## 2 System Components  
### PMSG, Three-Phase Diode Rectifier, and DC-DC Boost Converter  
The proposed system consists of five main blocks: the three-phase PMSG, the three-phase diode rectifier for AC-DC conversion, the DC-DC boost converter, the PUC MLI for DC-AC conversion, and the load. Furthermore, in the experimental study, the operation of a variable speed wind turbine in the laboratory environment is emulated using a three-phase induction motor controlled with a variable speed drive. Figure 2 demonstrates the PMSG-based WECS under study. Wind turbines are primarily made up of rotor wings. Wind kinetic energy is converted into rotational kinetic energy by employing these rotor wings. The PMSG is a device designed to transform the rotational kinetic energy into electrical energy [46; 47]. \begin{table}
\begin{tabular}{c c c c c c} \hline
**MLI** & **THD** & \
\begin{tabular}{c} **Voltage Rating** \\ **(V)** \\ \end{tabular} &
\begin{tabular}{c} **Switching** \\ **Frequency (kHz)** \\ \end{tabular} & **Load** & **Ref.** \\ \hline CHB & 17.48\% & 230 & 18 & 750 ohm, 240 mH & [35] \\ NPC & 19.14\% & 750 & - & - & [37] \\ 7L-SCMLI & 11.99\% & 175 & - & 150 ohm, 200 mH & [39] \\ 7L-Boost MLI & - & 100 & 2.5 & 100 ohm, 50 ohm, 100 mH, 50 mH & [40] \\ CHB & 31.44\% & 200 & - & - & [41] \\ CHB & 28.49\% & 200 & 2 & 20 ohm, 100 mH & [42] \\ C7L Full-Bridge MLI & - & 300 & 5 & 50 ohm, 20 mH & [43] \\ FC & 38.90\% & 250 & 10 & - & [44] \\ Proposed PUC MLI & 11.65\% & 45 & 4 & 30 ohm, 100 mH & \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison between proposed topology and recently introduced topologies. The power obtained from the wind is given by  
\[P_{Wind}=\frac{1}{2}\,\rho AV_{w}^{3} \tag{1}\]  
where \(\rho\) is the air density \(\left(\mathrm{kg}/\mathrm{m}^{3}\right)\), \(A=\pi R^{2}\) is the rotor swept area \(\left(\mathrm{m}^{2}\right)\), \(R\) is the blade radius \(\left(\mathrm{m}\right)\), and \(V_{w}\) is the wind speed \(\left(\mathrm{m}/\mathrm{s}\right)\). The type of voltage obtained from the PMSG is in the form of AC voltage. Thus, a three-phase diode rectifier circuit is used to convert AC power into the DC power that the PMSG produces, since a DC voltage is needed at the input of the MLI. In the following equations, the relations between the three-phase voltage and output DC voltage are given. Generally, the instant phase voltages at the input of the three-phase diode rectifier can be given as follows:  
\[V_{an}=V_{m}\angle 0^{\circ} \tag{2}\]  
\[V_{bn}=V_{m}\angle-120^{\circ} \tag{3}\]  
\[V_{cn}=V_{m}\angle-240^{\circ} \tag{4}\]  
where \(V_{m}\) is the peak value of the phase voltage. The average output voltage of the three-phase diode rectifier can be expressed as follows [48]:  
\[V_{avr}=\frac{3}{\pi}V_{m}=0.955V_{m} \tag{5}\]  
In the proposed PMSG-based WECS, a DC-DC boost converter, as shown in Figure 3, is used to increase the DC voltage obtained from the diode rectifier. In this way, a higher DC voltage \(\left(V_{\mathrm{DC2}}>V_{\mathrm{DC1}}\right)\) can be applied to one of the PUC MLI inputs. The relationship between the input voltage \(\left(V_{S}\right)\) and the output voltage \(\left(V_{0}\right)\) of the DC-DC boost converter is depicted as  
\[V_{0}=\frac{V_{s}}{1-D} \tag{6}\]  
where \(D\) is the duty cycle. For example, when \(V_{s}\) is 150 V and the duty cycle is 40%, the output voltage is increased to 250 V. As the value of \(D\) decreases, the output voltage approaches the input voltage. Figure 2: The proposed PMSG-based WECS. Theoretically, it is accepted in the literature that the fluctuation in the inductor current (\(i_{L}\)) should be between 0.2 and 0.4 times the current and the fluctuation in the output voltage should not exceed 5%.