Consider a c$-$Si PV module formed by $36$ solar cells. The module has two string of cells connected in parallel and the following specifications:

$-\backslash ($ V$\_\{\backslash$text $\{$oc $\}\}=12\mathrm{.}6[\backslash$mathrm$\{$~V$\}]\backslash )$

$-\backslash ($ I$\_\{\backslash$mathrm$\{$sc$\}\}=15\mathrm{.}4[\backslash$mathrm$\{$~A$\}]\backslash )$

$-\backslash ($ P$\_\{\backslash$mathrm$\{$mpp$\}\}=150[\backslash$mathrm$\{$~W$\}]\backslash )$

Consider an obstacle shading the module as shown in the figure below; the shaded area of each cell is equal to the $\backslash (70\backslash \%\backslash )$ of the total cell's area.

Assume that the effect of partial shading on the cell's voltage can be considered negligible and that the current of the module decreases linearly with the shading level.

A$)$ Calculate the maximum power output of the module under this condition. Give the answer in $[$W$]$ and with one decimal place.

Consider now a similar module in the same shading conditions but with $4$ by$-$pass diodes installed $(1$ across every $9$ cells$).$ Assume $($additionally to the previous assumptions$)$ that:

$-$ Bypass diodes are ideal, i$.$e$.,$ the forward voltage drop is zero.

$-$ The unshaded string $(18$ cells$)$ at STC generates $\backslash ($ P$\_\{$X$\}=75[\backslash$mathrm$\{$~W$\}]\backslash )$ and its voltage is $\backslash ($ V$\_\{$X$\}\backslash ).$

$-$ If the unshaded string $(18$ cells$)$ is operated at a voltage level $\backslash (\backslash$frac$\{$V$\_\{$X$\}\}\{2\}\backslash ),$ then it generates $60[$W$].$

B$)$ Calculate the maximum power output in this case. Give the answer in $\backslash ([\backslash$mathrm$\{$W$\}]\backslash )$ and with one decimal place.