The “Efficiency Transient Control” Concept for Optimal Load Control in Kaplan Turbine Hydroelectric Installations

Abstract

In the case of Kaplan turbines the consideration of the efficiency parameter is critical from the control strategy synthesis viewpoint. As it is not essential in hydrosystem analysis, explicit efficiency parameter relationships have not been deployed to date for linearized Kaplan mathematical models used in control design. The “efficiency transient control” concept is developed herein. Basically, this approach purports to optimize transient behavior by controlling so as to decrease efficiency during the early transient portion of load rejection and likewise maximizing efficiency for the load acceptance case. For each perturbation this method leads to minimal flow change and, therefore, minimal over or under-pressures. As applied to a dominant gate with blade follow-up control scheme, the efficiency transient control concept prescribes the appropriate delay to be employed for optimum performance within the constraint of a follow-up device. Where the early transient deviates from best efficiency operation, a return to steady-state or “cam” operation occurs as the follow-up. The standard equations describing Kaplan turbine operation in linearized form by partial derivatives have been revised to include the efficiency parameter explicitly and now present a comprehensive and intelligible approach to Kaplan turbine control synthesis. The effect of the efficiency transient control upon system stability is analyzed and recommendations are made for desirable deployment. Application to nonlinear system operation is discussed. The efficiency transient control is compared with present day control schemes to assess their effectiveness. It is determined that a delay imposed upon the blades for the load-on case is suboptimal performancewise. The one-to-one gate-to-blade control is optimal in that case.