Nonlinear Modal Decoupling Based Power System Transient Stability Analysis

Nonlinear modal decoupling (NMD) was recently proposed to nonlinearly transform a multi-oscillator system into as many decoupled oscillators as the oscillation modes of interests with the original system. Those decoupled oscillators together provide a fairly accurate approximation of behaviors of the original system in an extended neighborhood of the equilibrium. Each oscillator has just one degree of freedom and hence can easily be analyzed to infer the nonlinear dynamics of the original system associated with one oscillation mode. As the first attempt of applying the NMD methodology to realistic power system models, this paper proposes an NMD-based approach for the early warning of the oscillation mode that may most likely develop into a mode of transient instability. For a multi-machine power system, the approach first derives decoupled nonlinear oscillators by a coordinates transformation, and then applies Lyapunov stability analysis to decoupled oscillators to assess the stability of the original system. For large-scale power grids, the proposed approach can be efficiently applied by conducting NMD regarding only selected modes. Case studies on a 3-machine 9-bus system and an northeast power coordinating council (NPCC) 48-machine 140-bus system show the potentials of the approach in early warning of transient instability for multi-machine systems.