Abstract: The S-shape region of pump-turbine units, as the major difference from common turbines, is one of the key factors that cause the instability of unit operation. Previous studies derive the derivatives of unit discharge Q11 and unit torque T11 to unit speed n11 separately. This paper derives stability requirements for pump-turbine units running in turbine mode and reverse pump mode, considering the features of these two derivatives and combining them with the relationship of flow rate Q versus working head H in the two modes for a given guide vane opening. We use the static stability theory to build a relationship of Q versus H that must be satisfied by the working head disturbance factor for stable running in the two modes, and then define a stable turbine-mode working point and a S-shape region.

Key words: pump-turbine unit, S-shape region, static stability, working head disturbance factor, full characteristic