  Small signal analysis is a special case of analytical approaches using Taylor
expansions of power system differential equations with the truncation performed
at order one. The truncated Taylor expansions (TTEs) at higher orders can lead
to better approaches for stability analysis by considering higher order
nonlinearities, e.g. normal form, modal series and nonlinear modal decoupling.
This paper presents fundamental studies on how accurate transient stability
analysis results can be obtained from the TTE systems compared to that on the
original system. The analytical investigation is conducted on
single-machine-infinite-bus power systems. Conclusions are drawn from there and
verified on two multi-machine power systems by extensive numerical simulations.
