Selecting an initial condition for normal form analysis

In normal form (NF) analysis, the nonlinear dynamical system being analyzed is modeled with nonlinearities. If the second order NF is used in the analysis, the nonlinearities only up to second order are modeled. Due to the presence of nonlinearities in the model, the results of second order NF analysis is dependent in the initial conditions [C.-M. Lin et al., May 1996] [S. Zhu et al., November 2001]. If the state of the power system with respect to the stable equilibrium point (SEP), ΔXΔ₀, at the instant of removal of the fault is used as an initial condition, then NF analysis may fail to give correct results. It is shown in this paper that the initial condition must be chosen such that the two main assumptions made in NF analysis are met. If the system being studied is stable, the post fault system will eventually reach the SEP. We propose to select an initial condition at an instant subsequent to clearing a fault, to achieve more reliable results from the NF analysis. The time domain simulations are presented to support the analysis.