Abstract: With the gradual increase in the proportion of wind, solar and other intermittent energy sources in the power grid, the power system needs more flexible means of regulation, so the deep peaking regulation capacity of hydropower units is one of the key technologies to build a new power system. In order to explore the key factors affecting the system stability and oscillation damping characteristics during the deep peaking regulation of hydropower units, the method of Hopf bifurcation theory was employed in this study. Then the mathematical model of hydroelectric power plant of two units sharing one pipeline set up, with downstream surge tank under the power control mode was constructed, the influence of peaking conditions and system parameters on the power of the system was also analyzed. Finally, the concept of stability margin was introduced to explore the damping characteristics of low-frequency oscillations of the system at different operating points under the same attenuation degree, using the unit speed frequency and damping ratio as the measures. The results show that the smaller the steady state load under different peaking conditions, the larger the stability domain. The power fluctuation of the system can be effectively suppressed by reasonably setting the parameters. And the low-frequency oscillation of the system can be suppressed for the operating point with larger rotational speed damping ratio under the same degree of attenuation. The results of the study can provide certain methodological references and technical references for the stable operation of hydropower plants in the context of new power systems.