Decentralized Disturbance Observer-Based Sliding Mode Load Frequency Control in Multiarea Interconnected Power Systems

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.

This article addresses the static output feedback load frequency control (LFC) problem for semi‐Markov type interconnected multi‐area power systems (IMAPSs) through non‐fragile proportional‐integral (PI) strategy. Primarily, by roundly exploiting the dynamical properties and considering random mutations of the IMAPSs, the semi‐Markov jump process (MJP) is elaborately scheduled for establishing the dynamical model with precision. Subsequently, on account of the characteristic of geographical isolation, a memory‐like sampled‐data LFC mechanism considering time‐varying transmission delay for the semi‐Markov jump IMPASs is formulated accordingly. Additionally, the non‐fragile issue is explored for the PI controller gain fluctuations to meet the actual operation scenario. After that, a mode‐dependent two‐side polynomial‐type looped Lyapunov functional is constructed for enhancing flexibility. Then, in virtue of the stochastic analysis technique, some relaxed conditions guaranteeing stochastic stability with prescribed performance are thereby derived in the shape of linear matrix inequalities (LMIs). Ultimately, a numerical example is carried out to validate the efficacy of the developed control methodology.

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.

The stability control of nominal frequency and terminal voltage in an interconnected power system (IPS) is always a challenging task for researchers. The load variation or any disturbance affects the active and reactive power demands, which badly influence the normal working of IPS. In order to maintain frequency and terminal voltage at rated values, controllers are installed at generating stations to keep these parameters within the prescribed limits by varying the active and reactive power demands. This is accomplished by load frequency control (LFC) and automatic voltage regulator (AVR) loops, which are coupled to each other. Due to the complexity of the combined AVR-LFC model, the simultaneous control of frequency and terminal voltage in an IPS requires an intelligent control strategy. The performance of IPS solely depends upon the working of the controllers. This work presents the exploration of control methodology based on a proportional integral–proportional derivative (PI-PD) controller with combined LFC-AVR in a multi-area IPS. The PI-PD controller was tuned with recently developed nature-inspired computation algorithms including the Archimedes optimization algorithm (AOA), learner performance-based behavior optimization (LPBO), and modified particle swarm optimization (MPSO). In the earlier part of this work, the proposed methodology was applied to a two-area IPS, and the output responses of LPBO-PI-PD, AOA-PI-PD, and MPSO-PI-PD control schemes were compared with an existing nonlinear threshold-accepting algorithm-based PID (NLTA-PID) controller. After achieving satisfactory results in the two-area IPS, the proposed scheme was examined in a three-area IPS with combined AVR and LFC. Finally, the reliability and efficacy of the proposed methodology was investigated on a three-area IPS with LFC-AVR with variations in the system parameters over a range of  ± 50%. The simulation results and a comprehensive comparison between the controllers clearly demonstrates that the proposed control schemes including LPBO-PI-PD, AOA-PI-PD, and MPSO-PI-PD are very reliable, and they can effectively stabilize the frequency and terminal voltage in a multi-area IPS with combined LFC and AVR.

A Tilt Integral Derivative (TID) controller is designed in this paper for the Load Frequency Control (LFC) issue of a multi-area interconnected restructured power system. The suggested TID controller settings are fine-tuned using a novel optimization technique known as Hunger Games Search (HGS) algorithm. A multi-area interconnected power system with various generating units is used to test the performance of the proposed TID controller based on HGS. The suggested controller also takes into account system non-linearities such as Generation Rate Constraints (GRCs) and Governor Dead Band (GDB). The superiority of HGS's optimization over a range of other significant optimization techniques, such as the grey-wolf optimization algorithm, has been confirmed. The simulation results show that the proposed TID controller based on HGS improves system frequency stability significantly under a variety of load perturbation scenarios.

Event-triggered load frequency control of Markovian jump interconnected power systems under denial-of-service attacks

The growing integration of renewable distributed generators (DGs) poses significant frequency regulation challenges due to intermittency, uncertainties, and delays. This paper addresses these issues by designing and validating a robust Sliding Mode Controller (SMC) for Load Frequency Control (LFC) in complex power networks. The proposed control framework addresses a realistic multi-area system model incorporating nonlinearities such as Generation Rate Constraint (GRC), Governor Dead Band (GDB), and boiler dynamics, along with diversified generation units including thermal, hydro, gas, wind, solar photovoltaic, geothermal, and diesel-based DGs. To eliminate the chattering effect inherent in traditional SMC implementations, a saturation function is incorporated into the discontinuous control term. The SMC gains are optimally tuned using the Gannet Optimization Algorithm (GOA)—a novel bio-inspired technique modeled on the prey-capture dynamics of seabirds. Furthermore, a Modified GOA (MGOA) is proposed, where key parameters, such as the mass and velocity of gannets, are dynamically optimized using Particle Swarm Optimization (PSO) to enhance convergence precision. The comparative performance of GOA and MGOA is rigorously evaluated using six benchmark functions (e.g., Beale, Trid, Shekel), where MGOA consistently exhibits lower standard deviations and faster convergence rates, confirming its superiority in solution stability. Simulation studies conducted on MATLAB/Simulink reveal that the MGOA-SMC controller achieves superior transient performance compared to both PID and GOA-tuned SMC designs. Specifically, under a 1 % load disturbance, the proposed controller reduces frequency undershoot in area-1 from −0.7142×10−3Hz to−0.2678×10−3 Hz with an improvement of 62.5 %, overshoot in area-1 from 0.1627×10−3Hz to0.0315×10−3 Hz with an improvement of 80.6 %, and settling time from 0.15 sec to 0.02 sec with an improvement of 86.67 %. Similarly, tie-line power deviation in area-1 under the same load condition as improved by the proposed controller, such as undershoot from −0.2378×10−3p.u.MW to−0.0725×10−3p.u.MW with an improvement of 69.5 %, overshoot from 0.0543×10−3p.u.MW to 0.0267×10−3p.u.MW with an improvement of 50.8 %, and settling time from 0.06 sec to 0.02 sec with an improvement of 66.67 %. Robustness is further validated under scenarios involving nonlinearities, a 5-millisecond communication delay, random load variations, and ±20 % parameter perturbations, with minimal degradation in dynamic response. The sensitivity analysis confirms low standard deviation across performance indices, reinforcing the robustness of the control strategy. The standard deviation of undershoot, overshoot, and settling time for frequency in area-1 are (0.00065), (0.000084), and (1.85), respectively. Similarly, the standard deviation of undershoot, overshoot, and settling time for tie-line power are (0.00016), (0.00079), and (2.11), respectively. To demonstrate practical viability, the proposed system is implemented on an OPAL-RT 4510 real-time simulator. Hardware-in-the-loop results closely mirror the simulation outcomes, thereby validating the controller’s effectiveness in real-world environments. The study conclusively establishes that the MGOA-optimized SMC controller offers a scalable, computationally efficient, and resilient solution for load frequency regulation in nonlinear, DG-rich power systems. The proposed framework lays the groundwork for future extensions to address cyber-physical threats and decentralized control in smart grid applications.

A robust <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e2742" altimg="si774.svg"><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math> sliding mode control design for wind-integrated interconnected power system with time-delay and actuator saturation

This study focuses on designing an effective intelligent control method to stabilize the net frequency against load variations in multi-control-area interconnected power systems. Conventional controllers (e.g. Integral, PI, and PID) achieve only poor control performance with high overshoots and long settling times. They could be replaced with intelligent regulators that can update controller parameters for better control quality. The control strategy is based on fuzzy logic, which is one of the most effective intelligent strategies and can be a perfect substitute for such conventional controllers when dealing with network frequency stability problems. This paper proposes a kind of fuzzy logic controller based on the PID principle with a 49-rule set suitable to completely solve the problem of load frequency control in a two-area thermal power system. Such a novel PID-like fuzzy logic controller with modified scaling factors can be applied in various practical scenarios of an interconnected power system, namely varying load change conditions, changing system parameters in the range of ±50%, and considering Governor Dead-Band (GDB) along with Generation Rate Constraint (GRC) nonlinearities and time delay. Through the simulation results implemented in Matlab/Simulink software, this study demonstrates the effectiveness and feasibility of the proposed fuzzy logic controller over several counterparts in dealing with the load-frequency control of a practical interconnected power system considering the aforesaid conditions.

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.

Conventional control techniques such as proportional integral (PI) control and proportional integral derivative (PID) control are widely used as the load frequency controller in power system control applications; however, the increase in complexity of the power system is degrading the performance of classical control. Therefore, in this paper a new control approach using fractional calculus has been proposed for the load frequency control problem of two-area hydro-thermal power system. The paper presents an interconnected hydro-thermal power system working under different operating conditions introduced in the form of various nonlinearities. Four case studies have been presented in this paper considering transient analysis with (i) different loading conditions, (ii) parameter variations, (iii) different nonlinearities (governor dead band nonlinearity, time delay and generation rate constraints), and (iv) superconducting magnetic energy storage (SMES) device. A tilt integral derivative (TID) control has been presented as a secondary controller to stabilize the frequency deviations occurring in the two-area power system with the above-mentioned different operating conditions. The parameters of TID controller have been optimized using a differential evolution algorithm which solves an optimization problem formulated using the integral of time-weighted absolute error (ITAE) performance index. In addition, a comparison of dynamic system response obtained using TID control and PID control has been presented, which focusses on the better performance of TID control over PID control in an interconnected power system.

This paper proposes an optimal α-variable model-free adaptive barrier-function fractional-order nonlinear sliding mode control (α(t)-MF-ABFFONSMC) for the load frequency control (LFC) problem of a four-area interconnected hybrid power system with boiler dynamics and physical constraints. The proposed α(t)-MF-ABFFONSMC is comprised of the ultra-local model (ULM)-based sliding mode disturbance observer (SMDO), proportional-differential (PD) controller, and adaptive barrier-function fractional-order nonlinear sliding mode control (ABFFONSMC). The ULM mechanism is utilized to re-formulate the complex four-area interconnected hybrid power system so as to reduce the controller’s design complexity, wherein SMDO is utilized to observe and eliminate the uncertain dynamics or lumped disturbance. Then, the SMDO based-iPD controller is designed. However, there always exists non-null estimation error under the SMDO method and the control performance cannot be ensured. Therefore, the ABFFONSMC is proposed and inserted into the SMDO-iPD controller to avoid the impact of estimation error and improve the control performance. In addition, an adaptive gain based on barrier function is formulated to approximate the upper bound of SMDO’s estimation error and thus decrease the undesired chattering on the sliding surface. Correspondingly, the α(t)-MF-ABFFONSMC is established. Moreover, the parameter optimizer based on the Marine Predator Algorithm (MPA) is proposed to tune the parameters of the proposed α(t)-MF-ABFFONSMC controller. Furthermore, using the Lyapunov theorem, the stability of α(t)-MF-ABFFONSMC via a closed-loop system is verified. To validate the performance of the proposed controller, the numerical simulation on a four-area interconnected hybrid power system is carried out in a Matlab/Simulink environment. The corresponding simulation results are presented to show the superiority and effectiveness of the proposed technique.

The load frequency control (LFC) problem has been one of the major subjects in electric power system design and operation. LFC is becoming much more significant today in accordance with increasing size, changing structure and complexity in interconnected power systems. Practice LFC systems use simple proportional-integral (PI) controllers, but parameters of PI controllers are usually tuned based on the trial-and-error approaches and they are incapable to obtain good dynamic performance under a wide range of operating conditions. For this problem, in this paper quantitative feedback theory (QFT) method is used for LFC problem. A multi-area electric power system with a wide range of parametric uncertainties is given to illustrate proposed method. To show effectiveness of proposed method, a classical PI type controller optimized by genetic algorithms (GA) is designed to compare with QFT controller. The simulation results visibly show the validity of QFT method in comparison with traditional method. Key words: Multi-area electric power system, electric power system load frequency control, robust control, quantitative feedback theory method.

Design of sliding mode control optimised by the Bees algorithm for LFC in the Great Britain power system

Higher Order Degree of Freedom Controller for Load Frequency Control of Multi Area Interconnected Power System with Time Delays