# Design and Analysis of a Hybrid MPPT Method for PV Systems Under Partial Shading Conditions
## 2 Materials and Methods
### Design of DC-DC Boost Converter  
A DC-DC boost converter has been used in the PV system created for simple, fast, and reliable power transfer and voltage increase. The DC-DC boost converter has a structure consisting of five parts. These are the inductor, capacitor, diode, switching element, and output resistor. Generally, IGBTs (Insulated-Gate Bipolar Transistors) are used for switching. In this part of the system, the PV array is connected to the DC-DC boost converter through a parallel connected capacitor in the middle. This capacitor is used to correct the input voltage imbalance and reduce voltage fluctuations. The input capacitor value of 1 mF was selected. The characteristics of PV array used in the design are given in Table 2.  
In this simulation, IGBT is used for switching for the DC-DC boost converter. In this designed system, a PV Array output voltage of 346.71 V was selected. This value is the input voltage of the DC-DC boost converter. The DC voltage is increased by this DC-DC boost converter and 540 V DC voltage is obtained at the output. A switching frequency of \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Maximum Output Power at STC & 11.76 kW (P\({}_{\text{max}}\)) \\ Number of Panels (Series) & 7 \\ Number of Strings (Parallel) & 4 \\ Total Number of Panels & 28 \\ Total Output Voltage & 346.71 V (V\({}_{\text{mpp}}\)) \\ Total Output Current & 33.92 A (\({}_{\text{mpp}}\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Information about the PV array used in the designed system. Figure 1: Designed PV system. 20 kHz was selected. The parameters used in designing the DC-DC boost converter are shown in the equations below [57; 58]. The output current of the converter is shown below in Equation (1). \[I_{out}=\frac{P_{out}}{V_{out}}=\frac{11,\!760.40\ \mathrm{W}}{540\ \mathrm{V}}=21.78\ \mathrm{A} \tag{1}\]  
The load resistor value of the converter is shown below in Equation (2). \[R_{L}=\frac{V_{out}}{I_{out}}=\frac{540\ \mathrm{V}}{21.7785\ \mathrm{A}}=24.79\ \Omega \tag{2}\]  
The duty cycle of the converter is shown below in Equation (3). \[D=\left(1-\frac{V_{in}}{V_{out}}\right)=\left(1-\frac{346.71\ \mathrm{V}}{540\ \mathrm{V}} \right)=0.3579=35.79\% \tag{3}\]  
The voltage ripple of the converter is shown below in Equation (4). \[\Delta V_{\mathrm{out}}=0.01\times 540\ \mathrm{V}=5.4\ \mathrm{V} \tag{4}\]  
The current ripple of the converter is shown below in Equation (5). \[\Delta I_{\mathrm{out}}=0.1\times 21.78\ \mathrm{A}=2.18\ \mathrm{A} \tag{5}\]  
The capacitor value of the converter is shown below in Equation (6). \[C=\frac{I_{out}\times\left(1-\frac{V_{in}}{V_{out}}\right)}{f_{sw}\times \Delta V_{out}}=\frac{21.78\ \mathrm{A}\times\left(1-\frac{346.71\ \mathrm{V}}{540\ \mathrm{V}}\right)}{20\ \mathrm{kHz}\times 5.4\ \mathrm{V}}=72.18\ \mathrm{\mu F} \tag{6}\]  
The inductor current ripple of the converter is shown below in Equation (7). \[\Delta I_{L}=0.01\times I_{out}\times\frac{V_{out}}{V_{in}}=0.01\times 21.78 \ \mathrm{A}\times\frac{540\ \mathrm{V}}{346.71\ \mathrm{V}}=0.34\ \mathrm{A} \tag{7}\]  
The inductor value of the converter is shown below in Equation (8). \[L=\frac{V_{in}\times\left(V_{out}-V_{in}\right)}{f_{sw}\times\Delta I_{L} \times V_{out}}=\frac{346.71\ \mathrm{V}\times\left(540\ \mathrm{V}-346.71\ \mathrm{V}\right)}{20\ \mathrm{kHz}\times 0.34\ \mathrm{A}\times 540\ \mathrm{V}}=0.018\ \mathrm{H} \tag{8}\]  
The values obtained from the calculations of the DC-DC boost converter are shown in Figure 1:0  
The DC-DC boost converter in the designed circuit is shown in Figure 1:1 The switching element of the DC-DC boost converter control circuit receives the reference voltage coming