  Many natural and manmade dynamical systems that are modeled as large
nonlinear multi-oscillator systems like power systems are hard to analyze. For
such a system, we propose a nonlinear modal decoupling (NMD) approach inversely
constructing as many decoupled nonlinear oscillators as the system oscillation
modes so that individual decoupled oscillators can easily be analyzed to infer
dynamics and stability of the original system. The NMD follows a similar idea
to the normal form except that we eliminate inter-modal terms but allow
intra-modal terms of desired nonlinearities in decoupled systems, so decoupled
systems can flexibly be shaped into desired forms of nonlinear oscillators. The
NMD is then applied to power systems towards two types of nonlinear
oscillators, i.e. the single-machine-infinite-bus (SMIB) systems and a proposed
non-SMIB oscillator. Numerical studies on a 3-machine 9-bus system and New
England 10-machine 39-bus system show that (i) decoupled oscillators keep a
majority of the original system modal nonlinearities and the NMD provides a
bigger validity region than the normal form, and (ii) decoupled non-SMIB
oscillators may keep more authentic dynamics of the original system than
decoupled SMIB systems.
