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

• Published in: Journal of Applied Mathematics Vol. 2014; no. 2014; pp. 466 - 476-352
• Main Authors: Li, Junyi, Chen, Qijuan
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Limiteds 01.01.2014; Hindawi Puplishing Corporation; Hindawi Publishing Corporation; John Wiley & Sons, Inc; Hindawi Limited
• Subjects: Behavior; Chaos theory; Complex systems; Dynamical systems; Externality; Hydraulic turbines; Hydraulics; Laplace transforms; Lyapunov exponents; Mathematical models; Nonlinear dynamics; Nonlinearity; Oscillations; Studies; Turbines; United States
• ISSN: 1110-757X; 1687-0042
• DOI: 10.1155/2014/412578

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.