pvperfsolar performance modeling

Reference / Incidence-angle modifier, beam

Model option

Fresnel, direct

The Fresnel equations for coated or plain glass

Inputs used: ASHRAE b₀, AR-coated glass, module.iam_angles_deg, iam.angles_deg

Method

The accepted fraction comes from the Fresnel equations evaluated at every incidence angle, with no table. With the anti-reflective coating on (the Glass switch of the Module tab), the light crosses two surfaces, air to coating and coating to glass, and the light reflected back and forth inside the coating is added without interference (4). With the coating off, it crosses a single air-glass surface (3). The two polarisations are averaged, and the glass absorbs nothing. The curve is normalised to its value at perpendicular incidence (5).

Settings

Setting Value
Refractive index of the glass 1.526
Refractive index of the coating 1.29, with the coating on
Absorption in the glass none

The math

  1. Refraction at a surface
  2. Reflectances of a surface
  3. Plain glass
  4. Glass with the coating
  5. Accepted fraction
sin⁡θ2=n1n2sin⁡θ1(1)\sin\theta_2 = \frac{n_1}{n_2}\sin\theta_1 \tag{1} rs=(n1cos⁡θ1−n2cos⁡θ2n1cos⁡θ1+n2cos⁡θ2)2,rp=(n1cos⁡θ2−n2cos⁡θ1n1cos⁡θ2+n2cos⁡θ1)2(2)r_s = \left(\frac{n_1\cos\theta_1 - n_2\cos\theta_2}{n_1\cos\theta_1 + n_2\cos\theta_2}\right)^2,\qquad r_p = \left(\frac{n_1\cos\theta_2 - n_2\cos\theta_1}{n_1\cos\theta_2 + n_2\cos\theta_1}\right)^2 \tag{2} τ(θ)=1−12(rs+rp)(3)\tau(\theta) = 1 - \tfrac{1}{2}\left(r_s + r_p\right) \tag{3} τ(θ)=12∑x=s, p(1−R1,x)(1−R2,x)1−R1,x R2,x(4)\tau(\theta) = \frac{1}{2}\sum_{x = s,\,p} \frac{(1 - R_{1,x})(1 - R_{2,x})}{1 - R_{1,x}\,R_{2,x}} \tag{4} F(θ)=τ(θ)τ(0)(5)F(\theta) = \frac{\tau(\theta)}{\tau(0)} \tag{5}

where

Symbol Meaning Unit
θ1\theta_1 the angle of the light arriving at the surface degrees
θ2\theta_2 the angle of the light refracted through it degrees
n1,n2n_1, n_2 the refractive indices before and after the surface —
rs,rpr_s, r_p the reflectances of the two polarisations —
τ(θ)\tau(\theta) the transmittance of the cover at incidence angle θ\theta —
θ\theta the incidence angle: between the sun and the perpendicular to the module plane degrees
R1,x,R2,xR_{1,x}, R_{2,x} the reflectances of polarisation xx at the air-coating and at the coating-glass surface —
F(θ)F(\theta) the accepted fraction at incidence angle θ\theta —

References

  1. De Soto, Klein & Beckman 2006, Improvement and validation of a model for photovoltaic array performance, Solar Energy 80(1) 78–88

API

iam.kind = fresnel, iam.ar_coating = true|false

Symbols follow the symbol registry.