As power systems grow reliant on an increasing mix of intermittent renewables, hydropower units are being called upon to provide more aggressive power-frequency control. This dynamic is enlarging the significance of interaction between hydraulic and electrical subsystems in hydropower plants (HPPs). The influence from HPPs on power system stability is of great importance, especially for hydro-dominant power systems like the Nordic power system and the China Southern Power Grid. This paper aims to quantify and reveal the influencing mechanism of the hydraulic damping of low frequency oscillations in power systems. An equivalent hydraulic turbine damping coefficient is introduced, and a nonlinear HPP model that combines electrical subsystems with a refined hydraulic-mechanical subsystem is established and verified. A novel quantifying methodology is proposed through simulations by two different models based on case studies on a Swedish HPP. Then, the quantification results of the damping coefficient are presented and the influencing mechanism behind is revealed, by studying three representative factors from the hydraulic-mechanical system: the delay in turbine governor systems, governor parameter and penstock length. Observations and discussions of on-site measurements are included to support the analysis. The results show that the damping effect from hydraulic turbines can be considerable. Based on the limited cases in the HPP, the damping coefficient can vary from + 3.0 to -2.3, while previously the contribution has been unclear and normally assumed to be positive. The phase shift in the mechanical power response with respect to the rotational speed deviation is an important reason for the different damping performance. Furthermore, the effect and significance of implementing the damping coefficient on cases with power system stabilizer (PSS) are demonstrated.