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Mathematical Problems in Engineering
Volume 2018, Article ID 7232915, 11 pages
Research Article

Optimal Decentralized LQR Control to Enhance Multi-Area LFC System Stability

1Electronics and Communications Engineering Department, College of Engineering, Umm Al-Qura University, Al-Lith Branch, Saudi Arabia
2Electrical Engineering Department, Faculty of Engineering, Minia University, Minya, Egypt

Correspondence should be addressed to Ashraf M. Abdelhamid; moc.liamtoh@demfarhsa

Received 12 December 2017; Revised 8 March 2018; Accepted 1 April 2018; Published 12 August 2018

Academic Editor: Yurong Liu

Copyright © 2018 Ashraf M. Abdelhamid and Ahmed A. M. El-Gaafary. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Many studies have been made in the field of load frequency control (LFC) through the last few decades because of its importance to healthy power system. It is important to maintain frequency deviation at zero level after a load perturbation. In decentralized control, the multi-area power system is decomposed into many single input single output (SISO) subsystems and a local controller is designed for each subsystem. The controlled subsystems may have slow poles; these undesired poles may drive the aggregated overall system into the instability region. Thus, it is required to relocate these poles to much more stable places to avoid their effect upon the overall system stability. This study aims to design a new load frequency controller based on the powerful optimal linear quadratic regulator (LQR) technique. This technique can be applied over subsystem level to shift each subsystem undesired poles one by one into a prespecified stable location which in turn shift the overall system slow poles and reduce the effect of the interaction between the interconnected subsystems among each other. This procedure must be applied many times as the number of undesired poles (pairs) until all the desired poles are achieved. The main objective is considered to get a robust design when the system is affected by a physical disturbance and ±40% model uncertainties. LQR can be applied again over the aggregated system to enhance the stability degree. Simulation results are used to evaluate the effectiveness of the proposed method and compared to other research results.