## 1 Introduction  
The development in solid-state electronics is playing a major contribution to the development of modern society. However, the operation of these pieces of equipment is very sensitive to variation in the supplied voltage [1, 2]. The main source of their incorrect outputs is the decrease and increase in values of the supplied voltage. In power quality terminology, this problem is regarded as voltage sag if the line rms voltage is reduced (80% to 20%) with respect to nominal rated rms values during some input voltage cycles [3]. This situation requires the addition of voltage in the line that may achieve with the non-inverted output of the voltage stabilizers. The other type of voltage variation is characterized as voltage swell in which the line rms voltage is boosted to 110% to 180% of its normal rated value for a few milliseconds [4]. The correction of this situation requires injecting the voltage of opposite polarity of the line that can obtain from the inverted output of the voltage controllers. These problems are very frequent and challenging in power distribution systems during fault conditions [5; 6]. For example, once there is a line-to-ground fault, the faulty line faces voltage sag while other phases experience a voltage swell problem. They may be resolved by adding and subtracting the voltage generated by the voltage controllers. The magnitude of the correcting voltage may be less than the voltage of the faulty phase if the depth level of the voltage variation is less than 50%, which requires the voltage buck characteristics of the generated voltage. On the other side, it requires the voltage boost feature if the required level of the correcting voltage is more than 50%. Therefore, voltage buck and boost features with dual polarities are a mandatory requirement of the correcting voltage for any depth level problem. The traditional way to resolve these issues is the use of indirect approaches of AC-AC conversion [7; 8; 9; 10]. That requires power conversion in two stages where a DC-link capacitor is a mandatory requirement between the two converters. Here at the front stage, a low-frequency rectifier circuit transforms AC power to DC power to store in a DC-link capacitor. This stage may be a controlled rectifier if regulation of voltage at the DC-link level is required. This control highly decreases the power quality of input current that can only be tackled using harmonic suppression filters or complex switching arrangements. The second converting stage is responsible for DC to AC conversion, and once again, a complex control arrangement is required to tackle the low power quality. The other approach to address and tackle the low power quality issues is the execution of power conversion in multistage [8] or multilevel configuration [9; 10]. This overall arrangement is complicated to realize, and DC-link capacitors are a big source of poor system reliability [11]. This approach is not feasible or smart for applications where only voltage control is essential at source frequency. The direct AC-AC conversion is a smart solution for stabilizing the line voltage as it is realized without a DC-link capacitor. This solution approach is simple, less complex, and implementable in a single stage. So, it gains more attention from the researchers and developers. Thyristor-based AC voltage controllers (on-off or phase-angle) have some potency for low power application as the generated harmonics are always low frequency and have very severe power quality-related issues [12]. AC voltage controller based on high-frequency pulse-width modulation (PWM) control can be employed to tackle the low power quality concerns but their voltage gain is low (less than one) with unipolar capabilities. The voltage stabilization characteristics in direct AC-AC converters may be realized with the similar approach as adopted in direct DC-DC converters just with the replacement of unidirectional operating semiconductor devices with bidirectional devices as proposed in [13].