Time-variant Nonlinear Participation Factors Considering Resonances in Power Systems

TL;DR

This paper introduces a time-variant nonlinear participation factor for power systems that accounts for resonances and nonlinearities, transitioning smoothly to linear participation factors near equilibrium.

Contribution

It proposes a novel time-decaying nonlinear participation factor that considers resonances and nonlinearities, improving modal analysis accuracy after large disturbances.

Findings

The new PF correctly ranks generator participation in nonlinear oscillations.

It transitions seamlessly to linear PF near equilibrium.

The method effectively captures resonance effects in power system stability.

Abstract

The participation factor (PF), as an important modal property for small-signal stability, evaluates the linkage between a state variable and a mode. Applying the normal form theory, a nonlinear PF can be defined to evaluate the participation of a state variable into modal dynamics following a large disturbance, that gives considerations to resonances and nonlinearities up to a desired order. However, existing nonlinear PFs are inconsistent with the conventional linear PF when nonlinear dynamics following a large disturbance attenuate and linear modal dynamics become dominating. This paper proposes a time-variant nonlinear PF by introducing a time decaying factor and the definition of a nonlinear mode. The new PFs consider modes of resonances and their values naturally transition to a linear PF when the system state becomes close to its equilibrium. The case study on a two-area four-generator system shows that the new PF can correctly rank generators by their participations in natural and resonance modes of nonlinear oscillation subject to a large disturbance.