Abstract: Recent years have seen frequent problems of ultra-low frequency oscillations in power systems caused by hydropower units. Understanding the characteristics of such oscillations at hydropower stations is key to the stable operation of power systems, and an in-depth study is necessary in engineering practice on how to ensure the stability margin of a system along with a quantitative analysis of its oscillation attenuation characteristics. Aiming at this problem, this paper develops a mathematical model of hydraulic unit regulation based on the concept of a stability margin. By comparing theoretical analysis with numerical simulation, we discuss attenuation characteristics of the ultra-low frequency oscillations of the units in different stability margin regions, and reveal a relationship of the parameters of the regulating system versus the attenuation coefficient, together with a brief example of engineering application for demonstration. The results show that a stability margin can represent the attenuation of system responses in time domain. It is the power coefficient of the response envelope expressed in an exponential form, and equals the product of the response frequency and damping ratio of the system. When the parameters in a regulating system change, the attenuation characteristics of its ultra-low frequency oscillations can be obtained by deriving theoretically the variation in its stability margin region.

Key words: hydraulic turbine unit, frequency regulation, ultra-low frequency oscillation, region of stability margin, attenuation characteristics