Yellow = sun · Blue = panel face · White = sunlight direction
Electrical output
0 W
POA irradiance
0 W/m²
Incident angle
0°
Alignment
–
Direct on panel
0 W/m²
Diffuse
0 W/m²
Reflected
0 W/m²
Daily energy (5 h)
0 kWh
Physics, formulas & assumptions
1 · Direction vectors
Sun unit vector (α = elevation, φs = sun azimuth):
ŝ = ( cos α · sin φs , sin α , cos α · cos φs )
Panel surface normal (β = tilt, φp = panel azimuth):
n̂ = ( sin β · sin φp , cos β , sin β · cos φp )
2 · Incidence angle θ
cos θ = ŝ · n̂
θ = arccos( ŝ · n̂ )
θ = 0° → sun shines straight at the panel face (maximum capture). θ = 90° → sun grazes the edge (no direct capture).
3 · Plane-of-array (POA) irradiance
Ebeam = max(0, DNI · cos θ)
Ediff = DHI · (1 + cos β) / 2 isotropic sky
GHI = DNI · sin α + DHI
Erefl = GHI · ρ · (1 − cos β) / 2 ρ = 0.20
POA = Ebeam + Ediff + Erefl
4 · Electrical output
P = POA × A × η × PR (W)
Eday = P × 5 h ÷ 1000 (kWh/day)
A = panel area (m²) · η = module efficiency (fraction) · PR = performance ratio · 5 peak sun-hours assumed for a near-equatorial site.
Simplifications assumed
- Sun rays treated as perfectly parallel (infinite-distance point source).
- No shading, soiling, or spectral correction applied.
- Module temperature and low-irradiance de-rating ignored.
- Isotropic sky model — no circumsolar ring or horizon brightening.
- Ground albedo fixed at 0.20 (typical grass/light soil).
- Performance ratio (PR) lumps wiring loss, inverter efficiency, and mismatch.