b A large singlestory building supplies all its lighting req

(b) A large single-story building supplies all its lighting requirements using batteries charged by photovoltaic cells placed horizontally on its horizontal roof. If the average lighting requirement for the building is 8 W/m2, the photovoltaic efficiency is 10%, the battery charging-discharging efficiency is 80%, what percentage of the roof area needs to be occupied by photovoltaic cells. Assume the global average solar irradiance

Solution

Let A_roof= The area of the roof which is the same as the area of the ceiling.

The annual lighting energy required is

E_lighting=(8 W/m²)A_roof(8760 h/yr).

_l The annual lighting power produced by solar energy is

P_lighting(10%)(150 W/m²)A_PV(8760 h/yr),

where A_PV = the area of the photovoltaic solar collectors. The annual energy available, considering the 80% efficiency of battery charging and recharging is

E_annual=(80%)(10%)(150 W/m²)A_PV(8760 h/yr)

=>8A_roof(8760 h/yr)=0.80*0.1*150 *A_PV(8760 h/yr)

A_PV/A_roof = 8/(0.8*0.1*150)

A_PV/A_roof =0.6667 or 66.67 %