Design of LFC using Optimal Control Theory The optimal controller is designed to minimize the quadratic performance index of the following form For linear systems with quadratic performance index, Known as Linear Quadratic Regulator (LQR), The optimal Control Law is given by: Design of Load Frequency Controllers for Interconnected Power Systems By: Ezzedeen Abdulla Shehada and Ashraf Mohammed Abu Ghazzeh Supervisor: Dr. Khaled Ellithy Abstract Conclusion  Three load frequency controllers have been proposed to improve the damping and to reduce the overshoot of the frequency and tie-line power deviations for the interconnected two power areas and also to keep the interchanged power at the scheduled value.  The computer simulations results showed that the proposed decentralized optimal load frequency controller is a more effective tool for improving the dynamic performance of the two power areas compared to the PI and pole-placement controllers.  Moreover, the proposed decentralized optimal controller type is relatively simple and suitable for practical on-line implementation. Design of Load Frequency Controllers An optimal controller using linear quadratic regulator technique, a controller based on pole-placement technique and a proportional integral have been designed for load frequency control for interconnected power areas. The proposed controllers have been designed to improve the dynamic performance of the system frequency and the tie line power flow under any disturbance such as a sudden load change in the power areas. MATLAB/SIMULINK programs have been developed to determine the gains for the proposed deigned controllers and perform the time-domain simulations. The time-domain simulations results have been performed to demonstrate the effectiveness of the proposed controllers. The simulation results show that the designed decentralized optimal controller is the best one among the proposed controllers in that it provides good damping and reduces the overshoot. Block Diagram of LFC of two area power system with PI controller Where P is determined by solving the following Riccati equation The state-space equations of the linear time-invariant of the two area The disturbance matrix  : x(t) is the state variables vector. The input matrix B is given by is the disturbance to the system. is the input vector. Acknowledgements Introduction Load frequency control (LFC) is one of the major requirements in providing reliable and quality operation in interconnected power systems. The primary objectives of the LFC are to regulate the frequency to the nominal value and to maintain the interchange power between control areas at scheduled values by adjusting the MW output power of the selected generators so as to accommodate changing in load demands. Design of Proportional Integral LFC The Proportional Integral (PI) controller gains K i & Kp for both power area systems have been determined to improve the transient response of the two area frequency deviations under any disturbance such as change of the load demand. The system matrix A is given by Design of LFC using Pole-Placement Technique The problem is to find the state feedback-gains (K) of the pole placement LFC such that This allows all poles of the closed-loop system to be placed in any desirable locations The characteristic equation for the closed-loop system The gain vector K is obtained by equating the coefficient the two equations. (λ + μ 1 )(λ + μ 2 )…(λ + μ n ) = λ n + a n-1 λ n-1 + … + a 1 λ + a 0 =0 |λ I – A + BK| = λ n + (α n-1 +K n ) λ n-1 + … + (α 1 +K 2 ) λ + (α 0 +K1) =0 Participation Matrix Pole-Placement Gains SIMULINK Block Diagram of Pole-Placement LFC of two area power system under sudden load change in area 1 in system with Pole-Placement LFC of Area 1 under sudden load change in area 1 in system with Pole-Placement LFC of Area 2 Decentralized Optimal LFC Gains SIMULINK Block Diagram of decentralized optimal LFC of two area power system Comparison Between the Designed Controllers Overshoot and time to reach zero steady state for all designed LFC under sudden load change in area 1 in system with Different LFC of Area 1 under sudden load change in area 1 in system with Decentralized Optimal LFC of Area 1 under sudden load change in area 1 in system with Decentralized Optimal LFC of Area 2 under sudden load change in area 1 in system with PI controller in Area 1 under sudden load change in area 1 in system with PI controller in Area 2 Original and Desired Eigen values Department of Electrical Engineering College of Engineering The authors would like to thank their supervisor Dr. Khaled Ellithy and Department of Electrical Engineering. Thanks also go to Qatar Foundation- Undergraduate Research Experience Program (UREP) for the support and to engineer Ahmed Abdul-Qadder from the National Control Center-Kahramaa. The authors also wish to express their thanks to their family. Fall 2008