Abstract This paper aims to study the law that the stability of hydropower systems changes with the system operating point and clarify the impact of hydro-turbine nonlinearity and hydraulic nonlinearity on the system stability. Firstly, the piecewise linearized model of the hydro-turbine regulation system (HTRS) at various operating points is established. Then, the HTRS stability domain is calculated and analyzed under various working heads and guide vane openings, and the impact of head variation on system stability is researched from the perspectives of discharge and power. Finally, the stability of various operating conditions under ideal hydro-turbine conditions and rated hydraulic parameter conditions are and compared to clarify the role of the water system and turbine nonlinearity on the stability. The results show that hydro-turbine nonlinearity helps to improve the system stability of the overall operating conditions, but the stability of the HTRS is relatively weak during high-load and low-head operations. Moreover, the hydro-turbine nonlinearity plays a dominant role in the process of stability changing with the operating head. This paper provides a comprehensive analysis of the system stability at different operating points, which can help guide the control optimization of hydropower systems.