Polynomial approximation of the vector field in normal form analysis of power system

Normal form analysis helps in analyzing nonlinear behaviour. The method involves transforming the given nonlinear differential equations to linear differential equations if the terms of degree greater than a certain value are ignored. Conventionally, the first step in this method is to approximate the vector field on the right hand side of the equation \(\dfrac{d{\textbf {x}}}{dt}={\textbf {f}}({\textbf {x}})\) ${\displaystyle \frac{d\mathbf{x}}{\mathit{dt}}}=\mathbf{f}(\mathbf{x})$ by its Taylor polynomial about the stable equilibrium point. We propose an alternate polynomial. The proposed polynomial is validated by case studies.