Unified Performance Model for S-Shaped Characteristics of Pump–Turbines Considering Reverse Flow

Abstract

This study proposes a new unified performance model for the S-shaped characteristics of pump–turbines considering reverse flow. The turbine and reverse pump characteristic equations were unified using a sigmoid function considering the reverse flow. In the analysis, the torque coefficient is larger for small guide vane angles than for large guide vane angles due to an increase in the turbine Euler head. In the turbine mode, the runner shock loss and the circumferential discharge loss are directly proportional to the shock dynamic pressure and the circumferential dynamic pressure in the discharge section, respectively. In the reverse pump mode, the guide vane shock and friction losses are directly proportional to the shock dynamic pressure and the absolute dynamic pressure, respectively. The S-shaped characteristics of pump–turbines can be completely simulated using the proposed theoretical model.