Load Frequency Control of Multi-area Power Systems under Deception Attacks

This paper is mainly focused on the problem of the robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> sliding mode load frequency control (SMLFC) for the multi-area power system. The model of the i-th area power system load frequency control is given. Then, a designed sliding surface is providing for a common multi-area power system. Based on the designed sliding surface, the problem of the robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> stability is investigated by using the Lyapunov function. Later, we have got the stability factor under sliding mode load frequency control of the premise proper sliding surface and control law. At last, some simulations are given to describe the effectiveness of the results.

A memory output sliding mode load frequency control (MOSMLFC) strategy is proposed for multi-area interconnected power systems under historical-frequency-triggered denial-of-service (DoS) attacks. Due to the use of the open network, the multi-area power system is prone to cyber-attacks. Different types of attack models have been built to describe the actual attack behavior, so that effective strategies can be quickly formulated in the event of an attack. Therefore, a historical-frequency-triggered DoS attacks model is presented from the perspective of attackers, with the aim of destroying the stable state of the multi-area power system. It is assumed that attackers determine the timing of DoS attacks by monitoring the operational status of multi-area power systems and designing the triggering condition with historical frequency. A MOSMLFC strategy is investigated to ensure the security performance of multi-area power systems under historical-frequency-triggered DoS attacks, which applies the memory output information of the power system to realize the controller design. The security condition of multi-area power systems under historical-frequency-triggered DoS attacks is obtained by Lyapunov’s theorem and linear matrix inequality (LMI). Numerical examples are tested over the IEEE 10-generator 39-bus system and the results prove the usefulness and superiority of the proposed method. Note to Practitioners—Load frequency control is widely applied in multi-area power systems to achieve a balance between the load demand and generation. Frequent cyber-attacks are a threat to the normal operation of the power system. It is therefore necessary to develop appropriate strategies to defend against cyber-attacks. So far, there have been many different forms of cyber-attacks. This has prompted defenders to build different types of attack models to describe the actual attack behavior in order to preemptively formulate appropriate defensive strategies. Smart attacker may notice that certain characteristics of the target system are important, such as the power system frequency. This motivates us to propose a historical frequency-triggered DoS attack model that contributes to a deep understanding of the impact of cyber-attacks on the power system. We propose a unique sliding mode control approach to ensure the stable performance of power system state and output simultaneously.

AIn this paper, impact of communication delay on distributed load frequency control (dis-LFC) of multi-area interconnected power system (MAIPS) is investigated. Load frequency control (LFC), as one of ancillary services, is aimed at maintaining system frequency and inter-area tie-line power close to the scheduled values, by load reference set-point manipulation and consideration of the system constraints. Centralized LFC (cen-LFC) requires inherent communication bandwidth limitations, stability and computational complexity, as such, it is not a good technique for the control of large-scale and geographically wide power systems. To decrease the system dimensionality and increase performance efficiency, distributed and decentralized control techniques are adopted. In distributed LFC (dis-LFC) of MAIPS, each control area (CA) is equipped with a local controller and are made to exchange their control actions by communication with controllers in the neighboring areas. The delay in this communication can affect the performance of the LFC scheme and in a worst case deteriorates power system stability. To investigate the impact of this delay, model predictive controller (MPC) is employed in the presence of constraints and external disturbances to serve as LFC tracking control. The scheme discretizes the system and solves an on-line optimization at each time sample. The system is subjected to communication delay between the CAs, and the response to the step load perturbation with and without the delay. Time-based simulations were used on a three-area MAIPS in MATLAB/SIMULINK environment to verify the investigations. The overshoot and settling time in the results reveals deterioration of the control performance with delay. Also, the dis-LFC led to zero steady states errors for frequency deviations and enhanced the MAIPS’ performance. With this achievement, MPC proved its constraints handling capability, online rolling optimization and ability to predict future behavior of systems.

This paper deals with fault-tolerant-based load frequency control in multi-area power systems. First, by using sliding mode observer technique, the system states and faults are figured out combined with the designed derivative and proportional gains. Upon the state estimates, sliding mode controller is synthesized to keep the asymptotical stability performance of the fault system.

This paper investigates the problem of event-triggered ${H_\infty }$ load frequency control (LFC) for multiarea power systems under hybrid cyber attacks, including denial-of-service (DoS) attacks and deception attacks. An event-triggered transmission scheme is developed under the DoS attacks to lighten the load of network bandwidth while preserving a satisfactory system performance. Then, a new switched system model accounting for the simultaneous presence of DoS attacks and stochastic deception attacks is established with respect to the LFC for multiarea power system. On the basis of the new model, sufficient conditions ensuring multiarea power system exponentially mean-square stable with prescribed ${H_\infty }$ performance are obtained by using Lyapunov stability theory. Furthermore, criteria for simultaneously designing the weighting matrix in event-triggered scheme and the controller gain matrix are derived by utilizing the linear matrix inequality technique. Finally, a three-area power system is simulated to demonstrate the usefulness of the approaches proposed in this paper.

Maintaining frequency stability in modern multi-area interconnected power systems has become increasingly challenging due to the stochastic nature of wind power and reduced effective system inertia. Under these dynamic conditions, traditional fixed-gain PID controllers frequently fail to provide robust regulation. To address this limitation, this study proposes and evaluates a practical model-free secondary control strategy for multi-area Load Frequency Control (LFC). The proposed hybrid MFAC–PID framework integrates an incremental model-free adaptive control (MFAC) law with a low-gain incremental PID damping term. This combination leverages real-time input–output data to determine primary control actions without relying on an explicit plant model, while the PID component supplies supplementary damping based on recent control errors. Furthermore, the controller utilizes online pseudo-gradient estimation to dynamically adapt to stochastic wind fluctuations and ±5% parametric uncertainty. Simulation results demonstrate that the hybrid design substantially enhances Area Control Error (ACE) regulation. Under wind-disturbed conditions, it reduces the aggregated Integral Absolute Error (IAEtotal) from 92.76 to 41.10, representing an improvement of over 50% compared with the fixed-gain PID baseline. Additionally, the controller maintains a low computational overhead of 0.306 milliseconds per control cycle. These findings indicate that the hybrid MFAC–PID structure provides a robust, computationally efficient solution for real-time Automatic Generation Control (AGC) in renewable-integrated multi-area power grids.

Electric vehicles (EVs) can be employed intelligently in Vehicle-to-Grid (V2G) and Grid-to-Vehicle (G2V) modes for Load Frequency Control (LFC) in the power grid. Due to the rapid variation of charging or discharging power, EVs can perform frequency regulation tasks and serve as distributed energy storage devices. In this paper, a linearized model of an interconnected multi-area power system is formulated in the restructured environment to include Electric Vehicle Aggregators (EVA). The DISCO Participation Matrix (DPM) is used to model Poolco and bilateral contracts in restructured multi-area power systems along with the participation of EVs. The faster dynamic response of EVs can effectively control the deviations in area frequencies imposed by the DISCOs load demand. The gains of the integral controller employed in each area are tuned by Real Coded Genetic Algorithm (RGA) by minimizing the integral square error function for area frequency deviations. The efficacy of power support from the EVs for load frequency control is validated by simulating different Poolco and bilateral transactions. It is shown that the EVs have a significant impact on obtaining optimal transient response for area frequencies, tie-line powers and power generation of conventional thermal generating units for any type of transaction in a restructured environment.

Information and communication technology tremendously facilitates the operation efficiency and economy of modern power systems in recent years. However, risks such as bandwidth constraints and malicious attacks threaten the secure load frequency control (LFC) of power systems. To mitigate such risks, this paper proposes distributed observer-based event-triggered LFC schemes for multi-area power systems under cyber attacks. Considering the practical situation that only local system output information may be available, distributed observer-based LFC schemes are designed. Meanwhile, to reduce the communication burden, an event-triggered mechanism is adopted to design control laws, where both static and dynamic event-triggered approaches are taken and the dynamic one is proved to be more economical in terms of control cost. Verifiable sufficient conditions are established to guarantee the stability of the closed-loop system in the presence of cyber attacks and the controller gains are explicitly derived. Finally, validation studies on a three-area interconnected power system are carried out to demonstrate the proposed control schemes. Note to Practitioners—Load frequency is a crucial index for evaluating the quality of electric energy and thus LFC has brought considerable attention in the area of power systems control. Although many achievements have been made on the LFC of multi-area power systems, the risks such as bandwidth constraints and malicious attacks affect the normal operation of LFC due to the interconnection between different power systems. To deal with these risks, this paper focuses on designing event-triggered LFC to guarantee the stability of the frequency deviation while reducing the communication burden and mitigating cyber attacks. More importantly, the proposed event-triggered LFC is designed based on an observer and can be implemented in a distributed manner, which is relatively practical in real applications. The results presented in this paper aim to provide a helpful reference for stable and secure LFC design of multi-area power systems, such that the corresponding application research can be promoted.

Load frequency control is one of the most important issues in multi area power systems. In this context, due to growing development of wind turbines in power systems, this type of renewable power sources can be used efficiently in frequency control. This paper applies doubly-fed induction generators (DFIGs) along with other conventional generation units for frequency performance enhancement after disturbances in multi-area power systems. Proportional integral (PI) controller is the conventional controller which is used in DFIGs to contribute in frequency control. The parameters of PI controller for DFIG are optimized by improved particle swarm optimization (IPSO) method. Simulation results in a three-area power system illustrate the efficiency of the DFIGs for frequency and tie-line power oscillations improvement.

Critical Mode Identification and its Application to Load Frequency Control in Power Systems

In this article, the H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> dynamic triggering control design problem is concerned for a discrete-time switched control system with aperiodic and parameter uncertainty denial-of-service (DoS) attacks. First, by introducing dynamic trigger scheme, a switched delay system model under discrete-time can be established. Then, by integrating discrete piecewise Lyapunov-Krasovskii functional method with switch system method based on average dwell time (ADT), we obtain a criterion of preserving weighted H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> performance of the switched delay system. Derived from the criterion, since the DoS duration and frequency are constrained by upper/lower bounds, the dynamic output feedback control gain can be designed by solving a set of LMIs. Finally, by investigating a resilient H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> load frequency control (LFC) for a three-area power system, we verify the effectiveness of the method through numerical simulations.

This article addresses the design procedure and numerical validation of a robust fuzzy logic-based fine-tuning approach devised to enhance load frequency control capabilities in multi-area power systems. The founded robust fuzzy logic-based fine-tuning approach is intended for judicial parameter tuning of a proportional-integral controller encountering fault occurrences or severe changes in system loading conditions. Unlike conventional proportional-integral controllers that are generally designed for fixed operating conditions, the outlined approach demonstrates robust performance with power system uncertainties and disturbances. In this context, the projected robustness is principally emanated due to a fuzzy logic extensibility feature, furnishing the established framework to have a proliferated observability on control space. The design procedure of a robust fuzzy logic-based fine-tuning controller is substantially nourished by expert knowledge regarding the overall system performance. Apt fuzzified and defuzzified rule-based mechanisms are wisely included as the key building blocks of the fuzzy inference engine. Extensive numerical studies are launched in a thorough investigation of the proposed approach. As well, the robust fuzzy logic-based fine-tuning performance is compared with that of two extra robust methods, namely the H∞-iterative linear matrix inequality as well as the hybrid genetic algorithm and linear matrix inequality. The obtained results are deeply analyzed.

BackgroundAutomatic generation control (AGC) of multi-area interconnected power system (IPS) is often designed with negligible cross-coupling between the load frequency control (LFC) and automatic voltage regulation (AVR) loops. This is because the AVR loop is considerably faster than that of LFC. However, with the introduction of slow optimal control action on the AVR, positive damping effect can be achieved on the LFC loop thereby improving the frequency control. In this paper, LFC synchronized with AVR in three-area IPS is proposed. Model predictive controller (MPC) configured in a dense distributed pattern, due to its online set-point tacking is used as the supplementary controller. The dynamics of the IPS subjected to multi-area step and random load disturbances are studied. The efficacy of the developed scheme is ascertained by simulating the disturbed system in MATLAB/Simulink.ResultsBased on the comparative analysis on the system responses, it is established that by cross-coupling the LFC loop with AVR, reductions of 66.45% and 59.09% in the frequency and tie-line power maximum deviations respectively are observed, while the respective settling times are found to be reduced by 29.68% and 22.77% when compared with the uncoordinated control scheme. In addition, the standard deviation and variance of the integral time absolute error of the system’s responses have reduced by 23.21% and 20.83% respectively compared to those obtained in a similar study.ConclusionsThe reduction in the maximum deviations and settling times in the system states indicates that introducing the voltage control via AVR loop has improved the frequency control significantly. While the lower standard deviation and variance of the integral time absolute error signify improvement in the robustness of the developed algorithm. However, this improvement is at the detriment of the controller size and computational complexity. In the uncoordinated control scheme, the control vector is one-dimensional, while in the coordinated scheme, the control vector is two-dimensional for each CA.

This paper concentrates on the controller synthesis problem for load frequency control (LFC) of multi-area power systems under resilient event-triggering communication scheme (RETCS) and periodic denial-of-service (DoS) jamming attacks. Firstly, a periodic RETCS under the given DoS attacks is designed, which can eliminate impact of the periodic DoS jamming attacks effectively. Second, a state error dependent switched LFC model for multi-area power systems is given. Then, a co-design method for RETCS and LFC gains is developed. Finally, the effectiveness of the proposed method is demonstrated by a two-area power system.

This paper presents an adaptive neuro fuzzy (ANFIS) based load frequency control for multi-area non-reheat turbine power system. It can handle the non-linearity of the system and react to situation faster than the conventional controller. The changes in frequency and Tie-line power are subjects be controlled for 3-area power system. The system response with proposed controller is compared to that of with conventional controllers presented in literature. The comparison is carried-out in terms of over-shoot, under-shoot and settling-time of frequency and tie-line power. It is proposed that the intelligent controller (ANFIS) provides encouraging result as compared that of with PID controllers in literature. The robustness of the proposed controller is considered for a wide range of change in load.