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Journal of Applied Mathematics
Volume 2014, Article ID 412578, 11 pages
Research Article

Nonlinear Dynamical Analysis of Hydraulic Turbine Governing Systems with Nonelastic Water Hammer Effect

Power and Mechanical Engineering, Wuhan University, Wuhan, Hubei 430072, China

Received 27 March 2014; Revised 5 June 2014; Accepted 5 June 2014; Published 25 June 2014

Academic Editor: Hamid Reza Karimi

Copyright © 2014 Junyi Li and Qijuan Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A nonlinear mathematical model for hydroturbine governing system (HTGS) has been proposed. All essential components of HTGS, that is, conduit system, turbine, generator, and hydraulic servo system, are considered in the model. Using the proposed model, the existence and stability of Hopf bifurcation of an example HTGS are investigated. In addition, chaotic characteristics of the system with different system parameters are studied extensively and presented in the form of bifurcation diagrams, time waveforms, phase space trajectories, Lyapunov exponent, chaotic attractors, and Poincare maps. Good correlation can be found between the model predictions and theoretical analysis. The simulation results provide a reasonable explanation for the sustained oscillation phenomenon commonly seen in operation of hydroelectric generating set.