Operational flexibility assessment of a novel separated pumped hydro energy storage system based on residual-load coordination in multi-nozzle Pelton turbine units

Ultra-high-head separated pumped hydro energy storage (PHES) schemes rely on multi-nozzle Pelton units for flexible regulation, but unsteady jet–bucket interactions can generate residual hydrodynamic loads that restrict the admissible operating range. This study combines theoretical analysis with validated simulations of a 21-bucket Pelton runner to clarify the evolution of jet-induced resultant forces under ultra-low-load single-nozzle operation and multi-nozzle operation with 1–6 active nozzles. Under single-nozzle operation at 5–20% rated output, the time-averaged resultant force increases linearly with discharge, and a predictive model is established to estimate the residual load directly from the flow rate. Under multi-nozzle operation with fixed discharge per nozzle, the mean resultant force is classified into three severity levels: severe imbalance for 1 and 5-nozzle modes, moderate imbalance for 2 and 4-nozzle modes, and near-balanced behaviour for 3 and 6-nozzle modes. In the classical 6-nozzle/21-bucket layout, a characteristic antipodal imbalance induced by a half-bucket phase shift is identified. To generalise this mechanism, a GCD-based phase-matching criterion is proposed, showing that better periodic force matching is achieved when the greatest common divisor of nozzle number and bucket number is at least 3. These findings provide a physically transparent framework for selecting nozzle configurations and operating modes while limiting residual hydrodynamic loads in flexible Pelton-based PHES operation.