## 1 Introduction  
After asynchronous networking, the problem of low frequency oscillation caused by weak damping of the AC system in weakly interconnected large systems has been improved to a certain extent, but ultra-low-frequency oscillation occurs in non-synchronous hydropower high-proportion transmission systems. It has been shown that the ultra-low frequency oscillation of asynchronous network transmitter systems is mainly due to the water hammer effect of hydropower units. As an additional control of traditional direct current, DC modulation has been used to suppress ultra-low frequency oscillation. At present, there have been many studies on the use of DC additional control to suppress low-frequency oscillations. Based on the analysis of the action mechanism of governor and FLC, a decoupling coordination design method of governor and FLC was proposed in the literature [1]. The literature [2] proposed and used FLC fast modulation power to jointly improve the damping of oscillation mode of HVDC island system to suppress ultra-low-frequency oscillation and suggested that the FLC dead zone should be smaller than the governor dead zone to enhance the FLC effect. However, with the introduction of voltage source converter based high voltage direct current transmission (VSC-HVDC) technology based on a modular multilevel converter (MMC), a line-communated converter (LCC) combined with MMC forms a new direct current transmission topology [3, 4, 5, 6]. With the increasing scale of power grid interconnection, inter-regional low-frequency oscillation caused by system interconnection hasgradually become one of the bottlenecks that trouble the safe and stable operation of power grid and limit the transmission capacity of power grid [7; 8; 9; 10]. By controlling the active power output of HVDC system, the oscillation can be quickly suppressed so as to improve the dynamic stability of the AC system and increase the safe transmission capacity. The literature [11; 12] used emergency power support and coordinated power control to suppress low-frequency oscillation of AC power grid for a conventional HVDC system. Compared with the conventional HVDC system, VSC-HVDC technology has technical advantages such as self-phase change capability, active power and reactive power can be decoupled and controlled, and no phase change failure will occur. In recent years, it has been widely developed and applied in the world, and China is also vigorously building VSC-HVDC projects. Because VSC-HVDC technology has large degrees of control freedom and switching between operation modes of the converter station, it can further suppress the AC low-frequency oscillation in theory. For an AC-DC hybrid power grid with VSC-HVDC system, an additional controller is designed to adjust the active and reactive power of the flexible direct converter, which can effectively suppress interregional low-frequency oscillation and improve the dynamic performance of the system [13; 14; 15; 16; 17]. Based on a wide-area measurement system, the literature [13] determined the optimal value of active and reactive power of DC system through model predictive control, and it adopted fixed frequency prediction and adjustment power instructions to suppress low-frequency oscillation. In the literature [14], a design method of a centralized coordination controller suitable for multiple HVDC lines was proposed by adopting a centralized control scheme, which could improve the damping of small power systems considerably. In order to avoid the risk of losing centralized control communication, literature [15] applied the homologous ethics theory to the controller design of VSC-HVDC converter, and it obtains a robust distributed controller. In literature [16], the nonlinear system is transformed into a linearized system through input-output accurate feedback linearization. Then, the coordinated control structure of multiple HVDC lines is designed through the design method of a linear system controller to improve the stability of the system.