Spectral Behavior

The spectral shift factor is representative of how much the performance of a PV system will vary from the nameplate due to differences in outdoor spectrum from flash spectrum (AM 1.5/ASTM G173). In the context of a PV modeling tool, the spectral shift factor can be thought of as a loss factor similar to DC health or soiling. It varies throughout the course of the year and can be positive (a gain instead of a loss).

The spectral shift factor can be calculated in several ways, depending on the availability of weather data and PV module technology. Historically, the air mass portion of Sandia National Lab’s Photovoltaic Array Performance Model has been used to predict the spectral shift for c-Si modules. More recently, several studies have shown that for CdTe modules, this module is highly inaccurate and a model based on precipitable water is instead more appropriate. PlantPredict defaults to the Sandia air mass model for c-Si modules and the precipitable water model for CdTe modules.

The user can override these defaults by using the Spectral Override function in the Environmental Conditions. In the case that this option is selected, PlantPredict will not use the functions below and will use the static monthly values filled in by the user. The user can also turn off spectral calculations in the Advanced Simulation Settings section of the Prediction.

PlantPredict offers a choice of two spectral models in addition to the option to use monthly override or none:

1.) A 1-variable precipitable-water or Sandia model; (PWat)

2.) A 2-variable precipitable-water & air-mass model. (Am_PWat)

The 1-variable spectral response model can be selected at the module-level by a 4-way module-level switch {Off, Sandia, FS Series 4 & Earlier, and FS Series 4-2 & Later} as shown in Figure 33. The Sandia model requires the a0-a4 response coefficients defined under the “advanced parameters” of the module definition. A second set of response coefficients for the Am-PWat model, b0-b5, defines the behavior specifically for the Am-PWat model.

Figure 20. Spectral Model selection logic

Figure 33. Spectral Model selection logic

Sandia Method

This routine computes losses due to spectral response at the module level. This model uses the air mass coefficients computed by Sandia, and is referred to as the f₁ (AM_a) function in the Array Performance Model. The model is based on an empirically determined polynomial relating the solar spectral influence on the short circuit current to air mass variation over the day.

Inputs

Outputs

Algorithm

Reference

King, D. L., Kratochvil, J.A., Boyson, W.E., Measuring Solar Spectral and Angle-of-Incidence Effects on Photovoltaic Modules and Solar Irradiance Sensors. Sandia National Laboratories, Albuquerque, NM, September 1997.

King, D. L., Boyson, W.E., Kratochvil, J.A., Photovoltaic Array Performance Model. Sandia National Laboratories, Albuquerque, NM, December 2004.

Precipitable Water Method

The spectral shift factor for CdTe is primarily driven by the amount of precipitable water in the atmosphere, and consequently, the primary input to the calculation is precipitable water. There are several viable sources for precipitable water data: TMY3 data, free online websites, and approximations derived from either relative humidity and ambient temperature data or dewpoint temperature and ambient temperature data.

PlantPredict automatically chooses the best input data source for you, depending on what fields are available in your weather file. If precipitable water data is directly available in your weather file, PlantPredict will use that as input to the calculation. If precipitable water is not available, PlantPredict will estimate precipitable water from relative humidity and ambient temperature. Finally, if no relative humidity data is available, PlantPredict will estimate precipitable water from dewpoint temperature and ambient temperature.

Inputs

Precipitable Water Method Inputs

Outputs

Algorithm

1.) If neither relative humidity nor precipitable water data is available in the weather file, first estimate the relative humidity from dewpoint and ambient temperatures using the following approximation:

2.) If relative humidity is available in the weather file or if dewpoint was used to estimate relative humidity, estimate the precipitable water using the following approximation, where the air temperature is given in Kelvin, and the relative humidity is given as a percentage:

3.) Find the spectral shift factor:

a.) For First Solar Series 2, Series 3, and Series 4 modules:

b.) For First Solar Series 4-2 and newer modules:

Precipitable Water & Air Mass Spectral Shift Method

Lee et al, showed that the spectral shift of CdTe and c-Si are both dependent on precipitable water and absolute air mass. In CdTe PV modules, precipitable water is the primary driver of spectral shift, with air mass being of secondary importance. For c-Si PV modules, the opposite is true, and air mass is the primary variable effecting spectral shift.

Inputs

Outputs

Algorithm

Compute the spectral shift factor.

Precipitable Water & Air Mass Method Algo152

Note that this equation becomes unstable as U_W approaches 0 and the air mass gets large near sunrise & sunset, so the author suggests clamping these values as follows:

If monthly spectral shift factors are desired (e.g. to automatically populate monthly factors for a site), compute the irradiance-weighted monthly values from hourly or sub-hourly values. The subscript n denotes the month of the year; subscript i denotes the hourly (or sub-hourly) value within each month.

Precipitable Water & Air Mass Method Algo153

For example, if the January spectral shift factor is desired, sum the product of all hourly spectral shift factors and global horizontal irradiance for that month, and divide by the sum of the global horizontal irradiance for that month.

References

Accurate Measurement, Using Natural Sunlight, of Silicon Solar Cells by William M. Keogh and Andrew W. Blakers, http://cses.cecs.anu.edu.au/files/Natural_sunlight_PiPV.pdf

L. Nelson, M. Frichtl, A. Panchula, Changes in Cadmium Telluride Photovoltaic System Performance due to Spectrum by, IEEE Journal of Photovoltaics, Vol. 3, No. 1, January 2013.

M. Lee, L. Ngan, J. Sorenson and A. Panchula, Understanding Next Generation Cadmium Telluride Photovoltaic Performance due to Spectrum, 42nd IEEE Photovoltaic Specialists Conference, June 2015.

Lee, M, Panchula, A., Spectral Correction for Photovoltaic Module Performance Based on Air Mass and Precipitable Water, 43rd IEEE Photovoltaic Specialists Conference, June 2016