The nonlinear nature of power systems should be considered for the analysis of disturbances that result in large deviations from the stable equilibrium point. In the normal form analysis, the nonlinear nature can be included. The accuracy of normal form analysis is dependent on the convergence of Neumann series used to obtain the inverse of a matrix in one of the steps; it is shown that the results can be erroneous in spite of the convergence of Neumann series. Normal form analysis cannot be performed in the presence of nonsmooth functions such as the exciter limiter. We propose an approximation to the limiter so that normal form analysis can be used. Prony analysis, in addition to simulation, is proposed to verify the accuracy of the normal form approximation. The validity of the normal form analysis is investigated by studies on a SMIB system, a 3 machine system and a 50 machine system.