Optimal LQR Controller design with Bryson Approach and Frequency Domain Analysis for Stability

Due to weak interconnection, random changes in load and generation, heavily loaded lines, and excitation systems with high gain there are problems of low frequency oscillations in the system. If these oscillations are not controlled it will grow and cause the system separation. Power system stabilizers (PSS) are added in the system to damp these oscillations. PSS is effective for damping the local modes of oscillations. There are other modes of oscillation also in the system. PSS in coordination with TCSC, a series FACTS device is used to mitigate both the local and interarea modes of oscillations. In the proposed work the non -linear power system is linearized at a certain operating point to perform the eigen value analysis, stability improvement and for the application of Linear Quadratic Regulator (LQR) methodology based on optimal control theory using Taylor’s series expansion .In LQR by properly selecting the weighting matrices Q and R, the excursions in state variables are minimized which helped in improving the stability of the system. The Bryson approach for the Q and R matrices is considered here. The controller designed by the optimal control theory based LQR methodology is found to be robust. It takes into consideration the neglected dynamics, uncertainties in the system. The frequency domain analysis of the system is also performed