Optimal design of a robust discrete parallel FP + FI + FD controller for the Automatic Voltage Regulator system H. Shayeghi a,b,⇑ , A. Younesi a , Y. Hashemi a a Department of Technical Engineering, University of Mohaghegh Ardabili, Ardabil, Iran b Centre of Excellence for Power System Automation and Operation, Department of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran article info Article history: Received 25 January 2014 Received in revised form 9 October 2014 Accepted 15 November 2014 Keywords: AVR Fuzzy PID HGAPSO algorithm PID controllers abstract The purpose of this paper is to design a good tracking controller for the generator Automatic Voltage Reg- ulator (AVR) system. A fuzzy logic-based controller that is called Fuzzy P + Fuzzy I + Fuzzy D (FP + FI + FD) controller has been designed optimally and applied to AVR system. In the proposed method, optimal tun- ing of controller parameters is very important to achieve the desired level of robust performance. Thus, a hybrid of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) (HGAPSO) technique has been used to find a better fuzzy system control. The motivation for using this hybrid method is to increase dis- turbance rejection effort, reduce fuzzy system efforts and take large parametric uncertainties into account. The developed FP + FI + FD control strategy leads to a flexible controller with simple structure that is easy to implement. The simulation results have been compared with the conventional Propor- tional–Integral–Derivative (PID) and fuzzy PID controllers. Three cases of simulation have been per- formed, case 1: comparing the tracking capability of the controllers, case 2: comparing the disturbance rejection capability of the controller and case 3: evaluating the performance of the controllers assuming that amplifier and exciter system parameters have 50% uncertainty. The simulation results shows that the proposed parallel FP + FI + FD controller has good performance from the perspective of overshoot/under- shoot, settling time, and rise time in comparison with both conventional and fuzzy PID controllers. Ó 2014 Elsevier Ltd. All rights reserved. Introduction One of methods for increasing stability and achieving a nominal voltage level in an electric power grid is raising the voltage or employing series capacitors in power transmission lines, but con- trolling of generator exciter by using of AVR is attracting attention because of its inherent cost advantage. The AVR controls the termi- nal voltage by adjusting the exciter voltage of the generator [1,2]. During the past decades, the process control techniques in the industry have made great advances. Numerous control methods such as delf-PID controllers and fuzzy control have been studied for AVR system [3]. Due to the complexity of the power system such as nonlinear stochastic load characteristics and variable operating points the usage of artificial intelligence based optimization techniques like PSO, HGA–BF, ABC, ASO, TCGA, simplified PSO [1–6] have been reported for optimal tuning of PID controller in AVR system. Shayeghi and Dadashpour [2] addressed a robust method for tuning PID control of the AVR system by optimizing a time domain based objective function considering model uncertainties using an ASO optimizer. It was shown that the suggested self-tuning PID for AVR system has better performance than the recently Craziness based PSO (CRPSO) and Vector evaluated PSO optimized controllers with respect to reference input and plant parameter changes. In [3] was suggested a PSO based tuned PID type controller for AVR system in comparison with GA via minimizing a objective function composed of overshoot, steady state error, deviation between settling time and rise time. It has better tuning capability than GA. However, its performance is dependent on suitable choice of PSO control parameters. An HGA–BF optimization technique was represented by Kim [4] in order to improve the performance of the self-tuning PID controller for AVR system. Gozde and Taplama- cioglu [5] investigated tuning performance of ABC algorithm for AVR control system. The robustness analysis has been compared with PSO and differential evolution (DE) algorithms under different analysis methods such as transient response, root locus, bode and statistically receiver operating characteristic analyses. All analyses results have realized that ABC based optimized PID control of AVR system has better and robust performance than the PSO and DE algorithms. In [6] a simplified PSO method called many optimizing http://dx.doi.org/10.1016/j.ijepes.2014.11.013 0142-0615/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author at: Daneshgah Street, P.O. Box: 179, Ardabil, Iran. Tel.: +98 451 5517374; fax: +98 451 5512904. E-mail address: hshayeghi@gmail.com (H. Shayeghi). Electrical Power and Energy Systems 67 (2015) 66–75 Contents lists available at ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes