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.

I. Introduction

Modern power systems are sometime operated close to their stability limits. Care must be taken in the operation to avoid driving the system to cross any limit, or catastrophic consequences like wide-scale power outages and blackouts may occur. In reality, the instability is often developed from certain oscillation modes. For instance, before the occurrence of the August 10, 1996 Western Interconnection Blackout, poorly-damped oscillations at around 0.26 Hz were observed which later developed into an instability leading to an uncontrolled outage and interrupting the electric service to more than 7 million customers [1]. Similar for the August 14, 2003 Blackout, due to a lack of adequate real-time situational awareness, many power oscillation events were observed but no symptoms of instability were captured [2].