Nonlinear model-based control for minimum-time start of hydraulic turbines

Fast start of hydraulic turbines is mandatory for a successful integration of renewable sources of energy. Successful handling of this issue needs to operate close to the boundary of the admissible domain while fully exploiting the knowledge of the system dynamics. This paper introduces a simplified model of hydraulic turbines including the hydraulic nonlinear hill-chart and a first order model of the penstock. Based on the resulting reduced model, a graphical representation of the vector fields of the resulting controlled system is first obtained under the assumption of a band unlimited actuator. This ideal 2D-graphical representation enables an exact evaluation of the lower bound on the minimum achievable start-time as well as the time structure of the control profile. Based on this analysis, a real-life MPC scheme is proposed that takes into account realistic limitations on the actuator leading to feasible, almost time-optimal control design.