Q$1.$ PVWatts Version $6$ is the current version of the PVWatts API. The algorithms used to calculate energy output are the same as in Version $5.$ The manual for version $5$ has been included with this assignment. Use PVWatts to calculate the AC annual energy yield and electricity value in Ottawa, ON$.$ Use the NREL International solar resource data. Assume a $4$ kW DC system size, with south$-$facing premium fixed $($roof mount$)$ modules at an array tilt of $\backslash (45^\{\backslash$circ$\}\backslash ).$ Assume default system losses of $\backslash (14\mathrm{.}08\backslash \%\backslash )$ and an inverter efficiency of $\backslash (96\backslash \%\backslash ).$ Assume a flat residential rate of $\backslash (\backslash$$ $0\mathrm{.}20/\backslash$mathrm$\{$kWh$\}\backslash )($you will not directly use this data, but it is helpful for context$).$ Address the following questions.

$($a$)$ Calculate the AC annual energy yield and electricity value in Ottawa for a range of DC$-$to$-$AC ratios from $1$ to $2($suggested values: $1\mathrm{.}0,1\mathrm{.}2,1\mathrm{.}3,1\mathrm{.}4,1\mathrm{.}5$ and $2\mathrm{.}0).$ Download the hourly results also. Plot on a single figure the monthly AC energy over the year for all DC$-$to$-$AC ratios. What does this comparison suggest? Now show the impact of clipping on the hourly production by plotting the hourly AC system output as a function of time across the year $($i$.$e$.,$ in hours from $1$ to $8760).$

$($b$)$ Assume inverter costs are $\backslash (\backslash$$ $0\mathrm{.}2/\backslash$mathrm$\{$W$\}\backslash )$ and module costs are $\backslash (\backslash$$ $0\mathrm{.}35/\backslash$mathrm$\{$W$\}\backslash ).$ If the inverter cost savings for each DC$-$to$-$AC ratio case are translated into additional panels, with all else being equal, estimate the fiscally optimal DC$-$to$-$AC ratio for Ottawa. NB$.$ This is where you will use the hourly data. HINT: since the rate is flat, you can optimize for total annual energy. You MUST take clipping into consideration.

$($c$)$ Given the circumstances of part $($d$),$ what is the relative change $($i$.$e$.,$ percent difference$)$ in the annual energy yield? Plot the relative change in the monthly energy yield. Explain the origin of any variation in this change.