Question $3[28$ points$]$

A district cooling facility has the following load profile.

The utility company charges SR $0\mathrm{.}50/$kWh from $12$:$00$ to $18$:$00,$ and SR $0\mathrm{.}1/$kWh for all other times. The facility uses air$-$cooled chillers whose consumption varies with weather conditions as follows:

$1\mathrm{.}2k\frac{W}{?}$ ton from midnight until before $8$:$00$

$1\mathrm{.}4k\frac{W}{?}$ ton from $8$:$00$ until before $12$:$00$

$1\mathrm{.}6$ kW$/$ton from $12$:$00$ until before $18$:$00$

$1\mathrm{.}2k\frac{W}{?}$ ton from $18$:$00$ to midnight

The operation and maintenance cost of the plant is SR $2,000,000$ per year.

The facility owner would like to reduce electricity consumption, so the following options are considered:

Option A: Use a load shifting strategy between $12$:$00$ and $18$:$00$ to avoid paying the high tariff. The existing air$-$cooled chillers will continue to be used.

Option B: Similar to Option A$,$ but the air$-$cooled chillers are replaced with water$-$cooled chillers that consume $0\mathrm{.}8k\frac{W}{?}$ ton $($constant$,$ throughout the $24$ hours$).$

Option C: Continue operation without any changes

Option A requires a capital cost of SR $15,000,000$ for the thermal energy storage tank, and the operation and maintenance cost will become SR $2,500,000$ per year

Option B requires a capital cost of $SR45,000,000$ for the water$-$cooled chillers and thermal energy storage tank, and the operation and maintenance cost will become $SR4,000,000$ per year ${?}_{(})$

Assume that the planning period is $25$ years and the discount rate is $8\%.$

a$.$ Calculate the annual cost, in Saudi Riyals, for the original case $($Option C$).$ Include both electricity and operation and maintenance cost. $[4$ points$]$

b$.$ At what capacity $($in tons$)$ will the chillers operate when the load shifting strategy is implemented? $[3$ points$]$

c$.$ Calculate the annual savings $($in Saudi Riyals$)$ after implementing Option A$.[5$ points$]$

d$.$ Calculate the annual savings $($in Saudi Riyals$)$ after implementing Option B$.[5$ points$]$

e$.$ Draw the cash flow diagrams for Option A and Option B$.[4$ points$]$

f$.$ Calculate the net present value for Option A and Option B$.[4$ points$]$

g$.$ Which of the three options would you recommend? Justify your answer. $[3$ points$]$