An analysis of the hopf bifurcation in a hydroturbine governing system with saturation

Author

Ling, Daijian ; Tao, Yang

Author_Institution

Yangzhou Univ., China

Volume

21

Issue

2

fYear

2006

fDate

6/1/2006 12:00:00 AM

Firstpage

512

Lastpage

515

Abstract

A set of state equations of the polarization index governing system with saturation nonlinearity is established for a hydroturbine in small perturbation. The dynamic behavior of the proportional-integral governor (controller) governing system with saturation is analyzed and the conditions for the existence of a Hopf bifurcation are obtained by using a simple nonlinear model. The stability condition, which must be satisfied in the governing system, is simulated and supported by numerical calculations. The analysis and simulation show that a supercritical Hopf bifurcation may exist in hydraulic turbine systems. The results of this paper can be considered as an explanation for the sustained oscillations recorded in hydroelectric power stations.

Keywords

PI control; bifurcation; hydraulic turbines; hydroelectric power stations; nonlinear control systems; numerical analysis; polarisation; power generation control; Hopf bifurcation; hydraulic turbine systems; hydroelectric power stations; hydroturbine governing system; nonlinear model; numerical calculations; polarization index governing system; proportional-integral governor; saturation nonlinearity; stability condition; state equations; Analytical models; Bifurcation; Control system synthesis; Nonlinear control systems; Nonlinear dynamical systems; Nonlinear equations; Pi control; Polarization; Proportional control; Stability; Hopf bifurcation; hydroturbine governing system; saturation nonlinearity;

fLanguage

English

Journal_Title

Energy Conversion, IEEE Transactions on

Publisher

ieee

ISSN

0885-8969

Type

jour

DOI

10.1109/TEC.2005.860407

Filename

1634599