diff --git a/docs/examples/operating-temperature/README.rst b/docs/examples/operating-temperature/README.rst new file mode 100644 index 0000000000..30bd677577 --- /dev/null +++ b/docs/examples/operating-temperature/README.rst @@ -0,0 +1,3 @@ +Operating Temperature +--------------------- + diff --git a/docs/examples/operating-temperature/plot_dynamic_faiman.py b/docs/examples/operating-temperature/plot_dynamic_faiman.py new file mode 100644 index 0000000000..d084e782a9 --- /dev/null +++ b/docs/examples/operating-temperature/plot_dynamic_faiman.py @@ -0,0 +1,154 @@ +""" +A simple way to incorporate thermal inertia +=========================================== + +What can be simpler than a moving average? + +""" + +# %% +# +# Applying a moving average filter to the PV array operating conditions +# is a simple technique to compensate for the thermal inertia of the module, +# which delays and dampens temperature fluctuations. +# It is useful for simulating at small time steps, but even more useful for +# fitting models to field data as demonstrated in [1]_. +# The functions :py:func:`pvlib.temperature.faiman_dyn` and +# :py:func:`pvlib.temperature.fit_faiman_dyn` incorporate this moving average +# technique. +# +# This example reads a csv file containing one-minute average monitoring data. +# The function :py:func:`pvlib.temperature.fit_faiman_dyn` is used to determine +# the model parameters and the function :py:func:`pvlib.temperature.faiman_dyn` +# is used to demonstrate how well it worked. +# +# Contributed by Anton Driesse, PV Performance Labs, October 2023. +# +# References +# ---------- +# .. [1] Driesse, A. (2022) "Module operating temperature model parameter +# determination." Sandia National Laboratories, Albuquerque NM. +# :doi:`10.5281/zenodo.10003736` +# + +import os +import pandas as pd +import matplotlib.pyplot as plt + +import pvlib +from pvlib.temperature import faiman, faiman_dyn, fit_faiman_dyn +from pvlib.temperature import GenericLinearModel + +# %% +# +# Read a CSV file containing one week of weather data and module temperature +# + +PVLIB_DIR = pvlib.__path__[0] +DATA_FILE = os.path.join(PVLIB_DIR, 'data', 'tmod_sample_data_subset.csv') + +df = pd.read_csv(DATA_FILE, index_col=0, parse_dates=True) + +print(df.head()) + +# %% +# +# Estimate the dynamic Faiman model parameters using data where Gpoa > 10 +# to eliminate night time data. +# +# The fitting procedure takes a simple approach to finding the optimal +# thermal_inertia: it tries a range of values and chooses the one that +# produces the lowest RMSE. +# + +dff = df.copy() +dff = dff.where(df.poa_global > 10) + +params, details = fit_faiman_dyn(dff.temp_pv, dff.poa_global, + dff.temp_air, dff.wind_speed, + thermal_inertia=(0, 15, 0.5), + full_output=True) + +for k, v in params.items(): + print('%-15s = %5.2f' % (k, v)) + +# %% +# +# With the full_output option you can obtain the results for all the values +# of thermal_inertia that were evaluated. The optimal point is clearly visible +# below, but a minute shorter or longer actually doesn't make much difference +# in the RMSE. +# + +plt.figure() +plt.plot(details.thermal_inertia, details.rmse, '.-') +plt.grid(alpha=0.5) +plt.xlabel('Thermal inertia [minutes]') +plt.ylabel('RMSE [°C]') +plt.title('Optimal values: u0=%.2f, u1=%.2f, thermal_inertia=%.1f' + % tuple(params.values())) +plt.show() + +# %% +# +# Now calculate the modeled operating temperature of the PV modules. The +# u0 and u1 values found for the dynamic model can be used with the +# regular Faiman model too. +# + +df['temp_pv_faiman'] = faiman(df.poa_global, df.temp_air, df.wind_speed, + u0=params['u0'], u1=params['u1']) +df['temp_pv_faiman_dyn'] = faiman_dyn(df.poa_global, df.temp_air, + df.wind_speed, **params) + +DAY = slice('2020-03-20 7:00', '2020-03-20 19:00') +# sphinx_gallery_thumbnail_number = 2 +plt.figure() +plt.plot(df.temp_pv[DAY]) +plt.plot(df.temp_pv_faiman[DAY], alpha=0.5, zorder=0) +plt.plot(df.temp_pv_faiman_dyn[DAY]) +plt.legend(['measured', 'faiman', 'faiman_dyn']) +plt.grid(alpha=0.5) +plt.xlabel('2020-03-20') +plt.ylabel('PV temperature [°C]') +plt.show() + +# %% + +plt.figure() +l1 = plt.plot(df['temp_pv'], df['temp_pv_faiman'], '.', color='C1') +l2 = plt.plot(df['temp_pv'], df['temp_pv_faiman_dyn'], '.', color='C2') +plt.legend(['faiman', 'faiman_dyn']) +l1[0].set_alpha(0.5) +l2[0].set_alpha(0.25) +plt.grid(alpha=0.5) +plt.xlabel('Measured temperature [°C]') +plt.ylabel('Modeled temperature [°C]') +plt.show() + +# %% +# +# Both graphs above demonstrate that substantial improvement in modeled +# operating temperature is obtained by this simple technique. Perhaps more +# important than this, however, is the fact that parameter values can be +# extracted from field data with minimal or no filtering. +# +# Finally, translate the Faiman model parameters to other model parameters +# using :py:func:`pvlib.temperature.GenericLinearModel()` + +glm = GenericLinearModel(module_efficiency=0.19, absorptance=0.88) +glm = glm.use_faiman(u0=params['u0'], u1=params['u1']) + +# %% PVsyst paramaters + +params_pvsyst = glm.to_pvsyst() + +for k, v in params_pvsyst.items(): + print('%-17s = %5.2f' % (k, v)) + +# %% SAPM parameters + +params_sapm = glm.to_sapm() + +for k, v in params_sapm.items(): + print('%-1s = %5.2f' % (k, v)) diff --git a/docs/sphinx/source/reference/pv_modeling/temperature.rst b/docs/sphinx/source/reference/pv_modeling/temperature.rst index 4c0c7c596b..8d886d39ef 100644 --- a/docs/sphinx/source/reference/pv_modeling/temperature.rst +++ b/docs/sphinx/source/reference/pv_modeling/temperature.rst @@ -12,6 +12,8 @@ PV temperature models temperature.sapm_cell_from_module temperature.pvsyst_cell temperature.faiman + temperature.faiman_dyn + temperature.fit_faiman_dyn temperature.faiman_rad temperature.fuentes temperature.ross diff --git a/docs/sphinx/source/whatsnew/v0.10.3.rst b/docs/sphinx/source/whatsnew/v0.10.3.rst index 007eb8d34b..e58d9ca859 100644 --- a/docs/sphinx/source/whatsnew/v0.10.3.rst +++ b/docs/sphinx/source/whatsnew/v0.10.3.rst @@ -12,6 +12,10 @@ Enhancements * :py:func:`pvlib.bifacial.infinite_sheds.get_irradiance` and :py:func:`pvlib.bifacial.infinite_sheds.get_irradiance_poa` now include shaded fraction in returned variables. (:pull:`1871`) +* Add a simple dynamic version of the Faiman temperature model + :py:func:`pvlib.temperature.faiman_dyn` + and a function to obtain parameters from field data + :py:func:`pvlib.temperature.faiman_dyn`(:issue:`1877`, :pull:`1878`) Bug fixes ~~~~~~~~~ diff --git a/pvlib/data/tmod_sample_data_subset.csv b/pvlib/data/tmod_sample_data_subset.csv new file mode 100644 index 0000000000..61828362fd --- /dev/null +++ b/pvlib/data/tmod_sample_data_subset.csv @@ -0,0 +1,10081 @@ +time,poa_global,wind_speed,temp_air,temp_pv +2020-03-18 00:00:00,0.0,0.7,11.7,3.9 +2020-03-18 00:01:00,0.0,1.0,11.7,4.0 +2020-03-18 00:02:00,0.0,0.8,11.7,3.9 +2020-03-18 00:03:00,0.0,1.1,11.7,3.9 +2020-03-18 00:04:00,0.0,1.0,11.7,3.9 +2020-03-18 00:05:00,0.0,1.2,11.7,3.9 +2020-03-18 00:06:00,0.0,1.1,11.7,3.8 +2020-03-18 00:07:00,0.0,1.0,11.7,3.8 +2020-03-18 00:08:00,0.0,0.9,11.6,3.8 +2020-03-18 00:09:00,0.0,1.1,11.6,3.8 +2020-03-18 00:10:00,0.0,1.1,11.6,3.8 +2020-03-18 00:11:00,0.0,1.6,11.6,3.9 +2020-03-18 00:12:00,0.0,1.4,11.6,3.9 +2020-03-18 00:13:00,0.0,0.9,11.6,4.0 +2020-03-18 00:14:00,0.0,1.0,11.6,4.1 +2020-03-18 00:15:00,0.0,1.4,11.5,4.1 +2020-03-18 00:16:00,0.0,1.4,11.5,4.2 +2020-03-18 00:17:00,0.0,1.3,11.5,4.2 +2020-03-18 00:18:00,0.0,1.1,11.5,4.1 +2020-03-18 00:19:00,0.0,1.0,11.4,4.1 +2020-03-18 00:20:00,0.0,0.8,11.4,4.0 +2020-03-18 00:21:00,0.0,1.0,11.4,4.0 +2020-03-18 00:22:00,0.0,0.9,11.4,4.0 +2020-03-18 00:23:00,0.0,0.9,11.4,4.0 +2020-03-18 00:24:00,0.0,0.8,11.3,3.9 +2020-03-18 00:25:00,0.0,0.9,11.3,3.9 +2020-03-18 00:26:00,0.0,0.9,11.2,3.9 +2020-03-18 00:27:00,0.0,0.6,11.3,3.9 +2020-03-18 00:28:00,0.0,0.7,11.3,4.0 +2020-03-18 00:29:00,0.0,1.0,11.3,4.1 +2020-03-18 00:30:00,0.0,0.8,11.3,4.2 +2020-03-18 00:31:00,0.0,0.7,11.3,4.2 +2020-03-18 00:32:00,0.0,1.0,11.3,4.2 +2020-03-18 00:33:00,0.0,0.6,11.3,4.1 +2020-03-18 00:34:00,0.0,0.5,11.3,4.2 +2020-03-18 00:35:00,0.0,1.0,11.2,4.2 +2020-03-18 00:36:00,0.0,1.1,11.3,4.2 +2020-03-18 00:37:00,0.0,1.2,11.3,4.2 +2020-03-18 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23:52:00,0.0,2.3,11.9,6.0 +2020-03-24 23:53:00,0.0,2.0,11.9,6.1 +2020-03-24 23:54:00,0.0,2.0,11.8,6.1 +2020-03-24 23:55:00,0.0,1.8,11.8,6.1 +2020-03-24 23:56:00,0.0,1.3,11.8,6.1 +2020-03-24 23:57:00,0.0,2.0,11.8,6.1 +2020-03-24 23:58:00,0.0,2.0,11.8,6.1 +2020-03-24 23:59:00,0.0,2.3,11.9,6.1 diff --git a/pvlib/temperature.py b/pvlib/temperature.py index 63cf4baf79..64b5b888d6 100644 --- a/pvlib/temperature.py +++ b/pvlib/temperature.py @@ -6,8 +6,9 @@ import numpy as np import pandas as pd from pvlib.tools import sind -from pvlib._deprecation import warn_deprecated +# from pvlib._deprecation import warn_deprecated from pvlib.tools import _get_sample_intervals +from scipy.optimize import curve_fit import scipy import scipy.constants import warnings @@ -459,6 +460,248 @@ def faiman(poa_global, temp_air, wind_speed=1.0, u0=25.0, u1=6.84): return temp_air + temp_difference +def faiman_dyn(poa_global, temp_air, wind_speed=1.0, u0=25.0, u1=6.84, + thermal_inertia=0): + r''' + Calculate cell or module temperature using the Faiman model augmented + with a thermal inertia term. + + The Faiman model is an empirical heat loss factor model [1]_ and is + adopted in the IEC 61853 standards [2]_ and [3]_. The method of + accounting for thermal inertia was proposed and demonstrated + by Driesse in [4]_. + + The model can be used to represent cell or module temperature. + + Parameters + ---------- + poa_global : pandas.Series with DatetimeIndex + Total incident irradiance [W/m^2]. + + temp_air : numeric + Ambient dry bulb temperature [C]. + + wind_speed : numeric, default 1.0 + Wind speed in m/s measured at the same height for which the wind loss + factor was determined. The default value 1.0 m/s is the wind + speed at module height used to determine NOCT. [m/s] + + u0 : numeric, default 25.0 + Combined heat loss factor coefficient. The default value is one + determined by Faiman for 7 silicon modules + in the Negev desert on an open rack at 30.9° tilt. + :math:`\left[\frac{\text{W}/{\text{m}^2}}{\text{C}}\right]` + + u1 : numeric, default 6.84 + Combined heat loss factor influenced by wind. The default value is one + determined by Faiman for 7 silicon modules + in the Negev desert on an open rack at 30.9° tilt. + :math:`\left[ \frac{\text{W}/\text{m}^2}{\text{C}\ \left( \text{m/s} \right)} \right]` + + thermal_inertia : scalar numeric, default 0.0 + Represents the delay for a change in module temperature + in response to changes in operating conditions. + Typical values are 5-10 minutes. [minutes] + + Returns + ------- + numeric, values in degrees Celsius + + Notes + ----- + Thermal inertia is simulated using a simple moving average on the + operating conditions. + + + References + ---------- + .. [1] Faiman, D. (2008). "Assessing the outdoor operating temperature of + photovoltaic modules." Progress in Photovoltaics 16(4): 307-315. + :doi:`10.1002/pip.813` + + .. [2] "IEC 61853-2 Photovoltaic (PV) module performance testing and energy + rating - Part 2: Spectral responsivity, incidence angle and module + operating temperature measurements". IEC, Geneva, 2018. + + .. [3] "IEC 61853-3 Photovoltaic (PV) module performance testing and energy + rating - Part 3: Energy rating of PV modules". IEC, Geneva, 2018. + + .. [4] Driesse, A. (2022) "Module operating temperature model parameter + determination." Sandia National Laboratories, Albuquerque NM. + :doi:`10.5281/zenodo.10003736` + + See also + -------- + pvlib.temperature.fit_faiman_dyn + pvlib.temperature.faiman + + ''' # noQA: E501 + + if not isinstance(poa_global, pd.Series): + raise ValueError('poa_global must be a pandas Series') + + if not isinstance(poa_global.index, pd.DatetimeIndex): + raise ValueError('poa_global must have a Datetime index') + + # assume the first time increment represent the series time step + # later gaps or large steps will not cause the function to fail + # only some minor glitches in the module temperature may result + time = poa_global.index + timestep = time[1] - time[0] + timestep_minutes = timestep.seconds / 60 + + window = round(2 * thermal_inertia / timestep_minutes) + + if window > 1: + roll_options = dict(window=window, min_periods=1, center=False) + + poa_global = pd.Series(poa_global).rolling(**roll_options).mean() + temp_air = pd.Series(temp_air).rolling(**roll_options).mean() + wind_speed = pd.Series(wind_speed).rolling(**roll_options).mean() + + total_loss_factor = u0 + u1 * wind_speed + heat_input = poa_global + temp_difference = heat_input / total_loss_factor + return temp_air + temp_difference + + +def fit_faiman_dyn(temp_pv, poa_global, temp_air, wind_speed, + thermal_inertia=(0.0, 15.0, 1.0), + full_output=False, **kwargs): + ''' + Determine the optimal parameters for the faiman_dyn temperature model + from a set of measurements using a method proposed and demonstrated + by Driesse in [1]_. + + Parameters + ---------- + temp_pv : numeric + Cell or module temperature [C]. + + poa_global : pandas.Series with DatetimeIndex + Total incident irradiance [W/m^2]. + + temp_air : numeric + Ambient dry bulb temperature [C]. + + wind_speed : numeric, default 1.0 + Wind speed in m/s measured at the same height for which the wind loss + factor was determined. The default value 1.0 m/s is the wind + speed at module height used to determine NOCT. [m/s] + + thermal_inertia : tuple of numeric, default (0.0, 15.0, 1.0) + Represents the delay for a change in module temperature + in response to changes in operating conditions. + This tuple specifies the range of values to be evaluated + in the fitting process: (minimum value, maximum value, increment). + [minutes] + + full_output : boolean, default False + non-zero to return optional output + + kwargs : + Additional arguments passed to scipy curvefit. + + Returns + ------- + p: dict + A dictionary that has the three keys u0, 01, thermal_inertia + and contains the optimal parameter values. + + results : pandas DataFrame + Optional table of model parameters for each value of + thermal_inertia that was evaluated. + + Notes + ----- + Thermal inertia is simulated using a simple moving average of the + operating conditions. The fitting process is repeated for + the range of values specified by the thermal_inertia parameter. + From the collected results, the set of parameters producing the + smallest RMSE is identified as optimal. + + References + ---------- + .. [1] Driesse, A. (2022) "Module operating temperature model parameter + determination." Sandia National Laboratories, Albuquerque NM. + :doi:`10.5281/zenodo.10003736` + + See also + -------- + pvlib.temperature.faiman_dyn + pvlib.temperature.faiman + pvlib.temperature.GenericLinearModel + ''' + + if not isinstance(poa_global, pd.Series): + raise ValueError('poa_global must be a pandas Series') + + if not isinstance(poa_global.index, pd.DatetimeIndex): + raise ValueError('poa_global must have a Datetime index') + + # assume the first time increment represent the series time step + # later gaps or large steps will not cause the function to fail + # only some minor glitches in the module temperature may result + time = poa_global.index + timestep = time[1] - time[0] + timestep_minutes = timestep.seconds / 60 + + # prepare for fitting + def fitfun(xdata, *params): + return faiman(*xdata, *params) + + fit_options = dict(p0=[20, 5]) + fit_options.update(kwargs) + + min_window = max(1, round(2 * thermal_inertia[0] / timestep_minutes)) + max_window = max(1, round(2 * thermal_inertia[1] / timestep_minutes)) + window_inc = max(1, round(2 * thermal_inertia[2] / timestep_minutes)) + + results = [] + + # repeat fits using a range of averaging windows + for window in range(min_window, max_window + 1, window_inc): + + roll_options = dict(window=window, center=False) + + poa_global_mean = pd.Series(poa_global).rolling(**roll_options).mean() + temp_air_mean = pd.Series(temp_air).rolling(**roll_options).mean() + wind_speed_mean = pd.Series(wind_speed).rolling(**roll_options).mean() + + valid = True + for v in temp_pv, poa_global_mean, temp_air_mean, wind_speed_mean: + valid &= np.isfinite(v) + + xdata = [poa_global_mean[valid], + temp_air_mean[valid], + wind_speed_mean[valid]] + ydata = temp_pv[valid] + + popt, pcov = curve_fit(fitfun, xdata, ydata, **fit_options) + + # calculate RMSE + ymodel = fitfun(xdata, *popt) + rmse = np.sqrt(np.nanmean(np.square(ymodel - ydata))) + + inertia = (window / 2) * timestep_minutes + results.append((window, *popt, inertia, rmse)) + + # organize the results + param_names = ['u0', 'u1', 'thermal_inertia'] + result_columns = ['window', *param_names, 'rmse'] + + results = pd.DataFrame(results, columns=result_columns) + + # choose the solution with the smallest RMSE + best_window = results.rmse.idxmin() + best_params = results.loc[best_window, param_names].to_dict() + + if full_output: + return best_params, results + else: + return best_params + + def faiman_rad(poa_global, temp_air, wind_speed=1.0, ir_down=None, u0=25.0, u1=6.84, sky_view=1.0, emissivity=0.88): r''' diff --git a/pvlib/tests/test_temperature.py b/pvlib/tests/test_temperature.py index 6ab4b4730b..277f88a91b 100644 --- a/pvlib/tests/test_temperature.py +++ b/pvlib/tests/test_temperature.py @@ -127,6 +127,72 @@ def test_faiman_ndarray(): assert_allclose(expected, result, atol=0.001) +def test_faiman_dyn_good(): + time = pd.date_range('3/14/15 9:00', periods=13, freq='5T') + df = pd.DataFrame(index=time) + + df['poa_global'] = 0 + df['poa_global'][3:] = 1000 + df['temp_air'] = 25 + df['temp_air'][8:] = -15 + df['wind_speed'] = 1 + + # without thermal inertia + temp_pv = temperature.faiman_dyn(df.poa_global, df.temp_air, df.wind_speed, + u0=20, u1=5, thermal_inertia=0) + expected = [25, 25, 25, 65, 65, 65, 65, 65, 25, 25, 25, 25, 25] + assert_allclose(expected, temp_pv, atol=0.001) + + # with thermal inertia + temp_pv = temperature.faiman_dyn(df.poa_global, df.temp_air, df.wind_speed, + u0=20, u1=5, thermal_inertia=10) + expected = [25, 25, 25, 35, 45, 55, 65, 65, 55, 45, 35, 25, 25] + assert_allclose(expected, temp_pv, atol=0.001) + + +def test_faiman_dyn_bad(): + with pytest.raises(ValueError, match='pandas Series'): + temperature.faiman_dyn(1000, 25) + + with pytest.raises(ValueError, match='Datetime index'): + temperature.faiman_dyn(pd.Series(1000), 25) + + +def test_fit_faiman_dyn_bad(): + with pytest.raises(ValueError, match='pandas Series'): + temperature.fit_faiman_dyn(50, 1000, 25, 1) + + with pytest.raises(ValueError, match='Datetime index'): + temperature.fit_faiman_dyn(50, pd.Series(1000), 25, 1) + + +def test_fit_faiman_dyn_good(): + + time = pd.date_range('3/14/15 9:00', periods=30, freq='2T') + df = pd.DataFrame(index=time) + + df['poa_global'] = np.random.uniform(0, 1000, len(time)) + df['temp_air'] = np.random.uniform(10, 30, len(time)) + df['wind_speed'] = np.random.uniform(0, 5, len(time)) + + expected = dict(u0=26.5, u1=3.5, thermal_inertia=8) + temp_pv = temperature.faiman_dyn(df.poa_global, df.temp_air, df.wind_speed, + **expected) + + params = temperature.fit_faiman_dyn(temp_pv, df.poa_global, + df.temp_air, df.wind_speed, + thermal_inertia=(0, 15, 1)) + for k, v in expected.items(): + assert_allclose(params[k], v, atol=1e-4) + + result = temperature.fit_faiman_dyn(temp_pv, df.poa_global, + df.temp_air, df.wind_speed, + thermal_inertia=(0, 15, 1), + full_output=True) + params, detail = result + assert isinstance(detail, pd.DataFrame) + + def test_faiman_rad_no_ir(): expected = temperature.faiman(900, 20, 5) result = temperature.faiman_rad(900, 20, 5)