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 e is 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.