Nonlinear fast–slow dynamics of a coupled fractional order hydropower generation system

Internal effects of the dynamic behaviors and nonlinear characteristics of a coupled fractional order hydropower generation system (HGS) are analyzed. A mathematical model of hydro-turbine governing system (HTGS) with rigid water hammer and hydro-turbine generator unit (HTGU) with fractional order damping forces are proposed. Based on Lagrange equations, a coupled fractional order HGS is established. Considering the dynamic transfer coefficient eis variational during the operation, introduced e as a periodic excitation into the HGS. The internal relationship of the dynamic behaviors between HTGS and HTGU is analyzed under different parameter values and fractional order. The results show obvious fast–slow dynamic behaviors in the HGS, causing corresponding vibration of the system, and some remarkable evolution phenomena take place with the changing of the periodic excitation parameter values. (paper)