Spectral Correction

Summary

Spectral Correction accounts for —the difference between the module’s spectral response and the actual incident solar spectrum. PV modules are rated under a reference spectrum (AM1.5G), but the real spectrum varies with atmospheric conditions (e.g., , ). Different module technologies (e.g., crystalline silicon, CdTe) have different spectral responses, causing them to over- or under-perform relative to their rating depending on the incident spectrum. PlantPredict implements four spectral correction approaches: No Spectral Shift, Monthly Override, Single-Variable Models (technology-specific), and Two-Variable Model. The spectral correction factor $U_{spectr}$ is a multiplier applied to effective irradiance after corrections.

Inputs

Name	Symbol	Units	Description
Pressure-Corrected Air Mass	$AM'$	—	Air mass corrected for atmospheric pressure
Precipitable Water	$W$	cm	Column depth of precipitable water vapor
Relative Humidity	$RH$	%	Surface relative humidity
Ambient Air Temperature	$T_a$	°C	Ambient air temperature
Dewpoint Temperature	$T_d$	°C	Dewpoint temperature
Monthly Spectral Loss	$L_{spectr,month}$	%	User-specified spectral loss percentage for each month (Monthly Override model)
Sandia Polynomial Factors	$[a_0, ..., a_4]$	—	Polynomial coefficients for Sandia spectral model
Two-Variable Coefficients	$[b_0, ..., b_5]$	—	Coefficients for two-variable spectral model

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Outputs

Name	Symbol	Units	Description
Spectral Correction Factor	$U_{spectr}$	—	Multiplier applied to effective irradiance after IAM

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Detailed Description

Available Models

PlantPredict offers four Spectral Correction options:

1. No Spectral Shift: No spectral correction ($U_{spectr} = 1$)
2. Monthly Override: User-specified monthly values
3. Single-Variable Models: Technology-specific models using one atmospheric parameter:
   • Sandia: Uses air mass; for crystalline silicon modules
   • First Solar Series 4 & Earlier: Uses precipitable water; for First Solar Series ≤ 4 modules
   • First Solar Series 4-2 & Later: Uses precipitable water; for First Solar Series ≥ 4-2 modules
4. Two-Variable Model (Lee & Panchula): Uses both air mass and precipitable water with module-specific coefficients

No Spectral Shift

No spectral correction:

$$U_{spectr} = 1$$

Monthly Override

The user specifies a spectral loss percentage for each month. The percentage is converted to a correction factor:

$$U_{spectr} = 1 - \frac{L_{spectr,month}}{100}$$

where $L_{spectr,month}$ is the user-entered spectral loss (%) for the current month. A positive value represents a loss (e.g., 2% → $U_{spectr} = 0.98$); a negative value represents a spectral gain (e.g., −1% → $U_{spectr} = 1.01$).

Single-Variable Models

These models rely on atmospheric parameters, including precipitable water. If precipitable water cannot be determined (precipitable water, , and all missing from the weather file), all single-variable models default to $U_{spectr} = 1$—including the Sandia model.

Sandia Polynomial Model

Typically used for crystalline silicon (c-Si) modules, but applicable to any technology with user-defined polynomial coefficients:

$$U_{spectr} = a_0 + a_1 \cdot AM' + a_2 \cdot (AM')^2 + a_3 \cdot (AM')^3 + a_4 \cdot (AM')^4$$

where $[a_0, a_1, a_2, a_3, a_4]$ are user-defined Sandia polynomial factors and $AM'$ is the pressure-corrected air mass.

First Solar Models

Recommended for First Solar CdTe modules:

$$U_{spectr} = c_0 + c_1 \cdot e^{c_2 (W + c_3)^{c_4}}$$

where $W$ is the precipitable water (cm) and coefficients depend on module series:

Coefficient	Series 4 & Earlier	Series 4-2 & Later
$c_0$	0.6318	1.266
$c_1$	0.1341	−0.0913
$c_2$	0.9757	1.1987
$c_3$	0.05	0.5
$c_4$	0.0788	−0.21

Two-Variable Model

Six-parameter model from Lee and Panchula, accounting for pressure-corrected air mass $AM'$ and precipitable water $W$:

$$U_{spectr} = b_0 + b_1 AM' + b_2 W + b_3 \sqrt{AM'} + b_4 \sqrt{W} + b_5 \frac{AM'}{\sqrt{W}}$$

$b_0$ through $b_5$ are user-defined coefficients specific to the module technology.

To ensure numerical stability, precipitable water is clamped to a minimum of 0.1 cm and air mass is clamped to a maximum of 10. If precipitable water cannot be determined (precipitable water, relative humidity, and dewpoint all missing from the weather file), the model defaults to $U_{spectr} = 1$.

Precipitable Water Calculation

If precipitable water is not directly available in the weather file, it is calculated from relative humidity or dewpoint.

From Relative Humidity

Using the Gueymard (1994) model, which uses absolute temperature $T_K = T_a + 273.15$ (Kelvin) throughout.

First, the apparent water vapor scale height $H_v$ (km) is calculated. This represents the height of an equivalent column if all atmospheric water vapor were compressed to surface-level density.

$$H_v = 0.4976 + 1.5265 \frac{T_K}{273.15} + e^{13.6897 \frac{T_K}{273.15} - 14.9188 (\frac{T_K}{273.15})^3}$$

Next, the surface water vapor density $\rho_v$ (g/m³) is calculated from relative humidity $RH$ (%) and temperature:

$$\rho_v = \frac{216.7 \cdot RH}{100 \cdot T_K} \cdot e^{22.33 - \frac{4914}{T_K} - 10.922 (\frac{100}{T_K})^2 - 0.39015 \frac{T_K}{100}}$$

Finally, precipitable water $W$ (cm) is the product of scale height and vapor density, where the factor 0.1 converts from (km × g/m³) to cm of liquid water (with water density = 1000 kg/m³):

$$W = 0.1 \cdot H_v \cdot \rho_v$$

From Dewpoint

When only dewpoint temperature $T_d$ is available, relative humidity is calculated using the August-Roche-Magnus approximation for $e_s$ (hPa). The saturation vapor pressure is the maximum water vapor pressure that air can hold at a given temperature—at the dewpoint, the air is saturated ($RH = 100\%$).

The ratio of saturation vapor pressures at dewpoint and ambient temperature gives relative humidity:

$$RH = 100 \cdot \frac{e_s(T_d)}{e_s(T_a)}$$

where the saturation vapor pressure follows the August-Roche-Magnus equation:

$$e_s(T) = c_0 \cdot e^{\frac{c_1 \cdot T}{c_2 + T}}$$

with $T$ in °C and coefficients depending on PlantPredict version:

Software Version	$c_0$	$c_1$	$c_2$
≤ 10	6.11	17.1	234.2
≥ 11	6.1094	17.625	243.04

Version 11+ uses the improved coefficients from Alduchov and Eskridge (1996), which provide less than 0.4% error over the range -40°C to 50°C.

Then calculate $W$ from $RH$ using the Gueymard method above.

Application to Irradiance

Spectral correction factor applied after IAM:

$$G_{beam,spectral} = G_{beam,IAM} \times U_{spectr}$$ $$G_{sky,spectral} = G_{sky,IAM} \times U_{spectr}$$ $$G_{ground,spectral} = G_{ground,IAM} \times U_{spectr}$$

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References

• King, D. L., Boyson, W. E., & Kratochvil, J. A. (2004). Photovoltaic array performance model. SAND2004-3535, Sandia National Laboratories. DOI: 10.2172/919131
• Lee, M., & Panchula, A. (2016). Spectral correction for photovoltaic module performance based on air mass and precipitable water. 2016 IEEE 43rd Photovoltaic Specialists Conference (PVSC), 1351-1356. DOI: 10.1109/PVSC.2016.7749836
• Gueymard, C. (1994). Analysis of monthly average atmospheric precipitable water and turbidity in Canada and Northern United States. Solar Energy, 53(1), 57-71. DOI: 10.1016/0038-092X(94)90175-9
• Alduchov, O. A., & Eskridge, R. E. (1996). Improved Magnus form approximation of saturation vapor pressure. Journal of Applied Meteorology, 35(4), 601-609. DOI: 10.1175/1520-0450(1996)035%3C0601:IMFAOS%3E2.0.CO;2