## 1 Introduction  
In the last few decades, the micro-grid has attracted the interest of many scientists and researchers due to the advantages of improving power supply reliability and power quality through the flexible control of micro-power [1; 2]. To solve the energy crisis and environmental problems, more and more renewable energy [3; 4; 5], electric vehicles [6; 7] and energy storage systems [8; 9] were connected to the micro-grid through power electronic converters. Those devices can achieve two-way flow of electricity according to the demand of the power grid, which are called input/output bidirectional devices for convenience in this paper. The converter at the input/output bidirectional devices interface operates in the rectification mode by storing the energy at times of surplus. The converter operates in inverter mode and inverts stored electricity into alternating current when power is scarce [10]. Considerable research efforts have been devoted to the input/output bidirectional devices [11; 12; 13]. [PERSON] proposed the concept of a power electronics-enabled autonomous power system to provide a uniform interface mechanism for smart grid access so that new energy and loads can participate in grid frequency regulation like conventional power supplies [14]. Therefore, the input/output bidirectional devices are required to be able to participate in the regulation of the grid frequency autonomously in both the generator mode and motor mode. Therefore, the traditional static frequency analysis method needs to be improved and expanded. As a practical input/output bidirectional device, the PV storage system has been intensively investigated due to the improvement of power supply reliability. Concerning the control aspects, [PERSON] et al. [15] introduced several local voltage control strategies using PV storage systems. [PERSON] et al. [16] researched the supervision and control of grid connected PV storage systems with the five level diode clamped inverter. In addition, much work so far also has focused on the internal energy management of PV storage [17]. However, inverters as power electronics, do not have the same moment of inertia as synchronous machines. Therefore, PV storage systems can't provide frequency support for the grid. To solve this problem, [PERSON] et al. [18] presented a method to deal with the main grid code requirements by considering a PV plant with an energy storage device. Moreover, the cooperative control between PV storage and other energy sources has been investigated. [PERSON] et al. [19] presented a coordinated control method of the distributed PV inverters, energy storage systems, and electric vehicles. If the device's frequency regulation mechanism under different modes can be a detailed analysis and a new input/output bidirectional device with bidirectional frequency regulation capability is proposed, the development of input/output bidirectional device will be significantly promoted. Furthermore, it is very important to do that for the construction of the autonomous power system and the stability of grid frequency with a high penetration rate in the future. In this paper, a synthesis analysis method for system power-frequency considering source-load static frequency characteristics (S-L analysis method) suitable for input/output bidirectional devices is proposed to provide a solution for frequency analysis in new scenarios. A distributed PV storage virtual synchronous generator system that can participate in grid frequency regulation under generator/motor dual mode is established. With this solution, under a steady state, the system can output or store power according to the scheduling results and participate in the frequency regulation process of the power grid actively with the inertia characteristic of the synchronous generator under a transient state. Additionally, the matching method of inertia between power supplies in the power grid is discussed and studied.