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 = 10 W/m²
the annual average solar irradiance = 150 W/m²
the PV efficiency η = 10% = 0.1
battery charging/discharging efficiency η = 80% = 0.8
we know that; Annual average power to the light = × A
Now, the electrical power delivered by the solar cell battery system will be;
⇒ × A
× η
× η
A
=
× A
× η
× η
Such that;
A =
A
/
× A
× η
× η
A / A
=
/
× η
× η
so we substitute
A / A
= 10 W/m² / [ 150 W/m² × 0.1 × 0.8 ]
A / A
= 10 W/m² / 12 W/m²
A / A
= 0.8333
A / A
= (0.8333 × 100)%
A / A
= 83.33%
Therefore, 83.33% of the roof area will be occupied by the PV cells.