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
 -------

pvlib/snow.py

@@ -185,3 +185,107 @@ 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
+
+    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
+    return(np.where(N > 0, 0.5 * S * (1 + 1/N), 0))
+
+
+def loss_townsend(snow_total, snow_events, tilt, relative_humidity, temp_air,
+                  poa_global, row_len, H, P=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
+
+    snow_events : numeric
+        Number of snowfall events with snowfall > 1". Referred as N in the
+        paper
+
+    tilt : numeric
+        Array tilt in degrees
+
+    relative_humidity : numeric
+        Relative humidity in percentage
+
+    temp_air : numeric
+        Ambient temperature [C]
+
+    poa_global : numeric
+        Plane of array insolation in kWh/m2/month
+
+    row_len : float
+        Row length in the slanted plane of array dimension in inches
+
+    H : float
+        Drop height from array edge to ground in inches
+
+    P : float
+        piled snow angle, assumed to stabilize at 40° , the midpoint of
+        25°-55° avalanching slope angles
+
+    Returns
+    -------
+    loss : numeric
+        Average monthly DC capacity loss in percentage 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
+
+    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 = (row_len * Se_weighted * np.cos(np.deg2rad(tilt))) / \
+        (np.clip((H**2 - Se_weighted**2), a_min=0.01, a_max=None) / 2 /
+            np.tan(np.deg2rad(P)))
+
+    GIT = 1 - C2 * np.exp(-gamma)
+    loss = C1 * Se_weighted * (np.cos(np.deg2rad(tilt)))**2 * GIT * \
+        relative_humidity / (temp_air+273.15)**2 / poa_global**0.67
+
+    return (np.round(loss, 2))

pvlib/tests/test_snow.py

@@ -95,3 +95,30 @@ 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])
+    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])
+    P = 40
+    row_len = 100
+    H = 10
+    expected = np.array([7.7, 7.99, 6.22, 1.72, 0, 0, 0, 0, 0, 0, 2.64, 6.07])
+    actual = snow.loss_townsend(snow_total, snow_events, tilt,
+                                relative_humidity, temp_air,
+                                poa_global, row_len, H, P)
+    np.testing.assert_allclose(expected, actual, rtol=1e-07)