### Literature Review
The harmonics suppression through the paralleling of power converters requires a large number of power converters. This approach cannot be employed in the case where a converter is feeding power to an individual load. The direct AC-AC converters are more attractive over the sizeable indirect AC-AC converters (AC-DC-AC converters) as their operation is accomplished through single-stage power conversion. They are the more viable choice in most applications, such as motor speed drive, grid voltage compensation [22; 23; 24], and induction heating systems [25; 26]. Thyristor-based AC voltage controllers are used at the domestic level for speed regulation of the fans. They are also employed in some industrial drives. These topologies are simple to implement but they have certain serious drawbacks. The RMS values of the output voltage are controlled via the control of the firing delay. They have a problem of low order harmonics as the switching frequency is equal to the input source. That increases the total harmonic distortion (THD) and reduces the power factor (PF). On-off cycle control is another approach to control the output RMS voltage with the load having a high time constant. For example, heavy industrial load having a high mechanical time constant, or heating load having a high thermal time constant. This voltage control topology is also realized with thyristor-based converters. Here the switching of a thyristor is accomplished at zero crossings of the input voltage. The amplitude of the fundamental component and generated harmonics depends upon the number of on and off cycles. The generated harmonics also exist at low frequencies that cannot be easily suppressed. The generated harmonics are shifted at higher frequencies in the power converter implemented with the pulse-width modulation (PWM) approach by increasing the switching frequencies of operating devices [27]. The high-frequency harmonics can be easily eliminated by employing a low pass filter. The output voltage regulation is governed through the duty cycle control of the PWM signals. The AC voltage controller operated with bipolar voltage gain may regulate the output frequencies in discrete steps. This is accomplished by operating the converters in non-inverting and inverting modes according to the output frequency requirements [25; 26]. The output voltage and frequency control are realized through various switching schemes and converting topologies. Each switching scheme or power converting topology has a distinctive harmonic profile. Conventionally, the harmonic analysis based on FFT is employed in [28; 29; 30; 31] for harmonic analysis but it has the problem of aliasing and spectrum leakage as it is based on sampling frequency and window. The selection of the period of the wave is also a critical issue and it leads to incorrect results. The double Fourier series is employed in the Jacobi matrix [32] but its spectrum analysis is inaccurate as only two frequencies from the input, output, and sampling are considered. This problem is tackled in the triple Fourier series as in [33] but this approach is not mature due to some deficiencies. These approaches are employed in indirect AC-AC converters and cannot be employed in direct AC-AC converters due to complex mathematics. The harmonics of an uncontrolled three-phase rectifier are computed through sample delta and state-space approach in [34; 35] but these approaches are complex to apply in other power converting topologies. A novel approach for harmonic analysis is reported in [36] for a rectifier circuit realized through a multi-pulse approach. Here the three input phase currents are converted in the form of a stepped wave by employing the paralleling of four converters. The harmonics contents of each converter are suppressed through their elimination topologies. The harmonics contents of AC-AC converters are usually addressed in Simulink's dependent environment.