Dominant-Pole-Based Tuning Criterion for Coordinated Needle–Deflector Control in Pelton Turbines for Hybrid Wind–Hydro Power Systems

The increasing penetration of converter-interfaced renewable generation in hybrid wind–hydro power systems strengthens the frequency-regulation requirements imposed on hydropower plants, particularly in isolated power systems. In Pelton turbine installations, the deflector, traditionally used as a safety device, has recently been incorporated as an active element for frequency regulation. By rapidly modifying the fraction of the jet reaching the runner without immediately changing the penstock flow, the deflector mitigates the influence of pressure-wave dynamics on the plant response, although its operation entails hydraulic-energy losses due to jet diversion. This study proposes a modal-analysis-based tuning criterion for a coordinated needle–deflector control scheme (CCS) with a proportional-integral controller. In this configuration, the proportional action is assigned to the deflector and the integral action to the needle. The proposed method combines an eigenvalue sensitivity–speed assessment based on modal settling time and eigenvalue sensitivity with characteristic-polynomial coefficient matching to derive closed-form expressions for the controller gains. Root-locus trajectories and modal properties confirm the prescribed eigenvalue structure and demonstrate the advantages of the proposed tuning criterion over the conventional Paynter criterion. The resulting controller is evaluated using a detailed nonlinear elastic model based on one hydraulic branch of the Coca Codo Sinclair Hydropower Plant in Ecuador. Under a sudden increase in demand, the CCS improves the frequency nadir, reduces power oscillations, and accelerates frequency recovery compared with the conventional needle control scheme. Simulations of a hybrid wind–hydro power system under variable wind generation further show that the proposed controller can substantially increase the admissible wind-power penetration while maintaining adequate frequency regulation. For the analyzed scenario, the additional wind energy accommodated by the coordinated scheme exceeds the hydraulic-energy cost associated with jet diversion, indicating a favorable trade-off between frequency regulation performance, renewable-energy integration, and hydraulic losses.