# Unity Power Factor Operation in Microgrid Applications Using Fuzzy Type 2 Nested Controllers
## 1 Introduction  
Microgrids (MGs) are replacing remote central station power plants with localized, distributed generation, especially in cities, towns, and campuses [1]. MGs are durable and can supply competitive services due to their ability to operate in three distinct modes: on the grid, islanded, and autonomous [2]. Moreover, they provide positive social and environmental impacts globally [3]. However, the proliferation of MGs contributes topower quality problems at the distribution level [4]. One of these problems is the poor power factor and its measurements [4; 5]. The power factor is an essential index for economic and technical operations. Low power factor implies overloading of electrical equipment and might cause unnecessary tripping. It is well-known that electrical motors consume a significant fraction of the delivered electrical energy. Among the electrical motors, induction motors, either three-phase or single-phase, are the most common due to their merits such as being relatively cheap, rugged, and maintenance-free. However, induction motors draw current with a low power factor, particularly at medium and light loading conditions. For a 200-hp, three-phase induction motor, the low power factor operation cost was $7888 per year [6]. Therefore, continuously improving the power factor is highly desirable, which ultimately enhances the system's power quality. Many techniques and system configurations have been reported in the literature to enhance the power quality of induction-motor drives. For instance, 12- and 24-pulse AC to DC rectifiers were proposed and tested in [7] to improve the power up to 0.936 at full load. However, in such a system, the existence of the phase shift transformer causes the system to be bulky and expensive. An AC chopper with four switches and applying the hysteresis-band control was reported in [8]. Although the tested configuration in [8] is simple and cost-effective, the flexibility to control the speed or torque of the induction motor might be limited, and there is always a need to transfer between control modes to achieve a power factor improvement. To increase the system's power factor, ref. [9] presents a 9-switch AC-DC-AC converter that inserts a leading reactive power at the point of common connection. Even though the reported simulation and experimental findings demonstrate the converter and control's efficiency, this setup is still susceptible to grid-side disturbances and asymmetrical operation of the converter switches. Furthermore, real-world use requires an analysis of the switching losses, projected to be slightly larger than those of alternative systems. Various switching control approaches based on pulse-width modulation (PWM) have been used for the boost converter to increase its responsiveness while keeping it stable. Proportional integral derivative control is the most widely used PWM switching control method because of its ease of use. Voltage and current must have a dynamic response. Hence, double-loop control is required. Utilizing a model-based compact form, formulations in the design of a double-loop PI-based, the DC-DC boost converter controller produced excellent system responses to parameter variations and disturbances [10]. Sliding mode control is a robust closed-loop method for unpredictable and disturbed plants. One sliding surface makes a sturdy controller and removes inductor current measuring. A control scheme with a hysteresis loop prevented chattering caused by sliding mode control discontinuities [11]. Because it may approach any function by learning the system process, neural network control is ideal for nonlinear control systems and working with uncertainties and incomplete information [12]. Online learning strategies have been developed to increase neural network control performance. The neural network control produced better overshoot, oscillation, settling time, and fast response to track the required output voltage [13].