Design of Stabilizing Control for Synchronous Machines via Polynomial Modelling and Linear Matrix Inequalities Approach

This paper deals with the design and evaluation of a nonlinear state feedback controller to improve the global asymptotic stabilization and transient performance of synchronous machines. The nonlinear Park's model is developed around the working point on a third order polynomial system. An innovative technique is used to design a nonlinear polynomial controller, based on the Lyapunov's direct method and Linear Matrix Inequalities (LMIs) approach. The control laws are derived from the resolution of a sufficient LMI stabilization condition. The proposed polynomial control has been tested numerically on a generator infinite-bus power system and the simulations results show an excellent damping of the system oscillations over a wide range of operating conditions whilst retaining good voltage control.