# Unity Power Factor Operation in Microgrid Applications Using Fuzzy Type 2 Nested Controllers
## 2 Problem Formulation  
The MG has been innovated to fulfill the varying and dynamic needs of DC and AC loads. Other advantages include improved power management and stable performance [22]. The MG solves source and load compatibility difficulties and integrates energy sources and consumer loads with minimal conversion stages [23]. However, the problem of low power factor has been reported for many MG systems such as maritime MGs [24], MGs employing three-phase three-wire grid-connected inverters [25], MGs utilizing thyristor-based compensation (series or shunt) [26; 27], and AC MGs integrating wind-energy systems [28].  
In [29], the authors proposed a review of the norms and standards used in MGs that should be used for the interconnection and disconnection of MGs in the downstream network. This study found the IEEE 1547 to be the most comprehensive standard. In [30], it was specified that distributed generators should always try producing at a unity power factor. Even if standards such as the IEEE 1547 state that the converter output power factor can be 0.85 lead/lag or higher, the inverters are typically designed to work with a unity power factor [31]. Considering the integration of distributed generators (DG) in the power system, the authors in [32] investigated power quality issues for a distribution system first modeled in PSCAD and then integrated with a photovoltaic, forming a MG power system. Each DG's power factor can also be determined by regulating both the frequency and voltage [33].  
With this goal in mind, the authors of [34; 35; 36] exploited voltage regulation devices to improve the power quality in the MG configuration. They claimed that conventional reactive power compensators could not correct power factors, generally used as voltage regulating devices. They presented a novel strategy to use STATCOM devices to obtain the power factor correction in MG applications. Using regulation devices such as dynamic voltage restorers, the authors in [37] focused on the operation of unity power factor rectifier topology.  
In similar MG structures, the study in [38] considered islanded inverter-based MGs (IBMGs) considering various load types; the authors proposed calculating the voltage sensitivity to the system loading in each bus based on the load power factor. Always considering the local loads, in [39], a novel artificial neural network (ANN)-based control approach was proposed to control the power quality as per the IEEE/IEC standards in MG systems. In [40], a strategy to improve the power factor at the point of common coupling (PCC) for MG applications was presented, and the proposed compensation scheme for power factor improvement can be used dynamically for linear and nonlinear loads. The performance of the smart load at different power factors was also evaluated in [41].  
Although the techniques employed to improve the power factor in MGs, as described in Section 1, were implemented and tested, there are still many issues to be further elaborated on and considered. Among these issues are the accuracy in the steady state, the transient performance of the controllers, simplicity of implementation, and satisfying the power-quality standards of the amount of injected distortion. This paper presents a Fuzzy-type-2 based controller aiming to resolve such issues.