Lee and Panchula

Method

At every timestep the spectral modifier $M$ is computed from the air mass and the precipitable water with the formula of Lee and Panchula, and the module power is evaluated at the corrected irradiance $M\,G$. While the sun is below the horizon or no light reaches the modules, $M$ is 1. The coefficients were derived from the quantum-efficiency curve of each cell technology and spectra simulated with the SMARTS radiative-transfer model. The six coefficients are the published set of the module's cell technology; coefficients entered on the Physics tab replace them, and a module without a cell technology needs them. The precipitable water is the weather file's column. When the file has only relative humidity, the precipitable water is estimated from the humidity and the ambient temperature with the Gueymard 1994 formula. The sub-choice "Where the correction acts" sets the air-mass formula and whether the cell temperature is computed from the corrected irradiance. The automatic spectral mode runs this option for cadmium telluride modules only.

Settings

Setting	Value
Coefficients $c_0 \ldots c_5$, cadmium telluride	0.86273, −0.038948, −0.012506, 0.098871, 0.084658, −0.0042948
Coefficients $c_0 \ldots c_5$, monocrystalline silicon	0.85914, −0.02088, −0.0058853, 0.12029, 0.026814, −0.001781
Coefficients $c_0 \ldots c_5$, multicrystalline silicon	0.8409, −0.027539, −0.0079224, 0.1357, 0.038024, −0.0021218
Coefficients $c_0 \ldots c_5$, copper indium gallium selenide	0.85252, −0.022314, −0.0047216, 0.13666, 0.013342, −0.0008945
Coefficients $c_0 \ldots c_5$, amorphous silicon	1.12094, −0.04762, −0.0083627, −0.10443, 0.098382, −0.0033818
Air-mass floor	0.58
Precipitable water $P_w$	held between 0.1 and 8 cm

The math

1. Air mass
2. Spectral modifier
3. Module power
4. Spectral row

$$\text{AM} = \min\!\left(\max\!\left(f_{AM}\,\text{AM}_r,\ 0.58\right),\ \text{AM}_{max}\right) \tag{1}$$ $$M = c_0 + c_1\,\text{AM} + c_2\,P_w + c_3\sqrt{\text{AM}} + c_4\sqrt{P_w} + c_5\,\frac{\text{AM}}{\sqrt{P_w}} \tag{2}$$ $$P_{arr} = N\,P_{mpp}(M\,G,\ T),\qquad T = T_{cell}(M_T\,G_{th}) \tag{3}$$ $$\Delta P_{sp} = N\left[P_{lin}(G) - P_{lin}(M\,G)\right] \tag{4}$$

where

Symbol	Meaning	Unit
$\text{AM}$	the air mass: the path length of the sunlight through the atmosphere relative to a vertical path at sea level	—
$f_{AM}$	the altitude factor of the air mass, set by where the correction acts	—
$\text{AM}_r$	the relative air mass, from the formula set by where the correction acts	—
$\text{AM}_{max}$	the air-mass cap, set by where the correction acts or by the air-mass cap on the Physics tab	—
$M$	the spectral modifier of the timestep, a factor near 1	—
$c_0 \ldots c_5$	the six coefficients of the module's cell technology	—
$P_w$	the precipitable water, held between 0.1 and 8 cm	cm
$P_{arr}$	the array power at its maximum-power point, before the electrical shading and the flat derates	W
$N$	the number of modules	—
$P_{mpp}(g, T)$	the maximum power of one module at irradiance $g$ and cell temperature $T$	W
$G$	the effective irradiance on the modules before the correction, with the rear side's share on a bifacial array	W/m²
$T$	the cell temperature	°C
$T_{cell}(\cdot)$	the cell-temperature model of the Cell temperature step, as a function of the front irradiance	°C
$G_{th}$	the front irradiance the cell temperature is computed from, before the correction	W/m²
$M_T$	the factor on the irradiance of the cell temperature, 1 or $M$, set by where the correction acts	—
$\Delta P_{sp}$	the power the spectral correction removes at the timestep, the spectral row of the loss diagram; negative when $M$ exceeds 1	W
$P_{lin}(g)$	the module power the spectral row is measured on, at irradiance $g$, set by where the correction acts	W

References

1. Lee & Panchula 2016, Spectral correction for photovoltaic module performance based on air mass and precipitable water, IEEE 43rd Photovoltaic Specialists Conference
2. Gueymard 1994, Analysis of monthly average atmospheric precipitable water and turbidity in Canada and northern United States, Solar Energy 53(1) 57–71

API

spectral.mode = on, spectral.model = lee_panchula

Symbols follow the symbol registry.