Problem: A solar thermal plant with energy storage capability is to be constructed at about a 40° latitude to provide the electric energy to a power system whose 24-hr average load is 100 MWe during the winter. Assume that the solar thermal power plant will have a 25% energy conversion efficiency; that the nighttime load is 40% of the total daily load; and that 10% of the energy that must be stored is lost. Calculate the total land area (in km2) required for each of the following two solar thermal plant options: (a) fixed horizontal system, and (b) parabolic reflector system. The reflected energy collected at 40° latitude in winter is 6 kWꞏhr/(m2ꞏday) for a tracking system, and only 1.85 kW.hr/(m2.day) for a horizontal fixed system. It is believed that the parabolic reflector system can be set up so that the reflectors cover 45% of the land area on which they are placed without shading one another.

Daytime load = (100 MWe) (0.60) (24 hrs/day) = 1440 MW.hr/day

Nighttime load = (100 MWe) (0.40) (24 hrs/day) = 960 MW.hr/day

Total energy needed to fulfill the nighttime load, including stored energy loss

= (960 MW.hr/day) / (0.9) = 1067 MW.hr/day

Total daily electric energy needs = Daytime load + Nighttime load = 1440 + 1067 = 2507 MW.hr/day

Required thermal load = (2507 MW.hr/day) / (0.25) = 10,028 MW.hr/day

(a) For a fixed horizontal system: Energy collected = 1.85 kW.hr/(m².day)

Area= 10,028*10³ kW.hr/day/(1.85 kW.hr/m².day) = (54*10&sup6 m²)(1 km/1000)²

=5.4km²

(b) For a tracking system using reflectors: Energy collected = 6 kW.hr/(m².day)

Area= 10,028*10³ kW.hr/day/(6 kW.hr/m².day)(0.45) = (3.7*10&sup6 m²)(1 km/1000)²

=3.7km²

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