Nonlinear Dynamics of a PI Hydroturbine Governing System with Double Delays

Abstract

A PI hydroturbine governing system with saturation and double delays is generated in small perturbation. The nonlinear dynamic behavior of the system is investigated. More precisely, at first, we analyze the stability and Hopf bifurcation of the PI hydroturbine governing system with double delays under the four different cases. Corresponding stability theorem and Hopf bifurcation theorem of the system are obtained at equilibrium points. And then the stability of periodic solution and the direction of the Hopf bifurcation are illustrated by using the normal form method and center manifold theorem. We find out that the stability and direction of the Hopf bifurcation are determined by three parameters. The results have great realistic significance to guarantee the power system frequency stability and improve the stability of the hydropower system. At last, some numerical examples are given to verify the correctness of the theoretical results.

Stability and Sensitivity Analysis and Optimization Control of the Hydro-turbine Generator Unit

“…They are all complex nonlinear systems, and the study of their complex nonlinear dynamic behavior is of great significance for the realization of optimal economic operation control [6]. In previous works, the stability and dynamic characteristics of the HTGS were studied using the Routh-Hurwitz criterion [7], root locus method [8], state-space method [9], and Hopf bifurcation theory [10][11][12]. In [13], Hopf bifurcation theory is applied to analyze the influence of the structural parameters of the sloping ceiling tailrace tunnel on the stability domain of the PID control parameters.…”