Abstract: The negative damping characteristics of hydropower units are the intrinsic cause that induces ultra-low frequency oscillations of hydropower dominant power systems. Accurate and efficient quantification of the damping coefficients of units is crucial to the positioning and control of the dominant units of ultra-low frequency oscillations. To address the problem that the existing damping quantization methods for nonlinear system units are difficult to balance the operational simplicity and calculation accuracy, this paper analyzes the damping characteristics of single and multi-machine systems based on the damping torque theory and proposes a novel fast quantization method for damping coefficients. On the one hand, the quantified results of damping are compared with the theoretical values to verify the calculation accuracy of the method. On the other hand, the experimental analysis of ultra-low frequency oscillation of a multi-machine system and the measurement data of actual power stations are used to verify the validity of the method.The results show that the method is accurate and simple, and it can provide an effective technical means for the damping study of strongly nonlinear systems and the online evaluation of the damping in ultralow frequency oscillations.