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.
Dynamic systems analysis and achieve closed form time response of these systems has been an attractive field of interest for mathematicians and engineers. Unlike linear dynamic systems there isn't any general solution for nonlinear ones. This seems to be impossible and nobody can proposed exact solution of obtaining nonlinear systems closed form response. Therefore, for nonlinear systems the only way is using approximate closed form solutions. Modal series is a novel method of obtaining closed form solution ofnonlinear systems. Our purpose in this paper is to estimate modal coefficients of zero input response of nonlinear systems with a method without any complexity of analytical algorithms that satisfies our desire accuracy. The purpose is to obtain closed form response for nonlinear systems just from some observations and measurement values. In this research first modal contents of nonlinear system response was identified by Prony analysis then Modal series coefficients was evaluated with a new method based on linear matrix inequalities (LMI). Simulation results for a second order nonlinear system is available to verify the effectiveness of our approach.
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