From f978c860214bf9174536cb1bc99210d14fae0859 Mon Sep 17 00:00:00 2001 From: Kevin Anderson Date: Sat, 29 Aug 2020 10:03:37 -0600 Subject: [PATCH 01/14] add fuentes function --- pvlib/temperature.py | 169 +++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 169 insertions(+) diff --git a/pvlib/temperature.py b/pvlib/temperature.py index c9f77c5424..5ea8fc538f 100644 --- a/pvlib/temperature.py +++ b/pvlib/temperature.py @@ -423,3 +423,172 @@ def faiman(poa_global, temp_air, wind_speed=1.0, u0=25.0, u1=6.84): heat_input = poa_global temp_difference = heat_input / total_loss_factor return temp_air + temp_difference + + +def _fuentes_hconv(tave, windmod, tinoct, temp_delta, xlen, check_reynold): + # Calculate the convective coefficient as in Fuentes 1987 + densair = 0.003484 * 101325.0 / tave + visair = 0.24237e-6 * tave**0.76 / densair + condair = 2.1695e-4 * tave**0.84 + reynold = windmod * xlen / visair + if check_reynold and reynold > 1.2e5: + hforce = 0.0282 / reynold**0.2 * densair * windmod * 1007 / 0.71**0.4 + else: + hforce = 0.8600 / reynold**0.5 * densair * windmod * 1007 / 0.71**0.67 + + grashof = 9.8 / tave * temp_delta * xlen**3 / visair**2 * 0.5 + hfree = 0.21 * (grashof * 0.71)**0.32 * condair / xlen + hconv = (hfree**3 + hforce**3)**(1/3) + return hconv + + +def fuentes(poa_global, temp_air, wind_speed, inoct, module_height=5, + wind_height=9.144, emissivity=0.84, absorption=0.83, + hydraulic_diameter=0.5): + """ + Calculate cell or module temperature using the Fuentes model. + + The Fuentes model is a first-principles heat transfer energy balance + model [1]_ that is used in PVWatts for cell temperature modeling [2]_. + + Parameters + ---------- + poa_global : pandas Series + Total incident irradiance [W/m^2] + + temp_air : pandas Series + Ambient dry bulb temperature [C] + + wind_speed : pandas Series + Wind speed [m/s] + + inoct : float + The "installed" nominal operating cell temperature as defined in [1]_. + PVWatts assumes this value to be 45 C for rack-mounted arrays and + 49 C for roof mount systems with restricted air flow around the + module. [C] + + module_height : float, default 5.0 + The height above ground of the module above the ground. The PVWatts + default is 5.0 [m] + + wind_height : float, default 9.144 + The height above ground at which ``wind_speed`` is measured. The + PVWatts defauls is 9.144 [m] + + emissivity : float, default 0.84 + + absorption : float, default 0.83 + + hydraulic_diameter : float, default 0.5 + The hydraulic diameter of the module. The default value of 0.5 is + provided in [1]_ for a module with dimensions 0.3m x 1.2m. [m] + + Returns + ------- + temperature_cell : pandas Series + The modeled cell temperature [C] + + References + ---------- + .. [1] Fuentes, M. K. A Simplifed Thermal Model for Flat-Plate + Photovoltaic Arrays. SAND85-0330. 1987. + http://prod.sandia.gov/techlib/access-control.cgi/1985/850330.pdf + .. [2] Dobos, A. P. PVWatts Version 5 Manual. NREL/TP-6A20-62641. 2014. + doi:10.2172/1158421. + """ + # ported from the FORTRAN77 code provided in Appendix A of Fuentes 1987 + + boltz = 5.669e-8 + emiss = emissivity + absorp = absorption + xlen = hydraulic_diameter + cap0 = 11000 + tinoct = inoct + 273.15 + + # convective coefficient at NOCT + windmod = 1.0 + tave = (tinoct + 293.15) / 2 + hconv = _fuentes_hconv(tave, windmod, tinoct, tinoct - 293.15, xlen, False) + + # determine the ground temperature ratio and the ratio of the total + # convection to the top side convection + hground = emiss * boltz * (tinoct**2 + 293.15**2) * (tinoct + 293.15) + backrat = ( + absorp * 800.0 + - emiss * boltz * (tinoct**4 - 282.21**4) + - hconv * (tinoct - 293.15) + ) / ((hground + hconv) * (tinoct - 293.15)) + tground = (tinoct**4 - backrat * (tinoct**4 - 293.15**4))**0.25 + if tground > tinoct: + tground = tinoct + if tground < 293.15: + tground = 293.15 + + tgrat = (tground - 293.15) / (tinoct - 293.15) + convrat = (absorp * 800 - emiss * boltz * ( + 2 * tinoct**4 - 282.21**4 - tground**4)) / (hconv * (tinoct - 293.15)) + + # adjust the capacitance of the module based on the INOCT + cap = cap0 + if tinoct > 321.15: + cap = cap * (1 + (tinoct - 321.15) / 12) + + # iterate through timeseries inputs + sun0 = 0 + tmod0 = 293.15 + + # n.b. the way Fuentes calculates the first timedelta makes it seem like + # the value doesn't matter -- rather than recreate it here, just assume + # it's the same as the second timedelta: + timedelta_hours = np.diff(poa_global.index).astype(float) / 1e9 / 60 / 60 + timedelta_hours = np.append([timedelta_hours[0]], timedelta_hours) + + df = pd.DataFrame({ + 'tamb': temp_air + 273.15, + 'sun': poa_global * absorp, + 'wind_speed': wind_speed, + 'dtime': timedelta_hours, + }) + + # sky temperature + df['tsky'] = 0.68 * (0.0552 * df['tamb']**1.5) + 0.32 * df['tamb'] + + # wind speed at module height + df['windmod'] = df['wind_speed'] * (module_height/wind_height)**0.2 + 1e-4 + + tmod0 = 293.15 + + for idx, row in df.iterrows(): + + tamb = row['tamb'] + sun = row['sun'] + windmod = row['windmod'] + tsky = row['tsky'] + dtime = row['dtime'] + + tmod = tmod0 + for j in range(10): + # overall convective coefficient + tave = (tmod + tamb) / 2 + hconv = convrat * _fuentes_hconv(tave, windmod, tinoct, + abs(tmod-tamb), xlen, True) + # solve the heat transfer equation + hsky = emiss * boltz * (tmod**2 + tsky**2) * (tmod + tsky) + tground = tamb + tgrat * (tmod - tamb) + hground = emiss * boltz * (tmod**2 + tground**2) * (tmod + tground) + eigen = - (hconv + hsky + hground) / cap * dtime * 3600 + if eigen > -10: + ex = np.exp(eigen) + else: + ex = 0 + tmod = tmod0*ex + ((1 - ex) * ( + hconv*tamb + hsky * tsky + hground * tground + sun0 + + (sun - sun0) / eigen) + sun - sun0 + ) / (hconv + hsky + hground) + + df.loc[idx, 'tmod'] = tmod + tmod0 = tmod + sun0 = sun + + return df['tmod'] - 273.15 From adbe71ca05d18c103142273aa302e8b8b64028f2 Mon Sep 17 00:00:00 2001 From: Kevin Anderson Date: Sat, 29 Aug 2020 10:04:26 -0600 Subject: [PATCH 02/14] api.rst entry --- docs/sphinx/source/api.rst | 1 + 1 file changed, 1 insertion(+) diff --git a/docs/sphinx/source/api.rst b/docs/sphinx/source/api.rst index cd5b0ced40..ed91627565 100644 --- a/docs/sphinx/source/api.rst +++ b/docs/sphinx/source/api.rst @@ -237,6 +237,7 @@ PV temperature models temperature.sapm_cell_from_module temperature.pvsyst_cell temperature.faiman + temperature.fuentes Single diode models ------------------- From be226b37436e72e8a22ab235c01fc8bd4f7d5aca Mon Sep 17 00:00:00 2001 From: Kevin Anderson Date: Sat, 29 Aug 2020 11:38:55 -0600 Subject: [PATCH 03/14] add tests --- pvlib/data/pvwatts_8760_rackmount.csv | 8779 +++++++++++++++++++++++++ pvlib/data/pvwatts_8760_roofmount.csv | 8779 +++++++++++++++++++++++++ pvlib/temperature.py | 3 +- pvlib/tests/test_temperature.py | 50 +- 4 files changed, 17609 insertions(+), 2 deletions(-) create mode 100644 pvlib/data/pvwatts_8760_rackmount.csv create mode 100644 pvlib/data/pvwatts_8760_roofmount.csv diff --git a/pvlib/data/pvwatts_8760_rackmount.csv b/pvlib/data/pvwatts_8760_rackmount.csv new file mode 100644 index 0000000000..0d42f2b845 --- /dev/null +++ b/pvlib/data/pvwatts_8760_rackmount.csv @@ -0,0 +1,8779 @@ +PVWatts: Hourly PV Performance Data,,,,,,,,,, +Requested Location:,15013 Denver W Pkwy,,,,,,,,, +Location:,"Lat, Lon: 39.73, -105.18",,,,,,,,, +Lat (deg N):,39.73,,,,,,,,, +Long (deg W):,105.18,,,,,,,,, +Elev (m):,1819.599976,,,,,,,,, +DC System Size (kW):,4,,,,,,,,, +Module Type:,Standard,,,,,,,,, +Array Type:,Fixed (open rack),,,,,,,,, +Array Tilt (deg):,20,,,,,,,,, +Array Azimuth (deg):,180,,,,,,,,, +System Losses:,14.08,,,,,,,,, +Invert Efficiency:,96,,,,,,,,, +DC to AC Size Ratio:,1.2,,,,,,,,, +Average Cost of Electricity Purchased from Utility ($/kWh):,0.111,,,,,,,,, +Capacity Factor (%),"17.2 ",,,,,,,,, +,,,,,,,,,, +Month,Day,Hour,Beam Irradiance (W/m^2),Diffuse Irradiance (W/m^2),Ambient Temperature (C),Wind Speed (m/s),Plane 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b/pvlib/data/pvwatts_8760_roofmount.csv new file mode 100644 index 0000000000..750ec321ae --- /dev/null +++ b/pvlib/data/pvwatts_8760_roofmount.csv @@ -0,0 +1,8779 @@ +PVWatts: Hourly PV Performance Data,,,,,,,,,, +Requested Location:,15013 Denver W Pkwy,,,,,,,,, +Location:,"Lat, Lon: 39.73, -105.18",,,,,,,,, +Lat (deg N):,39.73,,,,,,,,, +Long (deg W):,105.18,,,,,,,,, +Elev (m):,1819.599976,,,,,,,,, +DC System Size (kW):,4,,,,,,,,, +Module Type:,Standard,,,,,,,,, +Array Type:,Fixed (roof mount),,,,,,,,, +Array Tilt (deg):,20,,,,,,,,, +Array Azimuth (deg):,180,,,,,,,,, +System Losses:,14.08,,,,,,,,, +Invert Efficiency:,96,,,,,,,,, +DC to AC Size Ratio:,1.2,,,,,,,,, +Average Cost of Electricity Purchased from Utility ($/kWh):,0.111,,,,,,,,, +Capacity Factor (%),"16.9 ",,,,,,,,, +,,,,,,,,,, +Month,Day,Hour,Beam Irradiance (W/m^2),Diffuse Irradiance (W/m^2),Ambient Temperature (C),Wind Speed (m/s),Plane of Array Irradiance (W/m^2),Cell Temperature (C),DC Array Output (W),AC System Output 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b/pvlib/temperature.py @@ -4,6 +4,7 @@ """ import numpy as np +import pandas as pd TEMPERATURE_MODEL_PARAMETERS = { @@ -571,7 +572,7 @@ def fuentes(poa_global, temp_air, wind_speed, inoct, module_height=5, for j in range(10): # overall convective coefficient tave = (tmod + tamb) / 2 - hconv = convrat * _fuentes_hconv(tave, windmod, tinoct, + hconv = convrat * _fuentes_hconv(tave, windmod, tinoct, abs(tmod-tamb), xlen, True) # solve the heat transfer equation hsky = emiss * boltz * (tmod**2 + tsky**2) * (tmod + tsky) diff --git a/pvlib/tests/test_temperature.py b/pvlib/tests/test_temperature.py index 19e65a05e3..416b8e74c7 100644 --- a/pvlib/tests/test_temperature.py +++ b/pvlib/tests/test_temperature.py @@ -2,7 +2,7 @@ import numpy as np import pytest -from conftest import assert_series_equal +from conftest import DATA_DIR, assert_series_equal from numpy.testing import assert_allclose from pvlib import temperature @@ -142,3 +142,51 @@ def test__temperature_model_params(): 'open_rack_glass_glass'] with pytest.raises(KeyError): temperature._temperature_model_params('sapm', 'not_a_parameter_set') + + +def _read_pvwatts_8760(filename): + df = pd.read_csv(filename, + skiprows=17, # ignore location/simulation metadata + skipfooter=1, # ignore "Totals" row + engine='python') + df['Year'] = 2019 + df.index = pd.to_datetime(df[['Year', 'Month', 'Day', 'Hour']]) + return df + + +@pytest.mark.parametrize('filename,inoct', [ + ('pvwatts_8760_rackmount.csv', 45), + ('pvwatts_8760_roofmount.csv', 49), +]) +def test_fuentes(filename, inoct): + # Test against data exported from pvwatts.nrel.gov + data = _read_pvwatts_8760(DATA_DIR / filename) + data = data.iloc[:24*7, :] # just use one week + inputs = { + 'poa_global': data['Plane of Array Irradiance (W/m^2)'], + 'temp_air': data['Ambient Temperature (C)'], + 'wind_speed': data['Wind Speed (m/s)'], + 'inoct': inoct, + } + expected_tcell = data['Cell Temperature (C)'] + expected_tcell.name = 'tmod' + actual_tcell = temperature.fuentes(**inputs) + # the SSC implementation of PVWatts diverges from the Fuentes model at + # at night by setting Tcell=Tamb when POA=0. This not only means that + # nighttime values are slightly different (Fuentes models cooling to sky + # at night), but because of the thermal inertia, there is a transient + # error after dawn as well. Test each case separately: + is_night = inputs['poa_global'] == 0 + is_dawn = is_night.shift(1) & ~is_night + is_daytime = (inputs['poa_global'] > 0) & ~is_dawn + # the accuracy is probably higher than 3 digits here, but the PVWatts + # export data has low precision so can only test up to 3 digits + assert_series_equal(expected_tcell[is_daytime].round(3), + actual_tcell[is_daytime].round(3)) + # use lower precision for dawn times to accommodate the dawn transient + error = actual_tcell[is_dawn] - expected_tcell[is_dawn] + assert (error.abs() < 0.1).all() + # sanity check on night values -- Fuentes not much lower than PVWatts + night_difference = expected_tcell[is_night] - actual_tcell[is_night] + assert night_difference.max() < 6 + assert night_difference.min() > 0 From b4bfafbdb623b042a8660a75afea14e47102dd49 Mon Sep 17 00:00:00 2001 From: Kevin Anderson Date: Sat, 29 Aug 2020 11:40:03 -0600 Subject: [PATCH 04/14] whatsnew --- docs/sphinx/source/whatsnew/v0.8.0.rst | 1 + 1 file changed, 1 insertion(+) diff --git a/docs/sphinx/source/whatsnew/v0.8.0.rst b/docs/sphinx/source/whatsnew/v0.8.0.rst index 6039c5bc2b..32fe9b1eab 100644 --- a/docs/sphinx/source/whatsnew/v0.8.0.rst +++ b/docs/sphinx/source/whatsnew/v0.8.0.rst @@ -92,6 +92,7 @@ Enhancements PVSystem, LocalizedPVSystem, SingleAxisTracker, and LocalizedSingleAxisTracker repr methods. (:issue:`1027`) * Added ability for :py:func:`pvlib.soiling.hsu` to accept arbitrary time intervals. (:pull:`980`) +* Added :py:func:`pvlib.temperature.fuentes` for cell temperature modeling. (:pull:`1037`) Bug fixes ~~~~~~~~~ From efe6a8773acc26d7107dd488975122b910771962 Mon Sep 17 00:00:00 2001 From: Kevin Anderson Date: Sat, 29 Aug 2020 12:12:44 -0600 Subject: [PATCH 05/14] refactor for coverage --- pvlib/temperature.py | 5 +---- 1 file changed, 1 insertion(+), 4 deletions(-) diff --git a/pvlib/temperature.py b/pvlib/temperature.py index 39d642a99a..91b01063b3 100644 --- a/pvlib/temperature.py +++ b/pvlib/temperature.py @@ -521,10 +521,7 @@ def fuentes(poa_global, temp_air, wind_speed, inoct, module_height=5, - hconv * (tinoct - 293.15) ) / ((hground + hconv) * (tinoct - 293.15)) tground = (tinoct**4 - backrat * (tinoct**4 - 293.15**4))**0.25 - if tground > tinoct: - tground = tinoct - if tground < 293.15: - tground = 293.15 + tground = np.clip(tground, 293.15, tinoct) tgrat = (tground - 293.15) / (tinoct - 293.15) convrat = (absorp * 800 - emiss * boltz * ( From 1d074b818fcd61149826161ab304e4a53350d26c Mon Sep 17 00:00:00 2001 From: Kevin Anderson Date: Sun, 30 Aug 2020 16:38:20 -0600 Subject: [PATCH 06/14] code comments --- pvlib/temperature.py | 60 +++++++++++++++++++++++++++++++++----------- 1 file changed, 45 insertions(+), 15 deletions(-) diff --git a/pvlib/temperature.py b/pvlib/temperature.py index 91b01063b3..7215d7b5f6 100644 --- a/pvlib/temperature.py +++ b/pvlib/temperature.py @@ -427,18 +427,26 @@ def faiman(poa_global, temp_air, wind_speed=1.0, u0=25.0, u1=6.84): def _fuentes_hconv(tave, windmod, tinoct, temp_delta, xlen, check_reynold): - # Calculate the convective coefficient as in Fuentes 1987 - densair = 0.003484 * 101325.0 / tave - visair = 0.24237e-6 * tave**0.76 / densair - condair = 2.1695e-4 * tave**0.84 + # Calculate the convective coefficient as in Fuentes 1987 -- a mixture of + # free, laminar, and turbulent convection. + densair = 0.003484 * 101325.0 / tave # density + visair = 0.24237e-6 * tave**0.76 / densair # kinematic viscosity + condair = 2.1695e-4 * tave**0.84 # thermal conductivity reynold = windmod * xlen / visair + # the boundary between laminar and turbulent is modeled as an abrupt + # change at Re = 1.2e5: if check_reynold and reynold > 1.2e5: + # turbulent convection hforce = 0.0282 / reynold**0.2 * densair * windmod * 1007 / 0.71**0.4 else: + # laminar convection hforce = 0.8600 / reynold**0.5 * densair * windmod * 1007 / 0.71**0.67 - + # free convection via Grashof number + # NB: the 0.5 factor is from assuming tilt=30; should tilt be a parameter? grashof = 9.8 / tave * temp_delta * xlen**3 / visair**2 * 0.5 + # product of Nusselt number and (k/l) hfree = 0.21 * (grashof * 0.71)**0.32 * condair / xlen + # combine free and forced components hconv = (hfree**3 + hforce**3)**(1/3) return hconv @@ -478,8 +486,11 @@ def fuentes(poa_global, temp_air, wind_speed, inoct, module_height=5, PVWatts defauls is 9.144 [m] emissivity : float, default 0.84 + The effectiveness of the module at radiating thermal energy. [unitless] absorption : float, default 0.83 + The fraction of incident irradiance that is converted to thermal + energy in the module. [unitless] hydraulic_diameter : float, default 0.5 The hydraulic diameter of the module. The default value of 0.5 is @@ -498,7 +509,8 @@ def fuentes(poa_global, temp_air, wind_speed, inoct, module_height=5, .. [2] Dobos, A. P. PVWatts Version 5 Manual. NREL/TP-6A20-62641. 2014. doi:10.2172/1158421. """ - # ported from the FORTRAN77 code provided in Appendix A of Fuentes 1987 + # ported from the FORTRAN77 code provided in Appendix A of Fuentes 1987; + # nearly all variable names are kept the same for ease of comparison. boltz = 5.669e-8 emiss = emissivity @@ -507,7 +519,7 @@ def fuentes(poa_global, temp_air, wind_speed, inoct, module_height=5, cap0 = 11000 tinoct = inoct + 273.15 - # convective coefficient at NOCT + # convective coefficient of top surface of module at NOCT windmod = 1.0 tave = (tinoct + 293.15) / 2 hconv = _fuentes_hconv(tave, windmod, tinoct, tinoct - 293.15, xlen, False) @@ -527,7 +539,10 @@ def fuentes(poa_global, temp_air, wind_speed, inoct, module_height=5, convrat = (absorp * 800 - emiss * boltz * ( 2 * tinoct**4 - 282.21**4 - tground**4)) / (hconv * (tinoct - 293.15)) - # adjust the capacitance of the module based on the INOCT + # adjust the capacitance (thermal mass) of the module based on the INOCT. + # It is a function of INOCT because high INOCT implies thermal coupling + # with the racking (e.g. roofmount), so the thermal mass is increased. + # `cap` has units J/(m^2 C) -- see Table 3, Equations 26 & 27 cap = cap0 if tinoct > 321.15: cap = cap * (1 + (tinoct - 321.15) / 12) @@ -549,10 +564,12 @@ def fuentes(poa_global, temp_air, wind_speed, inoct, module_height=5, 'dtime': timedelta_hours, }) - # sky temperature + # Two of the calculations are easily vectorized, so precalculate them: + # sky temperature -- Equation 24 df['tsky'] = 0.68 * (0.0552 * df['tamb']**1.5) + 0.32 * df['tamb'] - - # wind speed at module height + # wind speed at module height -- Equation 22 + # not sure why the 1e-4 factor is included -- maybe the equations don't + # behave well if wind == 0? df['windmod'] = df['wind_speed'] * (module_height/wind_height)**0.2 + 1e-4 tmod0 = 293.15 @@ -565,24 +582,37 @@ def fuentes(poa_global, temp_air, wind_speed, inoct, module_height=5, tsky = row['tsky'] dtime = row['dtime'] + # solve the heat transfer equation, iterating because the heat loss + # terms depend on tmod. NB Fuentes doesn't show that 10 iterations is + # sufficient for convergence. tmod = tmod0 for j in range(10): # overall convective coefficient tave = (tmod + tamb) / 2 hconv = convrat * _fuentes_hconv(tave, windmod, tinoct, abs(tmod-tamb), xlen, True) - # solve the heat transfer equation + # sky radiation coefficient (Equation 3) hsky = emiss * boltz * (tmod**2 + tsky**2) * (tmod + tsky) + # ground radiation coeffieicient (Equation 4) tground = tamb + tgrat * (tmod - tamb) hground = emiss * boltz * (tmod**2 + tground**2) * (tmod + tground) + # thermal lag -- Equation 8 eigen = - (hconv + hsky + hground) / cap * dtime * 3600 + # not sure why this check is done, maybe as a speed optimization? if eigen > -10: ex = np.exp(eigen) else: ex = 0 - tmod = tmod0*ex + ((1 - ex) * ( - hconv*tamb + hsky * tsky + hground * tground + sun0 - + (sun - sun0) / eigen) + sun - sun0 + # Equation 7 -- note that `sun` and `sun0` already account for + # absorption (alpha) + tmod = tmod0 * ex + ( + (1 - ex) * ( + hconv * tamb + + hsky * tsky + + hground * tground + + sun0 + + (sun - sun0) / eigen + ) + sun - sun0 ) / (hconv + hsky + hground) df.loc[idx, 'tmod'] = tmod From a11319f8c1bf9ea4be9660acdd266eebd133a30c Mon Sep 17 00:00:00 2001 From: Kevin Anderson Date: Sun, 30 Aug 2020 16:47:56 -0600 Subject: [PATCH 07/14] notes section --- pvlib/temperature.py | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/pvlib/temperature.py b/pvlib/temperature.py index 7215d7b5f6..42dc4e133d 100644 --- a/pvlib/temperature.py +++ b/pvlib/temperature.py @@ -501,6 +501,13 @@ def fuentes(poa_global, temp_air, wind_speed, inoct, module_height=5, temperature_cell : pandas Series The modeled cell temperature [C] + Notes + ----- + This function returns slightly different values from PVWatts at night + and just after dawn. This is because the SAM SSC assumes that module + temperature equals ambient temperature when irradiance is zero so it can + skip the heat balance calculation at night. + References ---------- .. [1] Fuentes, M. K. A Simplifed Thermal Model for Flat-Plate From 5b9c2b07fc063e7b2764349fcb7b59da423bb2b1 Mon Sep 17 00:00:00 2001 From: Kevin Anderson Date: Mon, 31 Aug 2020 20:01:45 -0600 Subject: [PATCH 08/14] pandas to numpy --- pvlib/temperature.py | 31 +++++++++++-------------------- 1 file changed, 11 insertions(+), 20 deletions(-) diff --git a/pvlib/temperature.py b/pvlib/temperature.py index 42dc4e133d..149cb8ca67 100644 --- a/pvlib/temperature.py +++ b/pvlib/temperature.py @@ -564,31 +564,23 @@ def fuentes(poa_global, temp_air, wind_speed, inoct, module_height=5, timedelta_hours = np.diff(poa_global.index).astype(float) / 1e9 / 60 / 60 timedelta_hours = np.append([timedelta_hours[0]], timedelta_hours) - df = pd.DataFrame({ - 'tamb': temp_air + 273.15, - 'sun': poa_global * absorp, - 'wind_speed': wind_speed, - 'dtime': timedelta_hours, - }) + tamb_array = temp_air + 273.15 + sun_array = poa_global * absorp # Two of the calculations are easily vectorized, so precalculate them: # sky temperature -- Equation 24 - df['tsky'] = 0.68 * (0.0552 * df['tamb']**1.5) + 0.32 * df['tamb'] + tsky_array = 0.68 * (0.0552 * tamb_array**1.5) + 0.32 * tamb_array # wind speed at module height -- Equation 22 # not sure why the 1e-4 factor is included -- maybe the equations don't # behave well if wind == 0? - df['windmod'] = df['wind_speed'] * (module_height/wind_height)**0.2 + 1e-4 + windmod_array = wind_speed * (module_height/wind_height)**0.2 + 1e-4 tmod0 = 293.15 - - for idx, row in df.iterrows(): - - tamb = row['tamb'] - sun = row['sun'] - windmod = row['windmod'] - tsky = row['tsky'] - dtime = row['dtime'] - + tmod_array = np.zeros_like(poa_global) + + iterator = zip(tamb_array, sun_array, windmod_array, tsky_array, + timedelta_hours) + for i, (tamb, sun, windmod, tsky, dtime) in enumerate(iterator): # solve the heat transfer equation, iterating because the heat loss # terms depend on tmod. NB Fuentes doesn't show that 10 iterations is # sufficient for convergence. @@ -621,9 +613,8 @@ def fuentes(poa_global, temp_air, wind_speed, inoct, module_height=5, + (sun - sun0) / eigen ) + sun - sun0 ) / (hconv + hsky + hground) - - df.loc[idx, 'tmod'] = tmod + tmod_array[i] = tmod tmod0 = tmod sun0 = sun - return df['tmod'] - 273.15 + return pd.Series(tmod_array - 273.15, index=poa_global.index, name='tmod') From 4ef72e5d10606d7040e9606dbdb2a37a3ab87c7f Mon Sep 17 00:00:00 2001 From: Kevin Anderson Date: Mon, 31 Aug 2020 20:05:46 -0600 Subject: [PATCH 09/14] inoct->noct_installed; copy reference format from sapm_cell --- pvlib/temperature.py | 12 +++++++----- 1 file changed, 7 insertions(+), 5 deletions(-) diff --git a/pvlib/temperature.py b/pvlib/temperature.py index 149cb8ca67..7657505f61 100644 --- a/pvlib/temperature.py +++ b/pvlib/temperature.py @@ -471,7 +471,7 @@ def fuentes(poa_global, temp_air, wind_speed, inoct, module_height=5, wind_speed : pandas Series Wind speed [m/s] - inoct : float + noct_installed : float The "installed" nominal operating cell temperature as defined in [1]_. PVWatts assumes this value to be 45 C for rack-mounted arrays and 49 C for roof mount systems with restricted air flow around the @@ -510,10 +510,12 @@ def fuentes(poa_global, temp_air, wind_speed, inoct, module_height=5, References ---------- - .. [1] Fuentes, M. K. A Simplifed Thermal Model for Flat-Plate - Photovoltaic Arrays. SAND85-0330. 1987. + .. [1] Fuentes, M. K., 1987, "A Simplifed Thermal Model for Flat-Plate + Photovoltaic Arrays", SAND85-0330, Sandia National Laboratories, + Albuquerque NM. http://prod.sandia.gov/techlib/access-control.cgi/1985/850330.pdf - .. [2] Dobos, A. P. PVWatts Version 5 Manual. NREL/TP-6A20-62641. 2014. + .. [2] Dobos, A. P., 2014, "PVWatts Version 5 Manual", NREL/TP-6A20-62641, + National Renewable Energy Laboratory, Golden CO. doi:10.2172/1158421. """ # ported from the FORTRAN77 code provided in Appendix A of Fuentes 1987; @@ -577,7 +579,7 @@ def fuentes(poa_global, temp_air, wind_speed, inoct, module_height=5, tmod0 = 293.15 tmod_array = np.zeros_like(poa_global) - + iterator = zip(tamb_array, sun_array, windmod_array, tsky_array, timedelta_hours) for i, (tamb, sun, windmod, tsky, dtime) in enumerate(iterator): From 6a4115e79c5b1c7815de9e9490419000da3ae549 Mon Sep 17 00:00:00 2001 From: Kevin Anderson Date: Mon, 31 Aug 2020 20:28:57 -0600 Subject: [PATCH 10/14] oops --- pvlib/temperature.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/pvlib/temperature.py b/pvlib/temperature.py index 7657505f61..bea5eb1f37 100644 --- a/pvlib/temperature.py +++ b/pvlib/temperature.py @@ -451,7 +451,7 @@ def _fuentes_hconv(tave, windmod, tinoct, temp_delta, xlen, check_reynold): return hconv -def fuentes(poa_global, temp_air, wind_speed, inoct, module_height=5, +def fuentes(poa_global, temp_air, wind_speed, noct_installed, module_height=5, wind_height=9.144, emissivity=0.84, absorption=0.83, hydraulic_diameter=0.5): """ From 32a006e17a76f7b5d0c9526239dda2d508a4d220 Mon Sep 17 00:00:00 2001 From: Kevin Anderson Date: Mon, 31 Aug 2020 20:42:46 -0600 Subject: [PATCH 11/14] fix the things I broke --- pvlib/temperature.py | 2 +- pvlib/tests/test_temperature.py | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/pvlib/temperature.py b/pvlib/temperature.py index bea5eb1f37..ce0d4cd504 100644 --- a/pvlib/temperature.py +++ b/pvlib/temperature.py @@ -526,7 +526,7 @@ def fuentes(poa_global, temp_air, wind_speed, noct_installed, module_height=5, absorp = absorption xlen = hydraulic_diameter cap0 = 11000 - tinoct = inoct + 273.15 + tinoct = noct_installed + 273.15 # convective coefficient of top surface of module at NOCT windmod = 1.0 diff --git a/pvlib/tests/test_temperature.py b/pvlib/tests/test_temperature.py index 416b8e74c7..245c5d2807 100644 --- a/pvlib/tests/test_temperature.py +++ b/pvlib/tests/test_temperature.py @@ -166,7 +166,7 @@ def test_fuentes(filename, inoct): 'poa_global': data['Plane of Array Irradiance (W/m^2)'], 'temp_air': data['Ambient Temperature (C)'], 'wind_speed': data['Wind Speed (m/s)'], - 'inoct': inoct, + 'noct_installed': inoct, } expected_tcell = data['Cell Temperature (C)'] expected_tcell.name = 'tmod' From 227b9e386e56df33aa2a11c429abc8697c53a0ee Mon Sep 17 00:00:00 2001 From: Kevin Anderson Date: Tue, 1 Sep 2020 21:55:15 -0600 Subject: [PATCH 12/14] expose surface_tilt param; change hydraulic_length to module width and length --- pvlib/temperature.py | 40 +++++++++++++++++++++++++++++----------- 1 file changed, 29 insertions(+), 11 deletions(-) diff --git a/pvlib/temperature.py b/pvlib/temperature.py index ce0d4cd504..4edd5402fe 100644 --- a/pvlib/temperature.py +++ b/pvlib/temperature.py @@ -5,7 +5,7 @@ import numpy as np import pandas as pd - +from pvlib.tools import sind TEMPERATURE_MODEL_PARAMETERS = { 'sapm': { @@ -426,7 +426,8 @@ def faiman(poa_global, temp_air, wind_speed=1.0, u0=25.0, u1=6.84): return temp_air + temp_difference -def _fuentes_hconv(tave, windmod, tinoct, temp_delta, xlen, check_reynold): +def _fuentes_hconv(tave, windmod, tinoct, temp_delta, xlen, tilt, + check_reynold): # Calculate the convective coefficient as in Fuentes 1987 -- a mixture of # free, laminar, and turbulent convection. densair = 0.003484 * 101325.0 / tave # density @@ -442,8 +443,8 @@ def _fuentes_hconv(tave, windmod, tinoct, temp_delta, xlen, check_reynold): # laminar convection hforce = 0.8600 / reynold**0.5 * densair * windmod * 1007 / 0.71**0.67 # free convection via Grashof number - # NB: the 0.5 factor is from assuming tilt=30; should tilt be a parameter? - grashof = 9.8 / tave * temp_delta * xlen**3 / visair**2 * 0.5 + # NB: Fuentes hardwires sind(tilt) as 0.5 for tilt=30 + grashof = 9.8 / tave * temp_delta * xlen**3 / visair**2 * sind(tilt) # product of Nusselt number and (k/l) hfree = 0.21 * (grashof * 0.71)**0.32 * condair / xlen # combine free and forced components @@ -451,9 +452,14 @@ def _fuentes_hconv(tave, windmod, tinoct, temp_delta, xlen, check_reynold): return hconv +def _hydraulic_diameter(width, height): + # calculate the hydraulic diameter of a rectangle + return 2 * (width * height) / (width + height) + + def fuentes(poa_global, temp_air, wind_speed, noct_installed, module_height=5, wind_height=9.144, emissivity=0.84, absorption=0.83, - hydraulic_diameter=0.5): + surface_tilt=30, module_width=0.31579, module_length=1.2): """ Calculate cell or module temperature using the Fuentes model. @@ -492,9 +498,19 @@ def fuentes(poa_global, temp_air, wind_speed, noct_installed, module_height=5, The fraction of incident irradiance that is converted to thermal energy in the module. [unitless] - hydraulic_diameter : float, default 0.5 - The hydraulic diameter of the module. The default value of 0.5 is - provided in [1]_ for a module with dimensions 0.3m x 1.2m. [m] + surface_tilt : float, default 30 + Module tilt from horizontal. If not provided, the default value + of 30 degrees from [1]_ and [2]_ is used. [degrees] + + module_width : float, default 0.31579 + Module width. The default value of 0.31579 meters in combination with + the default `module_length` gives a hydraulic diameter of 0.5 as + assumed in [1]_ and [2]_. [m] + + module_length : float, default 1.2 + Module length. The default value of 1.2 meters in combination with + the default `module_width` gives a hydraulic diameter of 0.5 as + assumed in [1]_ and [2]_. [m] Returns ------- @@ -524,14 +540,15 @@ def fuentes(poa_global, temp_air, wind_speed, noct_installed, module_height=5, boltz = 5.669e-8 emiss = emissivity absorp = absorption - xlen = hydraulic_diameter + xlen = _hydraulic_diameter(module_width, module_length) cap0 = 11000 tinoct = noct_installed + 273.15 # convective coefficient of top surface of module at NOCT windmod = 1.0 tave = (tinoct + 293.15) / 2 - hconv = _fuentes_hconv(tave, windmod, tinoct, tinoct - 293.15, xlen, False) + hconv = _fuentes_hconv(tave, windmod, tinoct, tinoct - 293.15, xlen, + surface_tilt, False) # determine the ground temperature ratio and the ratio of the total # convection to the top side convection @@ -591,7 +608,8 @@ def fuentes(poa_global, temp_air, wind_speed, noct_installed, module_height=5, # overall convective coefficient tave = (tmod + tamb) / 2 hconv = convrat * _fuentes_hconv(tave, windmod, tinoct, - abs(tmod-tamb), xlen, True) + abs(tmod-tamb), xlen, + surface_tilt, True) # sky radiation coefficient (Equation 3) hsky = emiss * boltz * (tmod**2 + tsky**2) * (tmod + tsky) # ground radiation coeffieicient (Equation 4) From dd34f2c82da83b8bf3612d574024e43a815a3306 Mon Sep 17 00:00:00 2001 From: Kevin Anderson <57452607+kanderso-nrel@users.noreply.github.com> Date: Wed, 2 Sep 2020 09:15:38 -0600 Subject: [PATCH 13/14] cap0 units Co-authored-by: Cliff Hansen --- pvlib/temperature.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/pvlib/temperature.py b/pvlib/temperature.py index 4edd5402fe..65a73e4ecc 100644 --- a/pvlib/temperature.py +++ b/pvlib/temperature.py @@ -541,7 +541,7 @@ def fuentes(poa_global, temp_air, wind_speed, noct_installed, module_height=5, emiss = emissivity absorp = absorption xlen = _hydraulic_diameter(module_width, module_length) - cap0 = 11000 + cap0 = 11000 # units of [J / (m^2 K)], equal to mass per unit area times specific heat of the module. tinoct = noct_installed + 273.15 # convective coefficient of top surface of module at NOCT From c186dbbd663edbe5e0fc07c5f04ce0d2e79dd908 Mon Sep 17 00:00:00 2001 From: Kevin Anderson Date: Wed, 2 Sep 2020 09:19:18 -0600 Subject: [PATCH 14/14] module_height description; stickler --- pvlib/temperature.py | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/pvlib/temperature.py b/pvlib/temperature.py index 65a73e4ecc..2b683d879e 100644 --- a/pvlib/temperature.py +++ b/pvlib/temperature.py @@ -484,7 +484,7 @@ def fuentes(poa_global, temp_air, wind_speed, noct_installed, module_height=5, module. [C] module_height : float, default 5.0 - The height above ground of the module above the ground. The PVWatts + The height above ground of the center of the module. The PVWatts default is 5.0 [m] wind_height : float, default 9.144 @@ -541,7 +541,9 @@ def fuentes(poa_global, temp_air, wind_speed, noct_installed, module_height=5, emiss = emissivity absorp = absorption xlen = _hydraulic_diameter(module_width, module_length) - cap0 = 11000 # units of [J / (m^2 K)], equal to mass per unit area times specific heat of the module. + # cap0 has units of [J / (m^2 K)], equal to mass per unit area times + # specific heat of the module. + cap0 = 11000 tinoct = noct_installed + 273.15 # convective coefficient of top surface of module at NOCT