Question $1$: A Photovoltaic $($PV$)$ generation system is enabled by two different converters:: the boost converter displayed in Fig. $1$a and the bidirectional $($half bridge$)$ converter shown in FIg. $1$b$.$ Both options share the following requirements:

$-$ Their output is always regulated to an average value of $\backslash ($ V$\_\{$o$\}=400\backslash$mathrm$\{$~V$\}\backslash ).$

$-$ The input source is composed by the series connection of four PV modules with the I$-$V cureves presented in Fig. $1$c$.$

$-$ The input inductance is $\backslash ($ L$=500\backslash$mu $\backslash$mathrm$\{$H$\}\backslash )$ and the output capacitor is $\backslash ($ C$\_\{$o$\}=6\mathrm{.}4\backslash$mu $\backslash$mathrm$\{$~F$\}\backslash ).$

$-$ A switching frequency of $20$ kHz is employed.

Then, consider the following scenarios: during a sunny day, the PV panels receive rated irradiance, hence each panel will be operating at $\backslash ($ v$\_\{\backslash$mathrm$\{$PV$\}\}=$V$\_\{\backslash$mathrm$\{$MPP$\}\_\{1\}\}=36\mathrm{.}2\backslash$mathrm$\{$~V$\}\backslash )$ while the converters supply the output with an average current of $4$ A $.$ The same system during cloudy days, will reduce the generated power and each module operates at $\backslash ($ v$\_\{\backslash$mathrm$\{$pv$\}\}=$V$\_\{\backslash$mathrm$\{$MPP$\}\_\{2\}\}=30\backslash$mathrm$\{$~V$\}\backslash )$ while the load is supplied with $0\mathrm{.}8$ A in average.

PV array

PV array

Figure $1$: Photovoltaic Energy Generation System. $($a$)$ Using a boost converter. $($b$)$ Using a half$-$bridge converter. $($c$)$ PV modules I$-$V curves.

Answer the following questions for both converters in each of the scenarios.

a$.$ Determine the required duty cycle for $\backslash ($ T$\_\{1\}\backslash )$ to keep the output voltage controlled. Justify your response based on the operation mode of the converter.

b$.$ Calculate the average, peak and ripple values for the inductor current.

c$.$ Sketch $($showing the maximum and minimum values$)$ the currents through the inductor, diode $($or transistor $\backslash ($ T$\_\{2\}\backslash ))$ and capacitor.

d$.$ Determine the output voltage ripple.

I have attached a screenshot of the whole question. Please note there are two converters in each scenario. Please keep a relatively nice handwriting! Appreciated. Will give a thumbup for satisfying answers.