## 1 Introduction  
Electrical energy plays a major role in our life, and it is a key driver in the industrial society. The significant increase of global power consumption, the extinction of conventional energy resources such as coal, oil and gas, and the environmental pollution which is caused by the energy production, are the main challenge for the electric utility. To handle these issues, the application of renewable energy in form of microgrid can be considered as the best alternative energy resource. However, the application of distributed generators based on renewable sources can cause as many problems as it may be solved. The inherently intermittent and power fluctuation of the renewable sources such as Photovoltaic (PV) and wind turbines, and the variation of power demand are the significant factors of system stability degradation, especially when the microgrid is operated in islanded mode. Hence, a sophistication microgrid control is a must. In a standalone microgrid, the entire consumption is fully supplied by the microgrid sources. The high penetration of renewable energy systems with its intermittent power output results in power supply-demand unbalancing and high-frequency variation. Therefore, to address these issues, the standalone microgrid highly relies on the Energy Storage System (ESS) which could function as energy buffer or backup to balance the system mismatch and to maintain the system frequency in a stipulate operation range [1]. The battery which is the most mature and the cheapest energy storage has been found in many applications such as frequency regulation by mitigating the impact of the PV and wind power fluctuation [2; 3], power losses reduction in distribution grids [4], and peak shaving applications [5]. The lead-acid battery storage based on the traditional moving average algorithm was used to smooth the PV fluctuation in [6]. In [7], the author used the absorb/release ability of the Battery Energy Storage System (BESS) to compensate the high power fluctuation of PV. A low-pass filter was used in this paper to generate the power reference for BESS. The method was reported to have the capability of limiting PV power fluctuations. However, the usage of battery in the above application could seriously shorten the battery lifespan. To improve the lifespan of the battery by reducing the battery stress, the Hybrid Energy Storage System (HESS) was introduced [8; 9]. Based on the characteristics of each energy storage system in Table 1[10], the battery and supercapacitor are two different energy storages which have complemented characteristics. The combination of these energy storages are expected to relieve the battery charging/discharging stress, to improve the lifespan of the battery storage and to enhance the system efficiency. In conventional power system, the synchronous generator plays a major rule as the electricity source. It could damp the effect of dynamic load transition and disturbance with the inherent droop control and inertia control. Hence, the system stability is maintained. Inspired by the synchronous generator dynamic behavior, an idea to add inertia artificially to the inverter-based generator has been emerged. The artificial inertia can be obtained by using energy storage-release/absorb characteristic together with the power electronic inverter/converter and the proper control mechanism in a system, so-called, Virtual Synchronous Generator (VSG). Since the VSG is expected to solve the major issues (low-inertia) in the microgrid, this relatively new scheme gains great attention and attracts many researchers from both universities and industries, and numerous scientific outcomes have been published recently [11; 12; 13; 14]. Novel control for VSG based on algebraic with a minimal number of the parameter was introduced in [15] to suppress the fluctuation of frequency and voltage.