite time that meets the preset control time conditions;

[0242] Based on finite time, obtain the second constraint condition of the Lyapunov stability criterion involving the integral sliding surface;

[0243] Based on the load frequency control model and the integral sliding surface, and under the condition of satisfying the second constraint, a sliding mode control strategy is determined to address the time delay effects corresponding to the historical state deviation and the time-varying delay characteristics.

[0244] In one embodiment, the sliding mode control strategy determination module 530 is further configured to:

[0245] Based on the state vector and state feedback gain of the load frequency control model, the reference state feedback control quantity is determined.

[0246] Based on the energy amplitude of the state vector under the time-varying delay characteristics and the preset time delay boundary parameters, the time delay effect compensation gain is determined;

[0247] Based on the polarity direction of the historical state deviation and the time delay effect compensation gain, the adaptive sliding mode control quantity is determined;

[0248] Based on the baseline state feedback control quantity and the adaptive sliding mode control quantity, the sliding mode control strategy corresponding to the finite time is determined under the condition that the second constraint is satisfied.

[0249] The modules in the aforementioned load frequency sliding mode defense control device against deception attacks can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the computer device's memory as software, so that the processor can call and execute the corresponding operations of each module.

[0250] In one exemplary embodiment, a computer device is provided, which may be a server, and its internal structure diagram may be as follows: Figure 6As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The database stores sliding mode control strategies. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a load frequency sliding mode defense control method against deception attacks.

[0251] Those skilled in the art will understand that Figure 6 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0252] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0253] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps in the above method embodiments.

[0254] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above method embodiments.

[0255] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0256] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile memory and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, artificial intelligence (AI) processors, etc., and are not limited to these.

[0257] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this application.

[0258] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A load frequency sliding mode defense control method for deception attacks, characterized in that, Applied to power systems, the method includes: Based on the pre-acquired operating parameters, pulse interference characteristics, and time-varying delay characteristics of the power system, a load frequency control model for the power system is determined; the pulse interference characteristics are used to describe spoofing attack behavior in cross-domain communication networks. Based on the load frequency control model, an integral sliding surface containing a system state integral term is constructed; the system state integral term is used to accumulate historical state deviations, which are determined based on the system state abrupt changes caused by the deception attack on the power system. Based on the load frequency control model and the integral sliding surface, and under the constraint of the Lyapunov stability criterion, a sliding mode control strategy is determined to address the time delay effects corresponding to the historical state deviation and the time-varying time delay characteristics. Based on the sliding mode control strategy, frequency regulation commands for the power system are generated.

2. The method according to claim 1, characterized in that, The power system includes generators, speed governors, steam turbines, and energy storage units; the determination of the load frequency control model of the power system based on pre-acquired operating parameters, pulse interference characteristics, and time-varying delay characteristics includes: Based on the operating parameters, the state vector of the power system is determined; the state vector includes frequency deviation, frequency preset value deviation, turbine valve position deviation, generator mechanical power deviation, and energy storage unit output power deviation. Based on the control input to the power system, the state vector, and the time-varying delay characteristics, the continuous dynamic equation of the power system is determined; The instantaneous switching process of the power system is determined based on the pulse frequency and pulse intensity indicated by the pulse interference characteristics; the pulse frequency and pulse intensity respectively satisfy preset pulse frequency conditions and pulse intensity conditions. Based on the continuous dynamic equations and the instantaneous jump process, the load frequency control model is determined.

3. The method according to claim 2, characterized in that, The construction of an integral sliding surface containing system state integral terms based on the load frequency control model includes: Based on the state vector of the load frequency control model and the preset sliding mode control parameters, the linear transformation term is determined; Based on the operating parameters, the system dynamic parameters and input coupling parameters of the power system are determined, and based on the system dynamic parameters, the input coupling parameters, and the state feedback gain, the target closed-loop dynamic characteristics are determined; the state feedback gain satisfies a preset state feedback gain condition. Based on the target closed-loop dynamic characteristics and the state vector, the state integral term is determined; The integral sliding surface is determined based on the linear transformation term and the state integral term.

4. The method according to claim 3, characterized in that, Based on the load frequency control model and the integral sliding surface, and under the constraint of the Lyapunov stability criterion, a sliding mode control strategy is determined to address the time delay effects corresponding to the historical state deviation and the time-varying delay characteristics, including: Based on the historical state deviation, the instantaneous change trend of the integral sliding surface is determined; Based on the instantaneous change trend and the preset sliding mode control conditions, the time delay deviation equation corresponding to the time delay effect is determined; Obtain the first constraint condition of the Lyapunov stability criterion containing the state vector; Based on the load frequency control model and the time delay deviation equation, and under the condition of satisfying the first constraint, a sliding mode control strategy is determined for the time delay effect corresponding to the time-varying time delay characteristics.

5. The method according to claim 3, characterized in that, Based on the load frequency control model and the integral sliding surface, and under the constraint of the Lyapunov stability criterion, a sliding mode control strategy is determined to address the time delay effects corresponding to the historical state deviation and the time-varying delay characteristics, including: Obtain a finite time that meets the preset control time conditions; Based on finite time, obtain the second constraint condition of the Lyapunov stability criterion involving the integral sliding surface; Based on the load frequency control model and the integral sliding surface, and under the condition of satisfying the second constraint, a sliding mode control strategy is determined to address the time delay effects corresponding to the historical state deviation and the time-varying delay characteristics.

6. The method according to claim 5, characterized in that, Based on the load frequency control model and the integral sliding surface, and under the condition of satisfying the second constraint, a sliding mode control strategy is determined for the time delay effects corresponding to the historical state deviation and the time-varying delay characteristics, including: Based on the state vector and state feedback gain of the load frequency control model, the reference state feedback control quantity is determined. Based on the energy amplitude of the state vector under the time-varying delay characteristics and the preset time delay boundary parameters, the time delay effect compensation gain is determined; Based on the polarity direction of the historical state deviation and the time delay effect compensation gain, the adaptive sliding mode control quantity is determined; Based on the baseline state feedback control quantity and the adaptive sliding mode control quantity, the sliding mode control strategy corresponding to the finite time is determined under the condition that the second constraint is satisfied.

7. A load frequency sliding mode defense control device for deception attacks, characterized in that, The device includes: The load frequency control model construction module is used to determine the load frequency control model of the power system based on the pre-acquired operating parameters, pulse interference characteristics, and time-varying delay characteristics of the power system; the pulse interference characteristics are used to describe spoofing attack behavior in cross-domain communication networks. An integral sliding surface establishment module is used to construct an integral sliding surface containing system state integral terms based on the load frequency control model; the system state integral terms are used to accumulate historical state deviations, which are determined based on the system state abrupt changes caused by the deception attack on the power system. The sliding mode control strategy determination module is used to determine the sliding mode control strategy for the time delay effects corresponding to the historical state deviation and the time-varying time delay characteristics based on the load frequency control model and the integral sliding surface, while satisfying the constraints of the Lyapunov stability criterion. The frequency regulation command determination module is used to generate frequency regulation commands for the power system based on the sliding mode control strategy.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

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