## 1 Introduction  
The microgrid composed of internal combustion engines and distributed power sources has attracted much attention for its flexible application scenarios. Meanwhile, natural gas as a fuel for generators mitigates the growing energy crisis [1]. In microgrids, it is very important to ensure the transient stability of natural gas generators, especially after the generators are subjected to impact loads [2]. In contrast to conventional loads, impact loads exhibit impact and cyclic operating modes, while their peak power is much higher than the average power. For natural gas generators, if their power angle or relative speed deviates too much from the operating point, it will lead to the loss of synchronization between the generator and the microgrid or even damage the rotor [3]. However, high-power internal combustion engines usually have a large moment of inertia. Therefore, the generator cannot satisfy the power balance of the grid at the moment when the impact load is connected. Engineers and researchers have conducted a lot of research to solve this problem in terms of control strategies and internal gas structures [4, 5]. In the last few decades, many researchers have believed that the moment the microgrid is impacted, an additional energy storage device must be used to release the energy required by the load [6, 7]. The most widely used forms of energy storage include lithium batteries [8],super capacitors [9; 10], flywheel energy storage [11; 12; 13], and superconducting magnetic energy storage [14; 15], etc. Among them, the safety of flywheel energy storage severely restricts its development, and the lithium battery has high requirements for ambient temperature. Although the energy density of super capacitors is lower than that of lithium batteries, they have a high power density, are maintenance-free, have a long service life, and have a wide range of applicable temperatures [16]. Therefore, super capacitors can be effectively used as an energy source for impact load compensation devices. Moreover, the impact load compensation trouble turns into the problem of control strategies for super capacitor compensation devices to achieve fast power response. The grid-connected inverters currently have two main control modes. One is to directly control the d-q axis current to regulate its grid-connected power while using a phase-locked loop to obtain the grid voltage phase [17]; this control method can equate the grid-connected inverter as a current source [18]. The other one is to regulate the grid-connected power directly by controlling the vector and phase of the output voltage, whose active power and reactive power are similar to the synchronous generator system in relation to the phase and amplitude of the voltage. In [PERSON] et al. [19], the authors propose a voltage-source inverter that does not use a PLL and has good stability in weak grids. For now, the voltage-source mode is usually based on droop control or a virtual synchronous generator to simulate the electromagnetic characteristics of an actual synchronous generator. Then, the vector amplitude and phase of the output voltage are regulated by the power outer loop, which in turn regulates the output power. In [PERSON] et al. [20], the authors review the conventional droop control and virtual synchronous generator techniques, and a generalized droop control method for grid-connected inverters is proposed on this basis. This proposed generalized sag control has a flexible active power control loop to meet various types of loads. In [PERSON] et al. [21], authors analyze the stability of the virtual synchronous generation technique at high line impedances. The results of the paper demonstrate that the voltage source mode is more stable than the current source mode under weak grids. Current-source grid-connected inverters usually use control strategies such as grid voltage feedforward and PLL.