The Study of Optimization Methods for Load Frequency Control in Multi-area Power System

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.

Son zamanlarda, artan enerji talebi ve yenilenebilir enerji kaynaklarının (YEK) elektrik güç sistemlerinde yer almasıyla, enterkonnekte güç sistemlerinde frekans ve gerilim kararlılığının önemi artmaktadır. Modern güç sistemlerinde tüketiciye kaliteli, sürekli ve kararlı elektrik enerjisi iletimi sağlanmalıdır. Güç sistemlerindeki ani yük değişimlerinde güç üretimi ile yük talebi arasındaki uyumsuzluk, üretim bölgeleri arasındaki frekansta istenmeyen salınımlara neden olur. Sistemdeki frekans salınımlarını minimize etmek için yük frekans kontrolü (YFK) uygulanır. Sistemdeki salınımları bastırmak için kullanılan denetleyiciler, istenen sistem kriterleri doğrultusunda tatmin edici bir şekilde çalışmalıdır. Bu bağlamda PID ve PID+DD denetleyici yapılarından yararlanılmıştır. Denetleyici parametrelerinin optimizasyonunda literatürde sunulan GBO, BSA ve BKA algoritmaları kullanılmıştır. YFK problemi, termal, hidroelektrik, gaz, rüzgar ve dizel enerji sistemlerini içeren çok kaynaklı tek alanlı test sisteminde incelenmiştir. Test sisteminin doğrusalsızlığını artırmak için kazan dinamiği yapısı kullanılmıştır. Optimizasyon işlemi sonucunda algoritmaların denetleyici parametrelerini optimize etme başarısı kendi içinde değerlendirilmiş ve BSA algoritmasının diğer algoritmalara göre daha başarılı olduğu görülmüştür.

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.

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.

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 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.

In this paper, the influence of a Superconducting Magnetic Energy Storage (SMES) unit on the performance of the Automatic Generation Control (AGC) is investigated. In which, the self-tuning Fuzzy PI Controller (FPIC) associated with the Automatic Generation Control (AGC) is proposed for the improvement of Load Frequency Control (LFC) in wind farm integrated large power system consisting of thermal and hydro power plants. The effects of the self-tuning FPIC in AGC on SMES control is compared with that of optimized fixed gain PI controlled AGC. The computer simulation of the two-area interconnected power system shows that the self-tuning fuzzy PI control scheme of AGC is very effective for SMES control to damp out of the oscillations caused by load disturbances in one or both of the areas and it is also seen that the proposed controlled AGC including SMES performs more effective primary frequency control compared to optimized fixed gain PI controlled AGC including SMES.

This paper proposes a robust control strategy involving a novel optimised fuzzy-PID controller tuning by particle swarm optimisation (PSO) algorithm. The proposed control strategy was suggested to design an intelligent load frequency control (LFC) scheme in multi-area interconnected power system. The PSO algorithm was employed to optimise the fuzzy-PID controller parameters including the scaling factors of fuzzy logic and the PID controller gains for minimisation of both system frequency deviation and tie-line power changes during load disturbances using the integral time multiply absolute error (ITAE) as objective function. To demonstrate the effectiveness of the proposed control strategy, the three-area 9-unit interconnected power system was used for the simulation. The superiority of the proposed approach was shown by comparing the obtained results to other strategies available in literature. Initially, the simulation was performed using the same controllers in each area, and then was extended with different controllers in each area. The comparative study demonstrates the potential of the proposed control strategy and shows its robustness to enhance frequency stability.

This work presents a comprehensive analytical performance evaluation and comparison of two advanced controllers for Automatic Generation Control (AGC) in Multi-Area Power Systems (MAPS). The first is the Hybrid Many Optimising Liaison and Modified Harris Hawk Optimised Proportional Derivative Proportional Integral and Proportional Integral Derivative with Derivative Filter (MOLMHHO PD-PI+PIDF) controller, while the second is an enhanced version incorporating double fuzzy logic (MOLMHHO Double Fuzzy PD-PI+PIDF) controller. These controllers were designed to address the problem of inadequate frequency regulation in MAPS, which often suffers from large disturbances and system nonlinearities. The proposed Hybrid MOLMHHO Double Fuzzy PD-PI+PIDF controller outperforms existing strategies in terms of sensitivity to load disturbances, providing significant improvements in Integral of Time Absolute Error (ITAE), such as 84.448%, 96.642%, 95.696%, 100%, 100% and 99.914 with respect to MOL Double Fuzzy PD-PI+PIDF, HHO Double Fuzzy PD-PI+PIDF, LUS-TLBO Fuzzy PIDF, TLBO PID, LUS PID and DE PI, respectively. Validation was performed through simulations on a two-area Non-Reheat Thermal Power System (NRTPS) and extended to a four-area Reheat Thermal Power System (RTPS). Real-time validation using the OPAL-RT platform confirmed the controller's practical applicability, exhibiting high stability with infinite gain margins and large phase margins in Bode plots.

In a companion paper [1], authors presented fundamental aspects of Load Frequency Control (LFC) and review of literature on different LFC methods that were proposed for pre-deregulation scenario. After deregulation of power system, LFC plays key role in providing better conditions for electricity trading. Although, complicacy has increased significantly with additional constraints, LFC has emerged as one of the most profitable ancillary services in the power market. The prime objective of the LFC is to efficiently track the load variations in a multi-area power system and thus maintain zero steady-state errors for frequency deviation. In a deregulated environment, independent generators and utility generators may or may not participate in the LFC, therefore more adaptive and market oriented control techniques are desirable for deregulated power systems. This paper provides literature review on LFC strategies suitable for deregulated power system scenario. Case studies on some of these techniques have been presented for clear illustration of these methods. Finally, key issues and challenges in LFC in deregulated environment have been highlighted.

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.

In this paper, oppositional biogeography based optimization (OBBO) algorithm for load frequency control with interconnected two-area hydro-hydro power system have been investigated. As a consequence of continually load variation, the frequency of the power system changes over time. To stabilize the system frequency oscillations, the active power can be controlled via superconducting magnetic energy storage device (SMES). The significant improvement of optimal transient performance is observed with the addition of SMES unit fitted in both areas. Analysis reveals that SMES unit fitted in either of the areas is as effective as SMES units fitted in both the areas and improves the dynamic performances to a considerable extent following a load disturbance in either of the areas. Gains of the integral controller in LFC loop and parameters of SMES are optimized with the help of OBBO technique. The performance of the proposed OBBO based controller is better as compared with BBO, CRPSO and RGO controller in the presence of SMES. The simulation results indicate the superiority of the proposed OBBO based controller with SMES in terms of system oscillations, settling time and frequency deviation.

Even the simplest version of the distribution networks face challenges such as maintaining load voltage and system frequency stability and at the same time minimizing the circulating reactive power in grid-forming nodes. As the consumers at the far end of the radial distribution network face serious voltage fluctuations and deviations once the load varies. Therefore, this paper presents an enhanced distributed control strategy to restore the load voltage magnitude and to realize power-sharing proportionally in islanded microgrids. This proposed study considers the voltage regulation at the load node as opposed to the inverter terminal. At the same time, a supervisory control layer is put on to observe and correct the load voltage and system frequency deviations. This presented method is aimed at replacing paralleled inverter control methods hitherto used. Stability analysis using system-wide methodical small-signal models, the MATLAB/Simulink, and experimental results obtained with conventional and proposed control schemes verify the effectiveness of the proposed methodology.

Since a Superconducting Magnetic Energy Storage (SMES) unit with a self–commutated converter is capable of controlling both the active and reactive powers simultaneously and quickly, increasing attention has been focused recently on power system stabilization by SMES control. This paper presents a novel control method of SMES with a self-tuned Fuzzy Proportional Integral (FPI) controller associated with the Automatic Generation Control (AGC) for improving Load Frequency Control (LFC) in a single area power system. Boiler dynamics and nonlinearities such as governor dead band (DB) and generator rate constraints (GRC) are considered in the developed comprehensive mathematical model of a single area isolated power system. The effects of the self–tuning configuration of FPI controller in AGC on SMES control is compared with that of fixed gain PI controlled AGC. It is seen that with addition of FPI controller, SMES can perform a more effective primary frequency control for single area power system. Key words: Load frequency control; single area power system; automatic generation control; superconducting magnetic energy storage unit; fuzzy proportional integral controller

Fractional order phase lead-lag controller (FOPLC) is a generalization of classical phase lead-lag controller (CPLC) using fractional calculus. Nowadays, fractional order controllers (FOC) have found wide applications in various aspects of power system control and operation. In this paper, FOPLC are used in structure of flexible ac transmission system (FACTS) based frequency stabilizer to enhance the dynamic performance of automatic generation control (AGC) system. So, Thyristor controlled series capacitor (TCSC) based damping controller with FOPLC structure is proposed in coordination with secondary integral load frequency controller (LFC). The controller is optimized via an improved particle swarm optimization (IPSO) algorithm. The dynamic performance of the proposed controller is compared with CPLC using eigenvalue analysis and time domain simulations. An interconnected multi-source realistic power system with TCSC in series with the tie-line is investigated considering the nonlinearity effects of generation rate constraint (GRC) and governor dead band (GDB). Simulation results reveal that FOPLC based TCSC damping controller achieves superior dynamic performance under various load perturbation patterns in terms of decreased performance index, settling time and amplitude of oscillations. Furthermore, the robustness of the proposed controller has been tested for large uncertainties in system parameter and loading condition.