SAPM spectral › Published

Method

The spectral modifier is the air-mass function of King's Sandia array performance model: a fourth-degree polynomial in the absolute air mass with the module's own coefficients (1, 2). The coefficients come from the module's entry in Sandia's module database. A module without them takes the crystalline-silicon set of De Soto, Klein and Beckman, with a notice. The air mass follows Kasten and Young with no limit on the zenith angle. A timestep with the sun at or below the horizon keeps its light uncorrected, as the air mass has no value there. The modifier scales the effective irradiance before the cell temperature.

The math

1. Absolute air mass
2. Spectral modifier

$$\text{AM}_a = \frac{e^{-0.0001184\,z}}{\cos\theta_z + 0.5057\,(96.080 - \theta_z)^{-1.634}} \tag{1}$$ $$M = \max\!\left(0,\ \sum_{k=0}^{4} a_k\,\text{AM}_a^{\,k}\right) \tag{2}$$

where

Symbol	Meaning	Unit
$\text{AM}_a$	the absolute air mass: the relative air mass times the altitude factor	—
$z$	the site elevation	m
$\theta_z$	the zenith angle of the sun, 90° minus its elevation	degrees
$M$	the spectral modifier	—
$a_k$	the module's air-mass coefficients $a_0 \ldots a_4$	—

References

1. King, Boyson & Kratochvil 2004, Photovoltaic Array Performance Model, Sandia report SAND2004-3535

API

spectral.model = king_published, spectral.mode = on, module.sapm_am_coefficients

Symbols follow the symbol registry.