## 6 Validation of the Generated Harmonics
### Validation through Practical Results  
No a new dedicated practical set-up is developed for the practical analysis of the power quality concerns. The practical results for power quality analysis are documented with the help of a practical set-up of our proposed power converting topologies reported in [25; 26]. The plots of Figure 10 are obtained with the practical set-up of [25] by synchronizing the gating signals with input source voltage by applying the output of the zero-detecting circuit to the signal generator (STM controller) in the form of an interrupt. In the same way, the practical outputs presented in Figure 11 are obtained with the help of the practical set-up presented in [26]. These practical set-ups are developed with high switching MOSFETs (IRF840), diodes (RGHG3060), transistors driving circuits (EXB840), isolated DC supplies, and passives components.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Harmonic Order (\(n\))**} & \multirow{2}{*}{**Harmonic Frequency (Hz)**} & \multicolumn{3}{c}{**Mathematical Results**} & \multicolumn{2}{c}{**Simulink Results**} \\ \cline{3-6}  & & **Magnitude (V)** & **Phase-Angle (Deg)** & **Magnitude (V)** & **Phase-Angle (Deg)** \\ \hline
1 & 50 & 46.28 & \(-50.69\) & 45.81 & \(-12.2\) \\
3 & 150 & 0 & 0 & 2.73 & 124.4 \\
5 & 250 & 20.67 & \(-60\) & 19.2 & 1  
Figure 10 demonstrates the practically recorded results of the output voltage and their FFTs for various switching control schemes. Figure 10a-d depicts the output voltage waveform of phase-angle with unipolar and bipolar, on-off cycle, and PWM voltage control, respectively. Their FFT results show the RMS value of the voltage fundamental components and some dominant harmonics. The practically obtained FFT of Figure 10a depicts the output voltage of the AC voltage controller realized with unipolar voltage control scheme has a DC component, and all even and odd harmonics. The FFT of Figure 10b shows that all even harmonics and DC components are suppressed from the output with the help of a bipolar voltage control scheme. The FFT plot of on-off control shown in Figure 10c depicts the dominant low-frequency harmonics. The shifting of low-frequency harmonics to high frequencies can be viewed from Figure 10d which is achieved by increasing the switching frequency.  
The harmonics in the output voltage with PWM control can be easily suppressed with a low pass filter like other voltage control techniques as the generated harmonics with PWM control can be moved to high frequencies (switching frequencies) by increasing the switching frequencies. Figure 11 shows the output voltage and its FFT if the PWM output is passed through a low pass filter.  
Similarly, the power quality analysis of the output voltage in variable frequency operation in [26] is explored by comparing the mathematical results with the simulation results. The output voltage waveforms for the output frequency of 25, 100, 150, and 200 Hz with their FFT results are plotted in Figure 12.  
Figure 11: The practical waveform of the output voltage with PWM control and a low pass filter.  
Comparing the results of Tables 2-9 depicts the effectiveness of the proposed analytical approach to compute the harmonics content of the various output of the direct AC-to-AC converters.