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Alex
3 years ago
6

A single-story retail store wishes to supply all its lighting requirement with batteries charged by photovoltaic cells. The PV c

ells will be mounted on the horizontal rooftop. The time-averaged lighting requirement is 10 W/m2 , the annual average solar irradiance is 150 W/m2 , the PV efficiency is 10%, and the battery charging/discharging efficiency is 80%. What percentage of the roof area will the PV cells occupy
Physics
1 answer:
Umnica [9.8K]3 years ago
7 0

Answer:

83.33% of the roof area will be occupied by the PV cells

Explanation:

Given the data in the question;

time-averaged lighting requirement P_{lighting = 10 W/m²

the annual average solar irradiance q_{solar = 150 W/m²

the PV efficiency η_{pv = 10% = 0.1

battery charging/discharging efficiency η_{battery = 80% = 0.8

we know that; Annual average power to the light = P_{lighting × A_{roof

Now, the electrical power delivered by the solar cell battery system will be;

⇒  q_{solar × A_{pv × η_{pv × η_{battery

P_{lightingA_{roof = q_{solar × A_{pv × η_{pv × η_{battery

Such that;

A_{pv = P_{lightingA_{roof / q_{solar × A_{pv × η_{pv × η_{battery

A_{pv / A_{roof = P_{lighting /  q_{solar × η_{pv × η_{battery

so we substitute

A_{pv / A_{roof = 10 W/m² / [ 150 W/m² × 0.1 × 0.8 ]

A_{pv / A_{roof = 10 W/m² / 12 W/m²

A_{pv / A_{roof = 0.8333

A_{pv / A_{roof = (0.8333 × 100)%

A_{pv / A_{roof = 83.33%

Therefore, 83.33% of the roof area will be occupied by the PV cells.

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