PV$-$On Grid: The figure below shows a Grid connected PV system in Beirut where the peak sun hour ht $=5($h$/$day$)$ under STC criteria.

The solar fraction of PV system is $50\%$ and the capacity factor of the system equal $1.$

The array is consisted of a number of PV module with capacity $500$ Wp that has the following electrical data:

$Vmp=45Vdc($voltage at maximum power point$)$

Imp$=11A($Current at maximum power point$)$

Voc $=50Vdc($Voltage of short circuit$)$

The global losses of array is $0\mathrm{.}75$ including:

array loss due to mismatch.

dirt loss

Differences in ambient condition

copper losses between PV modules and converter

The Grid connected Inverter has the following$-$parameters:

European or average efficiency of $80\%.$

Input DC voltage range: $300$ V $-700$ V $($preferable input voltage $500$ V $)$

Maximum input DC current $90$A

One MPPT

Rated capacity is selected as $45$ KW

The sizing of the system is based on the year $2023.$ The utility grid was available $\frac{24}{24}($take $1$ year$=365$ days$)$ The annual energy consumption read from meter was $W_{\text{c}\text{o}\text{n}\text{s}}=87600KWh.$

Calculate the followings:

Based on solar fraction factor, the reading of solar energy $W_{pv}$ is $$ KWh

The energy is Sold or Bought from utility grid $q,,$ how much KWh

The average ac output power of converter $P_{oc-\text{o}\text{u}\text{t}}q,$ KW

The average dc input power of converter $P_{dc-in}$ KW

The average efficiency of the system $($converter $+$ array$){}_{av}$ is $($one digit after decimal point$)$

The capacity of the PV system $P_{dc-pv}$ is $$ KWp

The number of PV modules $N_t$ is $$

The number of panels in series per string $Ns$ is $$

The number of strings in parallel $Np$ is $$

Assume now that utility has a daily outage equivalent to $2$ peak sun hour, what is the annual lost energy of solar system $W_{\text{l}\text{a}\text{s}\text{t}}$ is $$ kWh$.$

Urgent please