Hydraulic-turbine start-up with “S-shaped” characteristic

Fast response of hydraulic turbines is a key condition for the integration of renewable sources of energy. In this paper, a new start-up strategy is proposed for hydraulic turbines prone to “S” instability. This method is based on a complete nonlinear model of the turbine together with the upstream water pipe. More precisely, the control strategy is based on a gain scheduling approach that is computed using finite horizon predictive control. This yields a state feedback control law that tracks a time-optimal trajectory that is computed based on the nonlinear model of the system. Simulations are shown to assess the efficiency of the proposed law and its robustness to model discrepancies.