## 1 Introduction  
The research community is still exploring all possibilities to provide an alternative to traditional energy resources based on fossil fuels in order to reduce environmental issues such as greenhouse gas emissions and global warming [1]. In this context, the use of renewable energy resources has significantly increased in recent decades with more intention to integrate them in the utility grid [2]. For this reason, the smart grid has been created and developed to manage renewable energy resources in the utility grid. The smart grid is a new electricity transport and distribution network that allows a bidirectional communication between suppliers and consumers in order to adjust the flow of electricity in real time and enables more efficient management of the electricity grid [3]. The main components of the smart grid are microgrids (MGs). Indeed, an MG is based on the idea of providing electrical energy in a decentralized form: it combines loads, storage and multiple energy sources (traditional and renewable) in one unique entity. The MG is able to operate on-grid and off-grid. Thus, it is suggested to facilitate the realization of the smart grid, supply isolated areas, ensure power balancing and promote local energy consumption and production [3, 4]. There are three different structures of MGs depending on the common bus, i.e., DC or alternating current (AC), of its different components: AC MG, DC MG and hybrid AC/DC MG [5]. While the AC MG has been the subject of remarkable dynamic research for enhancing its performance, several works have presented the attractive uses of the DC MG thanks to its high efficiency to integrate DC native renewable energies. In this perspective, wind energy is forming part of DC MG's distributed energies and it fits well into this paradigm of using renewable energy resources for responding to environmental issues. Wind energy is earning more interest thanks to its lower space occupancy, significant power cost reduction and zero carbon emissions during operation [6]. This is true not only for high-power wind turbines (WTs) but also for small ones. According to the market reports of the World Wind Energy Association, the small wind capacity installed worldwide increases annually with a growth rate of 12%. Approximately 270 MW of new capacity is forecasted to be installed in 2020 and then 1.9 GW of cumulative installed capacity will be achieved by 2020 [7]. Small-scale wind turbines (SSWTs) provide electric energy, supply off-grid consumers like remote villages and can be used as distributed resources in MG systems [6]. Although the implementation of SSWTs has grown worldwide, the efficiency of wind energy systems is still impacted by many factors. For instance, the empirical extraction capacity of wind power makes the stability between supply and demand for energy very difficult to maintain. For a small wind energy conversion system (SWECS), several generators could be used to transform wind energy into electrical power. The most used amongst them are AC generators, particularly induction generators and permanent magnet synchronous generators (PMSGs). The latter are mostly used thanks to their high efficiency, low cost and low-priced maintenance [5; 8]. To apply the power control strategies to the WT, the PMSG is connected to power electronic converters. There are three types of converters, i.e., diode bridge rectifiers, boost converters and inverters that can be classified into two types of electrical structure: passive and active [9]. A three-phase diode bridge, as a passive structure, is an uncontrollable structure, robust and less expensive. An AC/DC converter (inverter) is an active structure fully controlled that may either require rotation speed or torque. The active converter's topology that is based on a three-phase diode rectifier with a boost converter is more suitable for SWECS applications, due to its low cost and high reliability [10].