Townsend snow

docs/sphinx/source/reference/effects_on_pv_system_output.rst

@@ -21,6 +21,7 @@ Snow
    snow.coverage_nrel
    snow.fully_covered_nrel
    snow.dc_loss_nrel
+   snow.loss_townsend
 
 Soiling
 -------

docs/sphinx/source/whatsnew/v0.9.1.rst

@@ -28,6 +28,8 @@ Enhancements
 * Added ``map_variables`` option to :func:`~pvlib.iotools.read_crn` (:pull:`1368`)
 * Added :py:func:`pvlib.temperature.prilliman` for modeling cell temperature
   at short time steps (:issue:`1081`, :pull:`1391`)
+* Added Townsend Powers Snow loss model in :py:func:`pvlib.snow`
+  (:issue:`1246`, :pull:`1251`)
 
 Bug fixes
 ~~~~~~~~~
@@ -83,3 +85,5 @@ Contributors
 * Jack Kelly (:ghuser:`JackKelly`)
 * Somasree Majumder(:ghuser:`soma2000-lang`)
 * Naman Priyadarshi (:ghuser:`Naman-Priyadarshi`)
+* Abhishek Parikh (:ghuser:`abhisheksparikh`)
+

pvlib/snow.py

@@ -5,7 +5,7 @@
 
 import numpy as np
 import pandas as pd
-from pvlib.tools import sind
+from pvlib.tools import sind, cosd, tand
 
 
 def _time_delta_in_hours(times):
@@ -185,3 +185,108 @@ def dc_loss_nrel(snow_coverage, num_strings):
        Available at https://www.nrel.gov/docs/fy18osti/67399.pdf
     '''
     return np.ceil(snow_coverage * num_strings) / num_strings
+
+
+def _townsend_Se(S, N):
+    '''
+    Calculates effective snow for a given month based upon the total snowfall
+    received in a month in inches and the number of events where snowfall is
+    greater than 1 inch
+
+    Parameters
+    ----------
+    S : numeric
+        Snowfall in inches received in a month [in]
+
+    N: numeric
+        Number of snowfall events with snowfall > 1" [-]
+
+    Returns
+    -------
+    effective_snowfall : numeric
+        Effective snowfall as defined in the townsend model
+
+    References
+    ----------
+    .. [1] Townsend, Tim & Powers, Loren. (2011). Photovoltaics and snow: An
+       update from two winters of measurements in the SIERRA. Conference
+       Record of the IEEE Photovoltaic Specialists Conference.
+       003231-003236. :doi:`10.1109/PVSC.2011.6186627`
+       Available at https://www.researchgate.net/publication/261042016_Photovoltaics_and_snow_An_update_from_two_winters_of_measurements_in_the_SIERRA
+
+    '''  # noqa: E501
+    return(np.where(N > 0, 0.5 * S * (1 + 1/N), 0))
+
+
+def loss_townsend(snow_total, snow_events, surface_tilt, relative_humidity,
+                  temp_air, poa_global, slant_height, lower_edge_drop_height,
+                  angle_of_repose=40):
+    '''
+    Calculates monthly snow loss based on a generalized monthly snow loss model
+    discussed in [1]_.
+
+    Parameters
+    ----------
+    snow_total : numeric
+        Inches of snow received in the current month. Referred as S in the
+        paper [in]
+
+    snow_events : numeric
+        Number of snowfall events with snowfall > 1". Referred as N in the
+        paper [-]
+
+    surface_tilt : numeric
+        Array surface_tilt [deg]
+
+    relative_humidity : numeric
+        Relative humidity [%]
+
+    temp_air : numeric
+        Ambient temperature [°C]
+
+    poa_global : numeric
+        Plane of array insolation [kWh/m2/month]
+
+    slant_height : float
+        Row length in the slanted plane of array dimension [in]
+
+    lower_edge_drop_height : float
+        Drop height from array edge to ground [in]
+
+    P : float
+        piled snow angle, assumed to stabilize at 40° , the midpoint of
+        25°-55° avalanching slope angles [deg]
+
+    Returns
+    -------
+    loss : numeric
+        Average monthly DC capacity loss due to snow coverage [%]
+
+    References
+    ----------
+    .. [1] Townsend, Tim & Powers, Loren. (2011). Photovoltaics and snow: An
+       update from two winters of measurements in the SIERRA. Conference
+       Record of the IEEE Photovoltaic Specialists Conference.
+       003231-003236. 10.1109/PVSC.2011.6186627.
+       Available at https://www.researchgate.net/publication/261042016_Photovoltaics_and_snow_An_update_from_two_winters_of_measurements_in_the_SIERRA
+    '''  # noqa: E501
+
+    C1 = 5.7e04
+    C2 = 0.51
+
+    snow_total_prev = np.roll(snow_total, 1)
+    snow_events_prev = np.roll(snow_events, 1)
+
+    Se = _townsend_Se(snow_total, snow_events)
+    Se_prev = _townsend_Se(snow_total_prev, snow_events_prev)
+
+    Se_weighted = 1/3 * Se_prev + 2/3 * Se
+    gamma = (slant_height * Se_weighted * cosd(surface_tilt)) / \
+        (np.clip((lower_edge_drop_height**2 - Se_weighted**2), a_min=0.01,
+         a_max=None) / 2 / tand(angle_of_repose))
+
+    GIT = 1 - C2 * np.exp(-gamma)
+    loss = (C1 * Se_weighted * (cosd(surface_tilt))**2 * GIT *
+            relative_humidity / (temp_air+273.15)**2 / poa_global**0.67) / 100
+
+    return loss

pvlib/tests/test_snow.py

@@ -95,3 +95,32 @@ def test_dc_loss_nrel():
     expected = pd.Series([1, 1, .5, .625, .25, .5, 0])
     actual = snow.dc_loss_nrel(snow_coverage, num_strings)
     assert_series_equal(expected, actual)
+
+
+def test__townsend_Se():
+    S = np.array([10, 10, 5, 1, 0, 0, 0, 0, 0, 0, 5, 10])
+    N = np.array([2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 3])
+    expected = np.array([7.5, 7.5, 5, 0, 0, 0, 0, 0, 0, 0, 3.75, 6.66666667])
+    actual = snow._townsend_Se(S, N)
+    np.testing.assert_allclose(expected, actual, rtol=1e-07)
+
+
+def test_loss_townsend():
+    snow_total = np.array([10, 10, 5, 1, 0, 0, 0, 0, 0, 0, 5, 10])
+    snow_events = np.array([2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 3])
+    surface_tilt = 20
+    relative_humidity = np.array([80, 80, 80, 80, 80, 80, 80, 80, 80, 80,
+                                  80, 80])
+    temp_air = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
+    poa_global = np.array([350, 350, 350, 350, 350, 350, 350, 350, 350, 350,
+                           350, 350])
+    angle_of_repose = 40
+    slant_height = 100
+    lower_edge_drop_height = 10
+    expected = np.array([0.07696253, 0.07992262, 0.06216201, 0.01715392, 0, 0,
+                         0, 0, 0, 0, 0.02643821, 0.06068194])
+    actual = snow.loss_townsend(snow_total, snow_events, surface_tilt,
+                                relative_humidity, temp_air,
+                                poa_global, slant_height,
+                                lower_edge_drop_height, angle_of_repose)
+    np.testing.assert_allclose(expected, actual, rtol=1e-05)