Should we apply consistent plane-of-array irradiance for calculating cell temperature and effective irradiance?

Hi there,

I have recently started working with pvlib-python (v0.8.0). I have gone through the basic A simple ModelChain example tutorial. It works well. But after exploring mc attributes, I got myself confused with irradiance for calculating cell temperature and effective irradiance, which I really appreciate your help.

I found that cell temperature could be calculated as:

# equal to mc.cell_temperature
mc.total_irrad['poa_global'] \
* (np.exp(temperature_model_parameters['a']
          +temperature_model_parameters['b']*weather['wind_speed'])) \
+ weather['temp_air'] \
+ mc.total_irrad['poa_global'] / 1000 * temperature_model_parameters['deltaT']

Hence cell temperature is based on E_POA without any reflection, shading, or soiling losses.

Then I found that effective irradiance could be calculated as:

# equal to mc.effective_irradiance
mc.spectral_modifier * (mc.aoi_modifier*mc.total_irrad['poa_direct']+mc.total_irrad['poa_diffuse'])

rather than:

# unequal to mc.effective_irradiance
mc.spectral_modifier * mc.total_irrad['poa_global']

Hence I believe that the reflection losses (i.e. AOI modifier) is taken into account in calculating effective irradiance.

This really bothers me despite small differences in results. I think that the only difference in calculating cell temperature and effective irradiance is that the later contains additional spectral losses? The two should be consistent in including/excluding reflection, shading, and soiling losses according to modeling steps described here or here?

Yours faithfully, Fei

[cwhanse]

@FeiYao-Edinburgh,

I suppose the explanation depends on how ‘plane of array irradiance’ is defined. In pvlib-python, ‘poa_global’ is the broadband irradiance reaching the face of the module, i.e., reduced by shading and soiling but not adjusted for spectrum or reflections. The tutorial page is a little confusing in that it does not define either plane-of-array or effective irradiance irradiance. I think that page is meant as a general guide rather than a precise description.

In pvlib effective irradiance is the irradiance reaching a module’s cells, i.e., ‘poa_global’ adjusted for spectrum and reflection.

The challenge is with the temperature model coefficients. The values supplied with pvlib have been determined by regressing measured module backsheet temperatures to plane-of-array irradiance measured with an in-plane broadband pyranometer (and also to ambient air temperature and wind speed). As a consequence, the irradiance used to fit the model is not adjusted for reflection or spectral modifiers. That’s why pvlib uses ‘poa_global’ in the temperature functions.

However, IMO when ‘poa_global’ is not available (e.g., when irradiance is measured in-plane with a reference cell) it is acceptable to use effective irradiance instead of poa_global with the same model parameters. The difference in model output will be on the order of one degree C, which is similar to the uncertainty of the temperature models.

[FeiYao-Edinburgh]

Do you see any other place where there’s a gap or snag in the calculation process?

No. I have just started learning and using pvlib-python.

The quantities between ‘poa_global’ and ‘effective_irradiance’ are possibilities for naming. I’ve seen “incident irradiance” used for the irradiance reaching the surface of a module, and “absorbed irradiance” for the irradiance reaching the cells prior to spectral adjustment.

This makes sense in that:

• incident irradiance: the irradiance reaching the surface of a module, accounting for shading and/or soiling losses
• absorbed irradiance: the irradiance reaching the cells, further accounting for reflection losses
• effective irradiance: the irradiance reaching used by cells with spectral adjustment

Yes I agree that it might be enough to make a memo on this issue for the time being.

Thanks for the discussion.