Stability and sensitivity analyses and multi-objective optimization control of the hydro-turbine generator unit

The hydro-turbine governing system (HTGS) and shafting system are mutually coupled. However, the interaction between them has always been neglected. In this study, we aim to explore the stability and sensitivity of the governor control parameters for the HTGS and shafting system and determine optimal control for the stable operation of the hydro-turbine generator unit (HTGU). First, the stability of the HTGS is examined by employing Hopf bifurcation theory and verified by using a bifurcation diagram and max Lyapunov exponent. Then, a novel HTGU motion equation is deduced to establish a relationship between the HTGS and shafting system. Thus, a nonlinear coupling mathematical model of the HTGS and shafting system is established. Based on the nonlinear mathematical model, the stability and sensitivity of the governor control parameters are obtained. Finally, a multi-objective proportional-integral-derivative (PID) parameter optimization strategy that considers HTGS and shafting vibrations is proposed. The chaotic-dominated sorting genetic algorithm II and multi-objective evolutionary algorithm based on decomposition are introduced to obtain the optimal control parameter and mutually verify the effectiveness of the optimization. Moreover, the nonlinear dynamic characteristics of the HTGU under optimal control are revealed. The simulation results show that the effect of shafting vibrations on the HTGS is almost negligible. The rotation speed deviation and shafting vibrations are sensitive to the PID parameters in certain ranges, and their stable region can be decreased by considering the shafting vibrations. The multi-objective PID parameter optimization strategy shows good control performance on the nonlinear dynamic characteristics of the HTGU. During load disturbance, the shafting system vibrations are quasi-periodic with several frequency components in a 3D space. Thus, the proposed dynamic models, optimization strategy, and analysis results can guide the design and stable operation of the HTGU.