Add an option to apply nonlinear irradiance response correction

[williamhobbs]

See https://groups.google.com/g/pvlib-python/c/-3UuvBtWByY for some discussion.

Right now, I think the best option is to implement the "improved model" from Marion 2008 [1]. Two notes about it:

1. There appears to be a typo in one of the equations in Fig. 5 - eq. 10 is different and seems to be correct.
2. I don't like that the linear portion of the piecewise correction (for irradiance > 200 W/m^2) continues to increase efficiency above nominal at irradiance above 1000 W/m^2. I think adding a third equation that sets the correction to 1.0 above 1000 would be better.

[1] B. Marion, "Comparison of Predictive Models for Photovoltaic Module Performance," IEEE PVSC 2008, https://docs.nrel.gov/docs/fy08osti/42511.pdf

[williamhobbs]

After this bit of code:

pv-system-model/pv_model.py

Lines 472 to 474 in 0b9e262

	# PVWatts dc power
	pdc_shaded = pvlib.pvsystem.pvwatts_dc(
	poa_effective, t_cell, nameplate_dc, gamma_pdc)

add:

    nonlinear_adj = pdc_shaded*0
    mask1 = (poa_effective<=200)  # Eg. 11 criteria in [1]
    mask2 = (poa_effective>200)  # Eq. 10 criteria in [1]
    np.putmask(nonlinear_adj, mask1, 1 - (k*(1-(1-poa_effective/200)**4))/(poa_effective/1000))  # Eq. 11 in [1]
    np.putmask(nonlinear_adj, mask2, 1 - (k*((1000-poa_effective) / (800)))/(poa_effective/1000))  # Eq. 10 in [1]
    pdc_shaded = pdc_shaded * nonlinear_adj

# [1] https://docs.nrel.gov/docs/fy08osti/42511.pdf

To address item 2 above (setting correction to 1.0 above 1000 W/m^2):

    nonlinear_adj = pdc_shaded*0
    mask1 = (poa_effective<=200)  # Eg. 11 criteria in [1]
    mask2 = (poa_effective>200) & (poa_effective<=1000)  # *MODIFIED* Eq. 10 criteria in [1]
    mask3 = (poa_effective>=1000)  # new custom criteria
    np.putmask(nonlinear_adj, mask1, 1 - (k*(1-(1-poa_effective/200)**4))/(poa_effective/1000))  # Eq. 11 in [1]
    np.putmask(nonlinear_adj, mask2, 1 - (k*((1000-poa_effective) / (800)))/(poa_effective/1000))  # Eq. 10 in [1]
    np.putmask(nonlinear_adj, mask3, 1)  # new custom eq.
    pdc_shaded = pdc_shaded * nonlinear_adj

# [1] https://docs.nrel.gov/docs/fy08osti/42511.pdf

[williamhobbs]

This is in the works for adding to pvlib.pvsystem.pvwatts_dc. See pvlib/pvlib-python#2569.

[williamhobbs]

In the PR above for pvlib.pvsystem.pvwatts_dc, the correction will be applied to dc power. But here, I think we might want to modify it slightly to apply it to effective irradiance so that we can return an effective irradiance value that has the nonlinearity adjustment applied to it... I need to talk to some other folks about this.