HVDC transmission has significant advantages in high-power and long-distance transmission, and at the same time brings great challenges to the stability of the interconnected asynchronous power system with HVDC links. Given this background, this paper investigates frequency stability of the sending subsystem in an interconnected asynchronous power system with HVDC links, with special background associated with Yunnan power grid of China. First, the mathematical models of governor systems in hydropower and thermal power generation units are presented, with secondary frequency control and Frequency Limit Control (FLC) considered. Then, the root locus method is used to study the frequency stability of the power system, and coordinated optimization between the secondary frequency control parameters and the FLC parameters addressed. Finally, numerical simulations of some operating scenarios in Yunnan power grid are employed to demonstrate the proposed frequency stability analysis method.