## 1 Introduction  
The AC-AC power converters based on the switching action of the solid-state devices allow the grid's constant voltage and frequency to vary as per the requirement. The variation in the grid frequency and voltage is required for a heating process through the induction phenomena, speed drive, and controlled power conversion from AC to DC and voltage correcting set up in a power distribution system. There are two basic AC power converting topologies, called indirect and direct conversion. The first approach is based on multistage power conversion that may include the conversion from AC to DC, DC to DC, and DC to AC. This approach is limited nowadays as it has some serious concerns such as the high value of the overall weight, losses, volume, cost, and an increase in system complexity [1; 2; 3]. In these converters, there is also the problem of low power factor and high value of the harmonic factor of output voltage and input current that requires harmonic elimination filters. The use of a DC-link capacitor curtails the reliability of the entire system. The limitations of the indirect AC converters are addressed in the converters based on the direct AC power conversion approaches. There is no concern about the system's reliability as there is no DC link stage. These converters are more attractive for applications that only require low output frequency in variable form. These applications include rolling in a steel manufacturing process, grinding systems for mining, and electrical traction systems [4; 5; 6]. Traditionally, the single-phase cycloconverters are used as a direct frequency regulator without involving the DC power stage. Still, its implementation requires more solid-state devices and corresponding gate control circuits. Conventionally, the cycloconverters are developed with thyristors. Nowadays, however, these devices are replaced with soft switching devices (transistors). The frequency controllers based on the high switching operation of the operating devices can govern the output frequency and rms voltage. The described circuit is one of the modified versions of AC converters that utilize a Z-source circuit for shoot-through compensation and voltage regulation. Such topologies are reported in [7; 8; 9; 10]. The circuit and control complications are the main concern in these topologies. Their realization needs a large number of circuit elements and solid-state devices. The current rating of these components has to increase as there is a flow of high surges of current during the shoot-through intervals. The protection circuits for operating devices are needed as there is induction of high voltage and current surges. The operating issues of the Z-source circuits are addressed in the other form of AC-AC topologies that do not need to use the Z-source structure in their implementation [11; 12; 13; 14]. These topologies can produce the regulated voltage of dual polarity required for output frequency control. The circuit stated in [11] requires six fast switching transistors and diodes, but its dual polarity voltage operation is non-symmetrical. Also, the issue of high voltage in these converters remains unaddressed. This problem is figured out in [13] by introducing various operating modes, but their control for dual polarity voltage operation remains non-symmetrical. The symmetry in the dual polarity voltage operation with a low operating voltage is ensured in the converter stated in [12]. However, the circuit realization of this topology needs eight transistors and eight fast switching diodes, thus increasing the overall weight, losses, and cost. Although all of the topologies stated in [11; 12; 13] can effectively be operated to produce low and high output frequency, their operational control schemes seem to be complex. Such power conversion approaches are not well suited for applications that just need frequency regulation. Various circuits are stated in literature to govern the output frequency by employing the direct form of the AC-AC converters.