## 1 Introduction  
With the increasing demand for energy and the maturity of distributed power generation technologies, the concept of a microgrid has gradually been put forward in order to better link renewable energy sources with the power grid [1]. Currently, the development of a traditional AC microgrid is more mature. In contrast to an AC microgrid, a DC microgrid [2, 3] can effectively connect many renewable energy sources with DC output forms such as photovoltaic and energy storage systems. In order to promote the intelligent process of power grids, the concept of a hybrid AC-DC microgrid has been proposed by scholars at home and abroad. A hybrid AC-DC microgrid links an AC microgrid and a DC microgrid through an interlinking converter (ILC), which inherits the advantages of both the AC microgrid and DC microgrid [4] and has a flexible topology [5] and operation mode. A hybrid AC-DC microgrid has both grid-connected and islanded modes [6], which can realize the mutual support of power between the AC and DC sub-microgrids [7]. The ability to operate in islanding mode is a unique advantage of hybrid AC-DC microgrids compared to traditional power grids. Hybrid AC-DC microgrids often use peer-to-peer control during islanded operation [8], which mainly utilizes the reference quantities of each distributed generation (DG) itself for control without communicating with other control units. When the operation mode is changed, there is no need to switch the control mode, and the \"plug and play\" function can be achieved [9]. Among peer-to-peer control,droop control is most commonly used. When the system load changes, the DGs in the AC sub-microgrid use _P-f_ droop control to maintain frequency stabilization. The DGs in the DC sub-microgrid use _P-U_dc droop control to maintain DC voltage stabilization. ILC, as an important device used to balance the power on both sides of the hybrid AC-DC microgrid, needs to realize the bidirectional flow of power at both sides of the hybrid AC-DC microgrid. Hybrid AC-DC microgrids in islanding mode will be more prone to voltage and frequency fluctuations as they are detached from the power grid. ILC, as a bridge linking the AC and DC sub-microgrids, plays a vital role in maintaining the stability of the system frequency and voltage [10]. Therefore, designing a suitable ILC control strategy is a key research focus for hybrid AC-DC microgrids operating in islanding mode. In islanding mode, the ILC needs to control the AC frequency and DC voltage as a way to maintain stability on both sides of the system. Traditional droop control methods that only consider active power and frequency on the AC side and reactive power and voltage are no longer suitable [11; 12]. For this reason, researchers have proposed a bidirectional droop control strategy capable of regulating AC frequency and DC voltage [13]. In [14; 15], a normalized droop control strategy was employed based on a typical hybrid AC-DC microgrid structure. In order to cope with the problem of large computation of normalized droop control, in [13], the droop relationship between frequency and voltage square was introduced based on the energy conservation relationship on the AC and DC sides, which realized the autonomous control of the ILC. In [16; 17], a droop control strategy based on angular characteristics was proposed to ensure power sharing at low frequency deviations. In [18; 19], a control strategy for the ILC was proposed in conjunction with energy storage devices inside the AC and DC sub-microgrids to improve the energy management capability of the hybrid microgrid. In [20; 21], a coordinated control strategy for multiple ILCs in parallel operation was proposed. To improve the dynamic performance of an ILC, an improved control strategy was proposed in [22] based on a virtual synchronous motor. In [23], a two-layer optimization method was proposed for a hybrid AC-DC microgrid, which incorporated secondary regulation and a DG cost optimization control strategy based on bidirectional droop control of the ILC.