## 3 DC/DC Boost Converter Design  
A DC-DC converter is installed between the PV module and load in an MPPT system to alter a DC voltage to another level of DC voltage. It is important to design the DC-DC converter correctly to ensure that the PV system is working at the best efficiency, as desired. In this work, a boost converter was chosen to alter the input voltage and control the level of output power to the load, as shown in Figure 3. Principally, the boost converter structure is established by an inductor, a diode, a high-frequency power metal oxide semiconductor field effect transistor (MOSFET) switch, and a capacitor [30]. The input voltage of the boost converter is controlled by the PV array output, and the duty cycle variation of the converter is performed according to the output of the MPPT. The operation of a boost converter mainly relies on the opening and closing of the switch, to enter the charging and discharging states, respectively [31]. For low to moderate power applications, a standard power diode and power MOSFET are frequently used [32]. Figure 3: Simulink model of the maximum power point tracking (MPPT) controller using a boost converter. Figure 2: Modelling of the PV array. **Selection of the resistor**: The load resistance \((R_{L})\) of the boost converter is related to the ideal internal resistance of the PV array at the MPP \((R_{MPP})\) by the following equation, as illustrated in [33]:  
\[R_{L}=\frac{R_{MPP}}{(1-D_{MPP})^{2}} \tag{1}\]  
For the target of maximum power extraction, the ideal internal resistance at the MPP has to be less than the load resistance of the boost converter \((R_{L}\leq R_{MPP})\)[34], since the domain of the duty ratio \((D_{MPP})\) is between 0 and 1. For determining the range of \(R_{MPP}\), we can simulate the array under rapidly varying solar illumination; two diverse levels of irradiance were chosen, among which the higher was at G = 1000 W/m\({}^{2}\) and the lower was at G = 200 W/m\({}^{2}\)[35]. Figure 11 in Appendix A illustrates the characteristic alteration of the curves of P-V, I-V, and ideal internal resistance for the PV array under three illumination intensities. The MPP declined from 640.6 W to 70.4 W when the radiation level was reduced from 1000 W/m\({}^{2}\) to 200 W/m\({}^{2}\). Accordingly, the \(R_{MPP}\) rose from 7.74 \(\Omega\) to 35.5 \(\Omega\); thus, the load resistance value was selected as 50 \(\Omega\) for this work, to be greater than \(R_{MPP}\) in the case of lowermost illumination. The output voltage of the converter \(V_{O}\) is specified for a load resistance of 50 \(\Omega\), supposing a lossless converter \((P_{O}=Ppv)\). Therefore, \(V_{O}\) and the duty ratio \(D_{MPP}\) were determined as  
\[V_{O}=\sqrt{(P_{O}\times R_{L})}=178.96\ \mathrm{V} \tag{2}\]  
\[D_{MPP}=1-\frac{Vpv}{V_{O}}=\ 0.61 \tag{3}\]  
The output voltage \(V_{O}\) and current \(I_{O}\) of the converter at the MPP were determined as  
\[V_{O}=\frac{V_{MPP}}{1-D_{MPP}} \tag{4}\]  
\[I_{O}=\frac{P_{MPP}}{V_{O}} \tag{5}\]  
**Selection of the inductor:** The value of the boost inductor is chosen depending on the maximum amount of acceptable current ripple at the MPP in the case of uppermost solar radiation (1000 W/m\({}^{2}\)) [34]. When the inductor value is high, the output current ripple will be low, and the opposite is also true, as shown in Equation (6). The switching frequency \(f_{s}\) was fixed at 10 kHz in this work, in order to reduce the oscillations at the MPP, and the value of the inductor was considered for input current ripple \(\Delta lpv\) of 1% [35]. Therefore, the minimum value of the inductor was designed as follows [34; 35; 36]:  
\[L_{\mathrm{min}}=\frac{Vpv\times D_{MPP}}{2\times\Delta lpv\times f_{s}} \tag{6}\]  
\[L_{\mathrm{min}}=0.59\ \mathrm{mH}.\]  
In this work, we chose \(L\) to be 1.6 mH to ensure minimal current ripple at the output of the boost converter, which is very important for this application.