Load frequency control (LFC) is a critical component in the design and operational management of stable and reliable power systems. Inherently, power systems are subject to dynamic and stochastic load variations, which introduce uncertainties that adversely impact system frequency stability [
1]. Such deviations from nominal frequency values are undesirable, as they compromise grid reliability and power quality. To mitigate these challenges, LFC mechanisms are employed to regulate frequency by dynamically adjusting generation output or minimizing frequency deviations, thereby maintaining system parameters within predefined operational thresholds. This regulatory process, referred to as load frequency control (LFC), is integral to ensuring the robustness and efficiency of modern power networks [
2].
1.1. Literature Review
The escalating complexity and evolving dynamics of contemporary power systems have positioned load frequency control (LFC) as a pivotal mechanism for preserving grid stability and operational reliability. Over recent decades, an extensive volume of scholarly work has been devoted to the domain of LFC in interconnected power networks. LFC functions as a key control strategy to mitigate the detrimental impacts of load fluctuations on system frequency and tie-line power flow, thereby ensuring reliable system operation [
4]. To confront these challenges, numerous control methodologies—ranging from conventional linear controllers to advanced intelligent techniques—have been explored to formulate resilient LFC frameworks capable of improving both transient performance and steady-state precision. Nevertheless, selecting the most appropriate LFC approach remains a complex endeavor, as each control scheme entails specific merits and drawbacks influenced by system nonlinearity, operational limitations, and regulatory conditions. Consequently, the practical realization of effective LFC systems demands in-depth domain expertise to navigate the inherent trade-offs between control complexity, flexibility, and performance robustness under dynamically varying grid environments [
5,
6].
The proportional–integral–derivative (PID) controller continues to serve as a fundamental component in LFC system design, primarily due to its structural simplicity, straightforward implementation, and well-established effectiveness in handling linear dynamics. Its widespread adoption extends far beyond power systems, with extensive use in industrial automation, robotics, and process control, reflecting its adaptability across engineering domains [
7]. Within LFC applications, the PID controller maintains system frequency by modulating generator output based on proportional, integral, and derivative error components. In Ref. [
8], a PI controller was optimized using the Flood Algorithm (FLA) for a two-area power system that integrates thermal and photovoltaic (PV) generation. The findings indicated that the FLA-optimized controller outperformed alternative metaheuristic approaches in terms of reduced settling time, minimal overshoot, and lower steady-state error, particularly under fluctuating solar input and variable load profiles. Similarly, the Firefly Algorithm (FA) was employed in Ref. [
9] to fine-tune a PI controller for frequency regulation in a two-area system with PV integration. In another instance, Particle Swarm Optimization (PSO), a widely adopted technique, was applied in Ref. [
10] to tune a PID controller in a stand-alone multi-source configuration for frequency control. Furthermore, the Artificial Bee Colony (ABC) algorithm was utilized in Ref. [
11] to optimize PID parameters for an LFC scheme implemented in a hydro–thermal interconnected system. This controller outperformed conventional PID controllers tuned using different algorithms, including the Chef-Based Optimization Algorithm (CBOA) and Sine–Cosine Algorithm (SCA). In Ref. [
12], the Lozi map-based Chaotic Optimization Algorithm (LCOA) was used to optimize parameters for a classical PID controller in a two-area interconnected power system for LFC. Furthermore, Ref. [
13] proposed a Rat Swarm Optimization (RSO)-based PID controller demonstrating improved stability, shorter settling time, and near-zero frequency deviations. This method surpassed traditional approaches by consistently maintaining frequency regulation under dynamic conditions, strengthening overall system resilience.
Recent studies confirm that conventional PID controllers fundamentally struggle to mitigate the nonlinearities, parametric uncertainties, and communication delays inherent in modern power grids. To overcome these limitations, researchers have developed advanced variants including fractional-order PID (FOPID), PID-Acceleration (PIDA), and Filtered/Double-Derivative PID (PIDF/PIDD), alongside cascaded structures like PID-PI and adaptive gain-scheduled architectures.
Fractional-order PID (FOPID) controllers incorporate non-integer-order differentiation and integration operators through fractional calculus, enabling enhanced tuning flexibility and robustness. Recent advances confirm significant FOPID performance improvements in power systems. Specifically, Ref. [
14] introduced optimized PID and FOPID controllers for load frequency control (LFC) in a three-area thermal–wind–hydro system, utilizing advanced metaheuristics—the Genetic Algorithm (GA), the Grey Wolf Optimizer (GWO), the Sine–Cosine Algorithm (SCA), and Atom Search Optimization (ASO)—with evaluation across multiple cost functions. The results demonstrated that ASO-tuned FOPID delivered superior transient performance and robustness under dynamic conditions. Complementarily, Ref. [
15] developed an FOPID controller for single-area LFC, tuned via Integral Error Criterion (IEC) and applied to distinct turbine configurations: non-reheat, reheat, and hydro turbines. The controller was tuned for robustness against ±50% parameter uncertainties and demonstrated superior disturbance rejection relative to traditional approaches. Simulation outcomes validated the FOPID controller’s capability to maintain performance under both nominal and uncertain system conditions. Concurrently, Ref. [
16] introduced a deregulated hybrid power system scenario in which an Aquila Optimizer (AO)-based FOPID controller was developed for LFC. Comparative analysis showed that the AO-FOPID configuration outperformed controllers optimized using Particle Swarm Optimization (PSO) and the Whale Optimization Algorithm (WOA), effectively reducing frequency deviations and tie-line power oscillations across a range of dynamic operating conditions.
Regarding PID-Acceleration (PIDA), Ref. [
17] developed hybrid strategies combining Teaching–Learning-Based Optimization (TLBO), Tabu Search (TS), and Equilibrium Optimizer (EDO) for PIDA tuning in two-area load frequency control. These methods enhanced convergence speed, dynamic response, and robustness against load variations and renewable energy fluctuations. The simulation results demonstrated that the TLBO-EDO-tuned PIDA controller outperformed conventional methods by minimizing peak-to-peak oscillations, root mean square (RMS) error, and tie-line power deviations under multiple contingencies. Regarding Filtered/Double Derivative PID (PIDF/PIDD), n Ref. [
18], a Modified Whale Optimization Algorithm (MWOA) was proposed to tune a proportional–integral–derivative with filter (PIDF) controller for load frequency control in a two-area photovoltaic–thermal power system. The simulation results demonstrated that the MWOA-optimized PIDF controller delivered improved damping characteristics and enhanced robustness compared to controllers tuned using conventional optimization techniques. In a separate study [
19], a proportional–integral–double-derivative (PIDD) controller was applied to an isolated hybrid power system (IHPS) comprising conventional generators, renewable energy sources, energy storage devices, and electric vehicles (EVs). The controller parameters were optimized using the Magneto-Tactic Bacteria Optimization (MBO) algorithm, with tuning guided by a peak-based integral square error (PISE) performance index. The simulation results indicated that the PIDD controller provided superior frequency regulation under combined load and generation disturbances, outperforming classical counterparts. However, nonlinearities, such as generation rate constraints and governor dead band, were not included in the control design. These variants attenuated high-frequency noise sensitivity while enhancing transient performance, with PIDD structures demonstrating superior robustness under load variations.
However, PID-based controllers require precise tuning and demonstrate limited effectiveness in highly nonlinear or stochastic environments. These limitations have motivated the development of advanced control methodologies aimed at overcoming the constraints of linear controller architectures:
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Sliding Mode Control (SMC): SMC is recognized for its robustness against uncertainties, directing system trajectories toward a predefined sliding surface. Recent studies on SMC for load frequency control (LFC) have introduced various advanced controller designs and optimization strategies. In Ref. [
20], an SMC design was developed for a simplified model of the Great Britain power system, utilizing a five-parameter sliding surface optimized through the Bees Algorithm (BA) and Particle Swarm Optimization (PSO), with performance evaluated using the ITAE criterion. The results were compared to a BA-tuned PID controller, showing that the SMC configuration delivered a superior dynamic response and stronger robustness to parameter uncertainties. In Ref. [
21], an output feedback SMC was proposed for a multi-area, multi-source power system, where Teaching–Learning-Based Optimization (TLBO) was used to tune feedback gains and switching vectors. This design outperformed other approaches based on Differential Evolution, PSO, and Genetic Algorithms and included consideration of HVDC link dynamics. The study in Ref. [
22] developed a four-parameter SMC controller optimized by PSO and Grey Wolf Optimization (GWO), implemented across single-, two-, and four-area systems. It demonstrated significant improvements in frequency regulation and robustness under load disturbances and system uncertainties. While all three works emphasized robust controller tuning under various disturbance scenarios, none explicitly incorporated nonlinear dynamics into the system models.
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Linear Quadratic Regulator (LQR): The studies in Refs. [
23,
24] proposed LQR-based approaches for load frequency control in power systems but omitted nonlinear considerations during controller design. In Ref. [
23], an advanced LQR scheme based on Linear Matrix Inequalities (LMIs) was implemented in a hybrid system incorporating wind turbines, diesel generators, fuel cells, aqua-electrolyzes, and battery energy storage. This controller exhibited improved performance under various disturbances when compared with conventional closed-loop LQR methods. In Ref. [
24], the LQR technique was applied to a two-area power system and assessed against a conventional PI controller under step load perturbations, with evaluation focusing on frequency regulation and system stability. While both studies demonstrated the effectiveness of optimal control strategies in enhancing LFC performance, they were constrained by their reliance on linearized models, limiting their applicability to real-world systems characterized by inherent nonlinear dynamics.
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Model Predictive Control (MPC) techniques enhance LFC performance under diverse operating conditions. In Ref. [
25], a hybrid Grey Wolf Optimizer–Pattern Search (HGWO–PS)-tuned MPC for a two-area islanded microgrid was used to improve frequency stability and reduce control complexity.
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Adaptive control strategies for LFC in interconnected power systems were proposed in Refs. [
26,
27] to enhance stability under disturbances and parameter variations. Specifically, Ref. [
26] introduced an adaptive PI controller that dynamically tuned gains during load/renewable fluctuations (including WECS and PV–thermal systems), exhibiting superior robustness and transient performance versus conventional PI/optimized PID methods. In contrast, Ref. [
27] implemented decentralized Model Reference Adaptive Control (MRAC) for two-area systems, utilizing local feedback signals with Lyapunov-based stability guarantees. Critically, both approaches neglected nonlinear elements (dead bands, valve limits), potentially compromising real-world applicability and reliability.
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H-infinity Control (H∞): The study in Ref. [
28] proposed a robust H∞-based LFC strategy for a two-area interconnected power system, addressing nonlinearities and parameter uncertainties using a sector-bounded formulation. The simulation results confirmed superior performance compared to conventional PI controllers, with reduced frequency deviations and enhanced stability under load disturbances and uncertainty. The method further demonstrated scalability to multi-area systems while sustaining robust performance across varying operating conditions.
Fuzzy Logic Control (FLC) offers a potent solution for LFC in nonlinear, stochastic, and model-agnostic environments by leveraging expert-defined linguistic rules for decision-making under uncertainty. Its key advantages include intrinsic nonlinearity handling [
29], enhanced robustness [
30], and compatibility with hybrid architectures [
31,
32]. However, FLC performance critically depends on the rule base and membership function design, demanding rigorous optimization that may challenge practical implementation.
Table 1 summarizes LFC systems reported in the literature.
Concisely, classical PID controllers remain a cornerstone of LFC because of their simplicity and cost-efficiency. Yet, their limited effectiveness under nonlinear and uncertain conditions necessitates the adoption of advanced control strategies:
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Enhanced PID variants—such as FOPID and PIDA—extend classical PID capabilities in robustness and adaptability, though at the cost of increased design and tuning complexity.
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Advanced controllers (SMC, MPC, H∞) provide precision and robustness but encounter computational and implementation challenges.
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Fuzzy Logic Control balances adaptability and implementation feasibility in hybrid architectures, positioning it as a viable strategy for modern power systems.
1.2. Objectives and Contributions
A critical gap remains in evaluating how nonlinearities, specifically generation rate constraints (GRCs) and governor dead band (GDB), influence frequency stability within load frequency control (LFC) systems. While prior work acknowledges their operational significance, few studies rigorously assess their impact when integrated into or excluded from LFC design. This underscores the need for a systematic investigation into how these elements affect LFC performance and overall system dynamics. This study conducts a comprehensive analysis of GRC and GDB effects on frequency regulation, addressing a pivotal research gap.
1.2.1. Challenges in LFC System Design
A core challenge in LFC design lies in balancing rapid dynamic response with system stability. Fast transient correction enables timely frequency stabilization in dynamic grids, particularly during load fluctuations, thereby minimizing downtime and maintaining operational continuity. However, aggressive responses risk overshoots that exceed safety thresholds, jeopardizing sensitive equipment. In contrast, slower corrections ensure frequency adherence but may introduce underfrequency or overfrequency deviations during transitions, reducing reliability. Thus, optimal LFC controllers must harmonize rapid stabilization with overshoot minimization to ensure both performance and operational safety.
1.2.2. Limitations of Existing Control Strategies
Traditional PID controllers remain prevalent in LFC applications because of their simplicity, cost-efficiency, and ease of implementation. However, their performance deteriorates in the presence of nonlinearities, parametric uncertainties, and system sensitivity—challenges typical of modern power networks. Notably, PID controllers often struggle to maintain voltage stability during dynamic load variations. Advanced methods, such as adaptive control and Sliding Mode Control (SMC), offer improved robustness. Adaptive control adjusts gains in real time, enhancing performance under uncertainty, though its complexity and tuning demands limit practical deployment. SMC provides robustness against matched uncertainties but introduces chattering—undesired high-frequency oscillations that impair performance and accelerate actuator wear. Fuzzy logic controllers (FLCs) eliminate the need for precise mathematical models by utilizing expert-defined linguistic rules. Nevertheless, many FLC implementations overlook robustness under variable operating conditions, limiting their reliability in dynamic environments.
1.2.3. Proposed Methodology and Contributions
This study proposes a novel hybrid fuzzy controller that integrates a fuzzy fractional-order proportional–integral–derivative (FOPID) structure with a classical PI controller, optimized using the Catch Fish Optimization (CFO) algorithm. The main contributions are outlined as follows:
Impact of Nonlinear Elements: This study conducts a systematic investigation of GRCs and GDB on power system stability, providing critical insights for future LFC design.
Innovative Controller Design: This study proposes a hybrid FOPID + PI configuration that synergizes fuzzy logic adaptability with classical control precision to enhance stability and dynamic response.
Optimization via Metaheuristic Algorithms: The CFO algorithm is applied for the first time in LFC contexts to optimize controller parameters, complemented by Particle Swarm Optimization (PSO) for comparative validation.
Comprehensive Performance Evaluation: This study conducts a rigorous comparative analysis against existing controllers, demonstrating superior transient response, overshoot mitigation, and robustness under parametric uncertainties. Also, the proposed controller is implemented in two different power systems under different operating conditions to validate its readiness for real-time operation.
Robustness Validation: The proposed controller exhibits resilience in maintaining frequency stability under diverse disturbances, including ±35% parametric variations and abrupt load changes.
By integrating fractional-order dynamics with fuzzy logic and metaheuristic optimization, this study advances LFC controller design, addressing the limitations of conventional and advanced methods. The hybrid Fuzzy FOPID + PI controller demonstrates enhanced reliability, robustness, and adaptability in dynamic environments, offering a viable solution for modern power systems. These findings underscore the imperative of incorporating nonlinear element analysis and innovative control architectures to ensure stable, efficient frequency regulation in increasingly complex grids.