Approximation of Closest Unstable Equilibrium Points via Nonlinear Modal Decoupling

The recently proposed Nonlinear Modal Decoupling (NMD) approach provides a new way for the stability analysis of large non-linear multi-oscillator systems such as power systems. NMD inversely constructs as many decoupled nonlinear oscillators as the system's oscillation modes so that individual decoupled oscillators can be easily analyzed to infer dynamics and stability of the original system. This paper presents a theoretical investigation of the consistency of the stability information between the decoupled system and the original system in terms of equilibrium points. A procedure for the approximation of closest unstable equilibrium point via nonlinear modal decoupling is proposed. The IEEE 9-bus power system is used to test the performance of this procedure.