Renewable energy transmission by high-voltage direct current (HVDC) has attracted increasing attention for the development and utilization of large-scale renewable energy under the Carbon Peak and Carbon Neutrality Strategy in China. High-penetration power electronic systems have gradually formed at the sending end of HVDC transmission. The operation of such systems has undergone profound changes compared with traditional power systems dominated by synchronous generators. New stability issues, such as broadband oscillation and transient over-voltage, have emerged, causing tripping accidents in large-scale renewable energy plants. The analysis methods and design principles of traditional power systems are no longer suitable for HPPESs. In this paper, the mechanisms of broadband oscillation and transient over-voltage are revealed, and analytical methods are proposed for HPPESs, including small-signal impedance analysis and electromagnetic transient simulation. Validation of the theoretical research has been accomplished through its application in several practical projects in north, northwest, and northeast region of China. Finally, suggestions for the construction and operation of the future renewable-energy-dominated power system are put forward.