A Robust Linear Optimal State Feedback Controller Design for Excitation Systems of Synchronous Generators in Single Machine Power Systems with Parametric Uncertainties

This paper proposes a robust linear optimal state feedback control scheme for the excitation system of a synchronous generator connected to an infinite bus. The proposed controller is designed for the seventh-order model of synchronous generators using a linear quadratic regulator (LQR) approach while considering parametric uncertainties within the model. The proposed robust optimal state feedback excitation controller is designed by bounding parametric uncertainties so that it can provide desired damping to ensure the transient stability under different operational constraints. The optimal control parameters are determined by solving linear matrix inequalities (LMIs) and convex optimization problems. The quadratic stability of an uncertain system representing parametric uncertainties in the synchronous generator model is analyzed using the Lyapunov stability analysis framework. Simulations studies are conducted to support the theoretical finding of the proposed controller and results are compared with a conventional power system stabilizer.