Question $3[20$ marks$]$:

A concentrated solar power plant operates with the following characteristics:

$-$ The solar field consists of parabolic trough collectors with a thermal efficiency of $\backslash (70\backslash \%\backslash ).$ The power block has a gross cficiency of $\backslash (45\backslash \%\backslash ).$

$-$ Direct normal irradiance $($DNI$)$ variation throughout $10$ days is shown in the table below.

$-$ The solar field area is $\backslash (300,000\backslash$mathrm$\{$~m$\}^\{2\}\backslash ).$

$-$ Electricity demand peaks after sunset and requires $5$ hours of contimous operation at full load.

$($a$)$ Propose a suitable storage capacity $($in hours$)$ for the plant to ensure $\backslash (90\backslash \%\backslash )$ reliability in meeting the demand. Justify your choice with calculations and explain how DNI variability influenced your design. $[3$ marks$]$

$($b$)$ Accounting for losses in the thermal storage and power block, calculate the percentage of stored thermal energy used and any shortfall or surplus of storage capacity for this demand. Assume $10$ hours of effective DNI that you have previously set as an average. $[3$ marks$]$

$($c$)$ Assume a day with $\backslash (20\backslash \%\backslash )$ lower DNI than the average. Calculate the amount of stored energy needed to meet the same $5-$hour evening demand and the impact of this reduced DNI on the plant's operational strategy and electricity generation. $[3$ marks$]$

$($d$)$ Discuss how seasonal DNI variations might influence the plant's storage requirements and suggest operational or design modifications to improve year$-$round performance. $[3$ marks$]$