Singular Perturbation and Small-Signal Stability for Inverter Networks

Modelling and Simulation of Low-Head Hydro Turbine for Small Signal Stability Analysis in Power System

The hydro turbine dynamics have a considerable influence on the dynamic stability of power system. In the study of dynamic stability, the system is modeled by the linear differential equations (small  signal analysis). Small signal stability of power systems is needed in all conditions and only is dependent on the conditions of power system performance before commotion occurrence. This paper pr...

Spectral Stability of Small-Amplitude Traveling Waves via Geometric Singular Perturbation Theory

This thesis is concerned with the spectral stability of small-amplitude traveling waves in two different systems: First, in a system of reaction-diffusion equations where the reaction term undergoes a pitchfork bifurcation; second, in a strictly hyperbolic system of viscous conservation laws with a characteristic family that is not genuinely nonlinear. In either case, there exist families φε, ε...

Stability Analysis of an UAV Controller Using Singular Perturbation Theory

∗ ONERA, DPRS-SAGP, BP 72 29 avenue de la Division Leclerc, F-92322 Châtillon Cedex, France (e-mail: [email protected]) ∗∗ I3S-UNSA-CNRS, Les Algorithmes, Bât. Euclide B, 2000 Route des Lucioles, BP 121 06903 Sophia Antipolis Cedex, France (e-mail: [email protected]) ∗∗∗ ONERA, DPRS-SAGP, BP 72 29 avenue de la Division Leclerc, F-92322 Châtillon Cedex, France (e-mail: helene.piet-laha...

Singular perturbation theory

When we apply the steady-state approximation (SSA) in chemical kinetics, we typically argue that some of the intermediates are highly reactive, so that they are removed as fast as they are made. We then set the corresponding rates of change to zero. What we are saying is not that these rates are identically zero, of course, but that they are much smaller than the other rates of reaction. The st...

Geometric Singular Perturbation Theory