## 1 Introduction  
The problem of poor power quality in power systems normally results from the extensive use and integration of renewable energy systems or resources, adverse loading, or the use of a non-linear load at an extensive level. This problem may include voltage fluctuation, imbalance of the voltage in the three-phase system, voltage sags and swells, etc. Among these problems, the voltage sags and swells are critical for loads that are very sensitive to voltage variation. These issues may lead to the missed or incorrect operation of sensitive electronic devices or equipment. To address these issues, the use of flexible AC transmission (FACTS) controllers may offer a possible solution if they are employed as a dynamic voltage restorer (DVR) [1; 2; 3]. The basic principle of protection in these devices is the series injection of voltage between the load and point of common coupling (source or transformer) in the power system. The DVRs may be employed in a DC-link-based system, as shown in Figure 1. The most commonly used configuration of DVR, as illustrated in [4; 5; 6], is depicted in Figure 1a, which is based on the use of a voltage source inverter and voltage injection transformer connected in series with the line. The input power of these types of DVRs is taken from DC energy-storing devices such as batteries. The duration of the compensation voltage in these configurations depends on the size and capacity of the energy-storing devices but cannot support longer-duration voltage variations. This issue is addressed and tackled in other configurations for voltage compensation [7; 8], as shown in Figure 1b. Here, a front-side AC-DC converter eliminates the use of energy-storing devices, enabling the compensator to deal with the longer-duration problems. In both previously discussed configurations, the use of a bulky DC-link capacitor is mandatory, which has very severe reliability issues. Therefore, these configurations are not suitable for applications where only voltage stabilization is required. In the other developed approaches of DVRs, the stabilization of the required voltage may be ensured by the PWM control of the direct AC-AC converters [9]. These configurations eliminate the use of a DC-link capacitor; hence, this improves the overall system's reliability. Direct AC-AC topologies may be realized with a Z-source structure [10; 11; 12; 13; 14] to increase the capability of the voltage transfer ratio. This also eliminates the risk of short-circuit problems or the paralleling of capacitors connected to input and output terminals. These problems may result from the turning on of the switching transistors connected in series, which must be operated in a complementary way. The usage of a number of passive elements and operating devices is a serious challenge in these power-converting approaches, which is the main cause of their large overall size and cost. The presence of the high-order elements in this arrangement also seriously impacts the dynamic response. There is also an issue of high current stresses conducted in the switching devices during the shoot-through intervals, which increase their power rating, resulting in high costs. These issues are tackled in power-converting approaches implemented without a Z-source configuration, as reported in [15; 16; 17; 18; 19; 20]. In these power-converting topologies, an inductor at the intermediate level is employed for energy storage and to avoid the shoot-through issue. The bidirectional current conduction capabilities of the switching MOSFETs in converters [15; 17; 18; 19; 20] are forced to be unidirectional by connecting a fast recovery at the source end. This arrangement always ensures the reverse biasing or blocking of the conduction of the MOSFET's body diode. This approach not only avoids the shoot-through problem but also simplifies the circuit configuration as well as the switching control techniques. The power quality validation of the AC voltage controllers realized with the direct approach of AC power conversion topologies is explored in [16].