Bifurcation analysis of hydro-turbine regulating system with saturation nonlinearity for hydropower station with upstream and downstream surge chambers

28th IAHR symposium on Hydraulic Machinery and Systems

Chen, J.P.^1 ; Yang, J.D.^1 ; Guo, W.C.^1,2

State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan

430072, China^1

Maha Fluid Power Research Center, Department of Agricultural and Biological Engineering, Purdue University, West Lafayette

47907, United States^2

关键词: Bifurcation analysis;    Bifurcation parameter;    Direction of hopf bifurcations;    Existence conditions;    Hydraulic turbine regulating system;    Nonlinear dynamic behaviours;    Nonlinear mathematical model;    Saturation nonlinearity;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/49/5/052010/pdf
DOI  :  10.1088/1755-1315/49/5/052010

来源: IOP

【 摘 要 】

A nonlinear mathematical model of hydraulic turbine regulating system is applied to describe hydropower stations with upstream and downstream surge chambers. This model features saturation nonlinearity including pipeline system and turbine regulating system used in stability analysis. First, the existence conditions and direction of Hopf bifurcation are obtained. Second, based on the algebraic criteria for the occurrence of Hopf bifurcation, the stability domain is drawn in a coordinate system, where the proportional gain Kpis the abscissa and the integral gain Kiis the ordinate. Third, the nonlinear dynamic behaviour of a regulating system with different state parameters are analyzed, and the variations of the system stability around the two sides of the bifurcation point are numerically calculated. Based on this work we conclude that the Hopf bifurcation of system is supercritical. The bifurcation parameters that are far from the bifurcation point would be advantageous to the rapid system regulation needed to sustain equilibrium. Furthermore, it is established that using a PID controller is more conducive to stability than a PI controller. The unit stability regulation gets worse by taking into account the saturation nonlinearity.