On the reduction of nonlinear electromechanical systems

TL;DR

This paper revisits the reduction of nonlinear electromechanical systems using a quasi-steady state hypothesis, clarifying fundamental aspects, deriving characteristic time scales, and validating the approach through numerical experiments.

Contribution

It provides a physical and mathematical analysis of the quasi-steady state reduction method, clarifying its validity and limits in nonlinear electromechanical systems.

Findings

Characteristic time scales derived from physical analysis.

Quasi-steady state assumption validated through numerical experiments.

Identification of boundary layer phenomena and validity limits.

Abstract

The present work revisits the reduction of the nonlinear dynamics of an electromechanical system through a quasi-steady state hypothesis, discussing the fundamental aspects of this type of approach and clarifying some confusing points found in the literature. Expressions for the characteristic time scales of dynamics are deduced from a physical analysis that establishes an analogy between electromechanical dynamics and the kinetics of a chemical reaction. It provides a physical justification, supplemented by non-dimensionalization and scaling of the equations, to reduce the dynamics of interest by assuming a quasi-steady state for the electrical subsystem, eliminating the inductive term from the electrical equation. Numerical experiments help to illustrate the typical behavior of the electromechanical system, a boundary layer phenomenon near the initial dynamic state, and the validity limits of the electromechanical quasi-steady-state assumption discussed here.