## 2 System Description
### Dimensioning of the Boost Converter  
The boost converter is a DC-DC converter, that increases the input voltage value, in order to generate an output voltage higher than the input. It is one of the most used converters in the solar industry [26]. In a solar PV system, it is either used individually, or coupled with a DC-AC converter, as seen in the three phase inverter used as reference for this study, which contains at least two boost converters in parallel, or the hybrid inverter as can be seen in Figure 4.  
The only difference between a hybrid and a three phase inverter, is that a three phase inverter can't be connected to a battery so it doesn't have the additional buck-boost converter. In these inverters, the boost converter purpose is to increase the output voltage to a desired value which is afterwards converted from Direct Current (DC) to Alternate Current (AC), to the voltage value of the electric grid. The schematic of the boost converter element of the inverter, of the PV system in analysis is presented in Figure 5.  
In the boost converters, the output voltage and input voltage, depends on the duty cycle (\(D\)) value, as can be seen in Equation (1). \[V_{out}=\frac{V_{in}}{(1-D)} \tag{1}\]  
In this converter when the switch (S) is closed, the converter is in its on state, the current stored in the coil is increased while the energy stored in the capacitor is sent to the load, as can be seen in Figure 6.  
Figure 4: Block diagram of a solar PV system with a hybrid inverter. Figure 5: Typical boost converter schematic. When the switch is open the converter is in its off state, the current stored in the coil in the previous state feeds both the condenser and the load, as can be seen in Figure 7.  
In this state, the output voltage (the voltage at the load) is bigger than the input voltage, which is given by the sum of the solar panels voltage in this system and the voltage drop in the coil. This happens because the coil inverts the polarity of its terminals in order to avoid the increase in current, since the output voltage is bigger than the input voltage this converter is named boost converter. For this particular PV system the components such as diodes, capacitors, coils and the switch which is an IGBT (Insulated Gate Bipolar Transistor) have to at least support a maximum voltage of 1000 V and a maximum current of 11 A [25]. The capacity of the input and output capacitors and the coil inductance, were calculated using Equations (2)-(4), respectively [27]. \[C_{in}=\frac{I_{out}\cdot r}{8\cdot r\cdot f\cdot\Delta V\cdot(1-D)} \tag{2}\]  
\[C_{out}=\frac{I_{out}\cdot(1-D)}{f\cdot\Delta V} \tag{3}\]  
\[L=\frac{V_{out}\cdot D\cdot(1-D)^{2}}{I_{out}\cdot r\cdot f} \tag{4}\]  
The capacitors will be dimensioned for a ripple voltage (\(\Delta V\)) of 5 V. The input voltage will be 160 V and the output voltage will be 800 V (although the inverter nominal voltage is 600 V [25]), which are the minimum and maximum possible values in the converter, this last value was obtained for a duty cycle of 0.80, this being the maximum recommended value for a boost converter as is explained in chart 1 of the Appendix of Switching Power Supplies A-Z [27]. The chosen diode are two schottky diodes VS-15 EVL06-M3 of Vishay in series, together they support a voltage higher than 1000 V and have a total voltage drop (\(V_{\mathrm{D}}\)) of 1.96 V [28]. The IGBT selected is IGW6T120 of Infineon, which has a voltage drop of 1.90 V [29]. These components were selected, for a switching frequency (\(f\)) of 20 kHz. Figure 5.0 Schematics of a boost converter with the switch closed (on state). Figure 5.1 Schematics of a boost converter with the switch open (off state). The output current is 3.94 A and was determined by the division between the nominal power of one boost converter (1575 W) [25] and the nominal output voltage considered for the inverter. The coefficient \(r\) is the ratio of the current ripple given by the division between the current variation and the medium value of the inductor current.