Bat Algorithm Optimized Controller for Automatic Generation Control of Interconnected Thermal Power System

In this paper, a self-tuning hierarchical controller in which a Fuzzy logic controller supervises the control actions of a conventional PID has been proposed, implemented and presented. The controller has been applied to a control study of Fluid Catalytic Cracking (FCC) unit riser temperature, and regenerator temperature respectively. Performance comparison of the proposed Fuzzy-PID controller and the conventional PID was made in simulation studies of regulatory and servo performances of the two controller types. Six performance measures: Percent overshoot (OS), settling time (ST), integral absolute error (IAE), integral square error (ISE), integral time absolute error (ITAE) and integral time square error (ITSE) were employed as the tools for performance comparison between the conventional PID and the Fuzzy-PID controller. For the tracking of riser temperature with a set point at 524oC, the performance indicators under PID control gave the following results overshoot (14.5%); settling time (40 seconds) Integral absolute error (8.246), integral square error (3.3); integral time absolute error(1762);integral time square error (43.77) while for the same indicators under Fuzzy-PID control the following values: overshoot (3.3%); settling time (40 seconds) ;Integral absolute error (8.811); integral square error (14.5); integral time absolute error(280),;integral time square error (31.11) .The results allude to the superiority of the fuzzy-PID scheme over the PID scheme in tracking the optimal set point of riser temperature. More so, for tracking the regenerator set point temperature of 746oC, comparative study of step response under the two schemes gave the following results in six performance indicators: overshoot (PID(12.6%)/Fuzzy-PID(6%)); settling time (PID(80 seconds)/Fuzzy-PID(20seconds));Integral absolute error(PID(14.29)/Fuzzy-PID(8.63)); integral square error(PID(6.713).Fuzzy-PID(4.506)); integral time absolute error(PID(2858)/Fuzzy-PID(305.9)), integral time square error (PID(77.55)/Fuzzy-PID(33.05)).Moreover, the fuzzy-PID controller also showed superior performance over the conventional PID controller in terms disturbance rejection (regulatory response) of both riser and regenerator temperature. The results from this study suggest that the application of fuzzy-PID scheme to temperature control offers good promise of improved fluid catalytic cracking unit (FCCU) operations.

This paper demonstrates the design and analysis of automatic generation control using intelligent genetic algorithm tuned fuzzy based controller. A two area thermal power system simulated for four different scenarios considers a reheat steam turbine in each area with Generator rate constraints. The Integral Time Squared Error (ITSE) employed to get an objective function for the optimization of controller gains. The simulation results compared with the conventional Proportional Integral Derivative (PID) controller, Genetic Algorithm (GA) tuned PID controller and GA tuned Fuzzy PID controller. The proposed GA tuned Fuzzy based PID Controller can generate the best performance for peak overshoot, undershoot and settling time with step load disturbances. Robustness of the performance of the proposed controller provided with system parametric uncertainties.

Firefly algorithm (FFA) optimization technique is a popular continuous optimization technique and also widely applied to tune controller gain values of proportional–integral–derivative (PID) controller. In the chaos-based firefly algorithm, the chaotic maps are included to improve the randomness when generating new solutions and thereby to increase the diversity of the population. It increases global search mobility for robust global optimization. The investigated power system incorporates two thermal power systems, and two areas are interconnected via tie-line. Also, this work system is equipped with a secondary (PID) controller. The gain value of the controller is optimized by implementing chaos-based firefly algorithm (CFFA) by applying step load in area 1. The effectiveness and supremacy of proposed optimization technique tuned controller performance are verified by comparing genetic algorithm (GA), particle swarm optimization (PSO) technique and firefly algorithm tuned PID controller performance in the same interconnected power system. The proposed optimization technique-based controller response is evaluated by considering time domain specifications parameters of the proposed optimization technique-based controller response. Further, effectiveness of recommended optimization technique is verified by adding nonlinearity’s [generation rate constraint (GRC) and governor dead band (GCB)] in the investigated power system with connecting unified power flow controller (UPFC) is applied, and it is a flexible alternating current transmission system (FACTS) controller family device connected parallel to the tie-line. Further, hydrogen aqua electrolyzer (HAE) energy storage unit with a fuel cell is connected in area 2 for improving the performance of the system during sudden load demand. Finally, simulation result proved that the proposed CFFA technique gives better controlled performance compared with GA, PSO and FFA technique tuned controller performance in terms of fast settled response with a minimum peak over and undershoot, damping oscillations during unexpected load demand conditions.

In the category of small signal stability problem, one of the major causes of unpredictability of power transfer in the inter-connected power system is due to low frequency oscillations (LFO). These oscillations in the inter-connected power system, affects the power transfer capability and thereby, needed to be suppressed. To damp the oscillation and protect the power system, power system stabilizers are used. In this study, a Kho-Kho optimization (KKO) based proportional integral derivative (PID) power system stabilizer is put forward which can suppress the LFO in the inter-connected power system. Optimization methods are widely being used to solve number of optimization problem. Therefore, in this work the specification of the stabilizer are calibrated using KKO technique by optimizing a objective function constructed using the Integral time square error (ITSE) of the speed deviation. To test the effectiveness of the designed optimal controller, a one machine infinite bus (OMIB) with IEEE type DC-1 exciter unit is also taken into consideration. The superiority of the proposed technique is examined by comparing the obtained results with some other existing techniques.

The artificial gorilla troops optimization (GTO) is a recently-introduced metaheuristic optimization technique for non-linear, non-convex and non-smooth problems with multiple types of variables. This algorithm, which is a nature-based technique, has been inspired by the social intelligence of gorilla troops. This study delves into how optimal can a power system stabilizer (PSS) unit be tuned incorporating GTO algorithm. The Integral Time Square Error (ITSE) was utilized as a fitness function, which desirably should be minimized. Four different controllers are employed to investigate the model of a single-machine scheme as a model for the infinite bus. The tilt-integral-derivative (TID) shows a better performance response in comparison with the PID controller, lead-lag controller, as well as fractional-order PID controller (FOPID) investigated. The results have implied that the GTO algorithm has obtained faster convergence over the other compared optimization techniques, while it has superiority in not trapping in local optimum points. It has shown also a high level of precision.

Abstract: This study presents a comparative analysis of five metaheuristic algorithms for optimizing Proportional Integral Derivative (PID) controller parameters in a vehicle cruise control system. The selected algorithms include the Rain Optimization Algorithm (ROA), Student Psychology-Based Optimization (SPBO), Sine Cosine Algorithm (SCA), Gradient-Based Optimization (GBO), and Grey Wolf Optimization (GWO). The PID parameters are optimized using four common performance criteria: Integral Time Absolute Error (ITAE), Integral Absolute Error (IAE), Integral SquareError (ISE), and Integral Time Square Error (ITSE). Unlike conventional tuning methods, metaheuristic approaches provide more flexible and adaptive parameter selection, enhancing the control system's robustness. The study analyses the algorithms under several internal and external disturbances, including road incline, passenger mass, and measurement noise. The findings demonstrate that no singular algorithm is universally superior; instead, efficacy is contingent upon the particular system conditions and control objectives. The Sine Conine Algorithm (SCA) has superior overall performance under typical settings, while GWO attains the quickest response time for slope fluctuations. Conversely, ROA reduces overshoot, rendering it appropriate for applications that necessitate stability. Additionally, the proposed methods are compared with the classical Ziegler-Nichols tuning approach, demonstrating the advantages of metaheuristic algorithms in terms of reduced overshoot, faster settling time, and improved robustness. The findings indicate that the SCA with the ITAE criterion yields superior performance under varying disturbance conditions. However, the fastest system response under different slope conditions isachieved with the parameter values determined by the GWO employing the ITSE criterion. The system model is designed in a MATLAB environment and the detailed comparative results are provided in figures and tables.Cite this article as: F. Heybetli, Y. Danayiyen, A. Begüm Taşdemir and Ş. Şenyiğit, "Comparative analysis of metaheuristic algorithms in PID-based vehicle cruisecontrol systems," Electrica, 25, 0051, 2025. doi: 10.5152/electrica.2025.24051.

The cart‐inverted pendulum is a non‐minimum phase system having right half s‐plane pole and zero in close vicinity to each other. Linear time invariant (LTI) classical controllers cannot achieve satisfactory loop robustness for such systems. Therefore, in the present work the fractional order PIλDμ (FOPID) controller is addressed for robust stabilization of the system, since fractional order controller design allows more degrees of freedom compared to its integer order counterparts by virtue of its two parameters λ and μ. The controller parameters are tuned by three evolutionary optimization techniques. In order to select the controller parameters optimally, a novel non‐linear fitness function using integral time square error (ITSE), settling‐time, and rise time is proposed here. The control algorithm is implemented successfully in real‐time. Moreover, stability analysis of the system compensated with a fractional order controller is presented using Riemann surface. Robustness of the physical cart‐inverted pendulum system towards multiplicative gain variations and plant parameter variations is verified. In this regard, it is shown that the fractional order controller provides satisfactory robust performance in both simulation and real‐time system.

This study presents the exponential distribution optimization (EDO) technique for tuning the proportional-integral-derivative (PID) controller parameters in combined load frequency control (LFC) and automatic voltage regulation (AVR) for both single- and two-area electrical power system models. The objective is to enhance system performance by minimizing frequency and voltage deviations. The proposed approach leverages widely adopted objective functions, namely, the integral time squared error (ITSE) and the integral time absolute error (ITAE) to effectively reduce control errors while improving system stability and transient response. The EDO algorithm iteratively refines PID parameters by selecting optimal values from evolving solution populations, with system disturbances introduced to evaluate robustness under varying operating conditions. Simulation results demonstrate significant improvements, including a 16.52% reduction in LFC undershoots and a 33.3% improvement in AVR steady-state error in single-area systems, and up to 13.2% faster settling times in two-area systems. The EDO-based controller achieves faster dynamic responses, smoother operation, and complete elimination of steady-state errors while maintaining balanced frequency overshoot and minimized transient oscillations. Comparative analyses confirm the method’s superiority over established optimization techniques. A comprehensive robustness further validates the reliability and effectiveness of the EDO-tuned PID controller, underscoring its strong potential for ensuring power system stability.

Automatic generation control of multi-area power systems with diverse energy sources using Teaching Learning Based Optimization algorithm

This work presents an analysis, design, and comparison of the PI (Proportional and Integral) controller and control schemes PI linear and nonlinear controllers reset-based. The parameters of these control schemes have been set by trial and error to finally be tested in a nonlinear process with variable dead time. Controller performance is measured using integral square error (ISE), integral time square error (ITSE), total variations of control efforts (TVU), maximum overshoot (\(M_{p}\)) and settling time \(\left( {t_{s} } \right)\). The results show that reset control systems overcome fundamental limitations coming from linear control systems.

This paper presents a new neural network based model reference adaptive system (MRAS) to solve low speed problems for estimating rotor resistance in vector control of induction motor (IM). The MRAS using rotor flux as the state variable with a two layer online trained neural network rotor flux estimator as the adaptive model (FLUX-MRAS) for rotor resistance estimation is popularly used in vector control. In this scheme, the reference model used is the flux estimator using voltage model equations. The voltage model encounters major drawbacks at low speeds, namely, integrator drift and stator resistance variation problems. These lead to a significant error in the estimation of rotor resistance at low speed. To address these problems, an offline trained NN with data incorporating stator resistance variation is proposed to estimate flux, and used instead of the voltage model. The offline trained NN, modeled using the cascade neural network, is used as a reference model instead of the voltage model to form a new scheme named as “NN-FLUXMRAS.” The NN-FLUX-MRAS uses two neural networks, namely, offline trained NN as the reference model and online trained NN as the adaptive model. The performance of the novel NN-FLUX-MRAS is compared with the FLUX-MRAS for low speed problems in terms of integral square error (ISE), integral time square error (ITSE), integral absolute error (IAE) and integral time absolute error (ITAE). The proposed NN-FLUX-MRAS is shown to overcome the low speed problems in Matlab simulation.

In this paper, an optimal PID (proportional-integral-derivative) controller is designed for controlling the non-minimum phase system with time delay and performed greater than the conventional control approaches. When there is an increment in time delay then complications related to NMP system determines the undershoot response due to presence of zeros in the right half plane. Furthermore, Ziegler-Nichols, Internal Model Control (IMC) and Chien-Hrones & Reswick tuning approaches are developed for the conventional PID controller. The time-domain characteristics obtained are unable to persuade the requirements of the system. In order to improve the performance criteria, Smith’s predictor is used for controlling the NMP system. Smith’s predictor is better than the conventional PID controller techniques for tuning the parameters but has the incapability to achieve all the design requirements. For improving the performance requirements, the optimal PID controller is designed with the employment of Linear Quadratic Regulator (LQR). The tuning parameters of PID controller are optimal values using popular technique that is Linear Quadratic Regulator (LQR). In order to minimize integral time absolute error (ITAE) and integral time square error (ITSE), the tuning parameters are optimal and give precise values of rising time, peak time, % overshoot and settling time. The simulation results are obtained and according to that LQR gives better results than Smith Predictor and other conventional PID controller techniques.KeywordsNon-minimum phase systemPID controllerSmith predictorConventional tuning methodsLinear quadratic regulator

Reactive Power Control of Isolated Wind-diesel Hybrid Power System Using Grey Wolf Optimization Technique

In this study, liquid level control in a coupled tank system is realized with PI controllers whose parameters are adapted using fuzzy logic approximation methods. Type-1 fuzzy PI control, interval type-2 fuzzy PI control and classical PI+Feedforward control methods are applied to the tank system in real time for different reference liquid levels. The performances of the controllers are compared in terms of system response parameters such as rise time, settling time and overshoot percentage. In addition, the performance evaluation of the controllers over a certain period of time is also compared by calculating integral-based concepts that express error performance metrics such as integral square error (ISE), integral time square error (ITSE), integral absolute error (IAE) and integral time absolute error (ITAE). The obtained results show that the type-2 fuzzy PI controller shows the best performance, followed by type-1 fuzzy PI control and classical PI+FF controller, respectively.

Modeling, design and control of a 4-arm delta parallel manipulator employing type-1 and interval type-2 fuzzy logic-based techniques for precision applications