Solar Equations

Q: What is the solar constant E0 and its typical value?

A: Solar constant ≈ 1360–1367 W/m² at 1 AU, measured perpendicular to rays, outside atmosphere

Q: Why is irradiance on Earth lower than in space?

A: Due to atmospheric reflection, absorption (O₃, H₂O, O₂, CO₂), Rayleigh scattering (small particles), and Mie scattering (large particles).

Q: Define air mass ratio (AM) and give its formula.

A: Relative optical path length through atmosphere; m=1/cosψ, where ψ is solar zenith angle.

Q: What is AM 1.5 and why is it important?

A: Standard spectrum for PV testing; represents sunlight at 1.5× vertical path length, typical of mid-latitudes.

Q: What is the declination angle (θ_d)?

A: Angle between Sun’s rays and Earth’s equatorial plane; ranges from –23.5° to +23.5° annually.

Q: Formula for irradiance normal to a tilted plane (α)?

A: E_n = Ecos⁡θ_dsin⁡(θ+α)sin⁡ϕ + Esin⁡θ_dcos⁡(θ+α)

Q: State the Hottel equation for direct beam irradiance at surface.

A: E=E0(b0+b1e−km)E=E0​(b0​+b1​e−km), where m = air mass ratio and b0,b1,kb0​,b1​,k depend on visibility.

Q: Condition for optimal fixed panel tilt at noon on a given day?

A: θ+α+θ_d = 90∘ ; where θ is the solar zenith angle and α is the panel tilt angle.

Q: Formula for minimum row spacing to avoid shading at noon?

A: D_min= Lcos⁡α+(Lsin⁡α)cot⁡β, with β=θ−23.5∘ (NH).

Q: What happens when photon energy < semiconductor band gap?

A: No electron–hole pairs; photon passes through or is reflected.

Q: How does doping change silicon for PV?

A: n-type (Group V) adds electrons; p-type (Group III) creates holes; p–n junction forms depletion region. Doping introduces charge carriers in silicon.

Q: Name the four key PV I–V curve parameters.

: Effect of increasing irradiance on I–V curve?

A: I_sc increases; MPP shifts upward; V_oc increases slightly.

Q: Formula for PV module efficiency.

Q: How to split energy in a PV-T system?

Q: Formula for power through a vertical window.

A: P= τAE_n , with α = 90∘

Q: Why can tracking underperform fixed on overcast days?

A: Diffuse radiation is isotropic; tracking panels may be steep at morning/evening, capturing less diffuse light.