Design State Space Feedback and Optimal LQR Controllers for Load Frequency in Hydraulic Power System

In electrical grids all generators work and provide the power to the loads. When the load on the generator increases, the speed of generator rotor decreases resulting in a reduction in the frequency of the grid. During restoration, it is needed to keep frequency response in the allowable range. For this purpose, this work is dedicated to present a method to keep frequency response of a hydro-power system at a required value. In this paper, firstly, the state space model for Hydro-power system unit was presented, and the controllability and observability of the system was discussed. Next, full state feedback controller and tracking gain were designed to optimize the performance of the system and decrease the effect of the frequency load. Then, an optimal closed-loop controller using algebraic Riccati equation was developed. We studied the frequency load effect before and after these designs and trying to decrease this effect. In simulation results, state space feedback controller decreases the average over shoot from 10.73% to 6.5% and the average error from 47.8 to zero. For comparison between the two controllers, LQR optimal controller decreases the settling time to 8 sec instead of 11.6 sec that is obtained from state space feedback controller. In general, the designed LQR optimal controller provides best performance in terms of overshoot, error, and time.