As one of the most widely installed utility-scale storage facilities, pumped storage hydro (PSH) plays an essential role in providing flexibility for power systems worldwide. Thus, to accurately quantify the flexibility of PSH units in operational optimization problems is important. The conventional PSH models in the literature rarely consider detailed state transitions due to their hourly-based settings. However, it becomes imperative for operational optimization on short-term intervals, especially with increasing shares of renewable energy in power systems. To this end, this paper presents a novel deterministic PSH model that considers the transition time and trajectory between three states of PSH units in look-ahead dispatch. Moreover, to better characterize the varying efficiency of PSH units with water head and flow rate, this paper proposes to model detailed head-dependent efficiency curves (hereafter called input-output curves) in look-ahead dispatch, which encounters heavy computational burdens when short time intervals are applied. In this work, a zig-zag piece-wise linear approximation method is used for input-output curve modeling. This can enable an accurate quantification for variable efficiency and head dependence in a computationally effective manner. Numerical results are presented to show performances of the proposed PSH model in both flexibility quantification and computation time.