LMI-based approach and estimation of Modal series representation in power systems

Power system is inherently a nonlinear system. It is a general practice in small signal analysis to linearize the dynamic equations of this system and deduce dynamic behaviors and stability properties and design controllers based on linear system theory. Unlike linear dynamic systems there isn´t any general solution for nonlinear ones. This seems to be impossible to obtain exact solution of nonlinear systems closed form response in general and so as for power systems. Therefore, for nonlinear systems the only way is using approximate closed form solutions. Modal series is a novel method of obtaining closed form solution of nonlinear systems. Our purpose in this paper is to estimate modal coefficients of power system zero input response which represents by Modal series, with a method without any complexity of analytical algorithms that satisfies our desire accuracy. The method has been applied on turbo-generator system output signal. First, modal contents of turbo-generator system response have been identified by Prony analysis then modal series coefficients evaluated with a method based on linear matrix inequalities (LMI). Simulation results for turbo-generator system are available to verify accuracy and effectiveness of our approach. The proposed method is general and simply could be extended applying on large scale power system.