8000 Townsend snow by abhisheksparikh · Pull Request #1251 · pvlib/pvlib-python · GitHub
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Townsend snow #1251

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0b736d4
first experimental commit
Jun 25, 2021
3f2c40d
Added numpy array support
Jul 2, 2021
974d516
changed var names
Jul 16, 2021
655fa79
changed townsend_Se to private
Jul 20, 2021
c0c8b4d
removed snow.loss_townsend in api.rst
abhisheksparikh Mar 17, 2022
f0e1f3a
Merge branch 'master' of https://github.com/abhisheksparikh/pvlib-pyt…
abhisheksparikh Mar 17, 2022
78716f7
added loss_townsend description in effects_on_pv_system_output.rst
abhisheksparikh Mar 17, 2022
5e06a40
fixed stickler checks
abhisheksparikh Mar 17, 2022
a5c5315
removed rounding of loss and changed to 0-1 range
abhisheksparikh Mar 18, 2022
f79e906
Merge branch 'master' into townsend_snow
abhisheksparikh Mar 18, 2022
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Added numpy array support
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Abhishek Parikh committed Jul 2, 2021
commit 3f2c40dfd98c0858e3f27169e36a4954ec7b39a6
63 changes: 48 additions & 15 deletions pvlib/snow.py
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Expand Up @@ -214,26 +214,52 @@ def townsend_Se(S, N):
Available at https://www.researchgate.net/publication/261042016_Photovoltaics_and_snow_An_update_from_two_winters_of_measurements_in_the_SIERRA

'''
return (0.5 * S * (1 + 1/N))
return(np.where(N>0, 0.5 * S * (1 + 1/N), 0))

def townsend_snow_loss_model(x):
def townsend_snow_loss_model(S, N, tilt, RH, T_air, POA, R, H, P=40):
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Prefer loss_townsend, and would prefer more descriptive parameter names e.g., snow_total instead of S, num_events instead of N. It's a good idea to maintain traceability to the terms used in the reference but we can do that in the description of each parameter.

'''
Loss, % = C1 x Se’ x cos2
(tilt) x GIT x RH / TAIR2
/ POA0.67Eqn. 3
Calculates monthly snow loss based on a generalized monthly snow loss model discussed in [1]_.

Parameters
----------
snow_coverage : numeric
The fraction of row slant height covered by snow at each time step.
S : numeric
Inches of snow received in the current month

num_strings: int
The number of parallel-connected strings along a row slant height.
N : numeric
Number of snowfall events with snowfall > 1"

tilt : numeric
Array tilt in degrees

RH : numeric
Relative humidity in percentage

T_air : numeric
Ambient temperature in celcius

POA : numeric
Plane of array irradiance in kWh/m2/month

R : numeric
Row length in the slanted plane of array dimension in inches

H : numeric
Drop height from array edge to ground in inches

P : numeric
piled snow angle, assumed to stabilize at 40° , the midpoint of
25°-55° avalanching slope angles

S_prev : numeric
Inches of snow received in the previous month

N_prev : numeric
Number of 1" or greater snow events in the previous month

Returns
-------
loss : numeric
fraction of DC capacity loss due to snow coverage at each time step.
Average monthly DC capacity loss in percentage due to snow coverage

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Let's add a Notes section here pointing out that this model has not been validated for tracking arrays, but the reference suggests using the maximum rotation angle in place of surface_tilt.

References
----------
Expand All @@ -243,13 +269,20 @@ def townsend_snow_loss_model(x):
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
'''

C1 = 5.7e04
C2 = 0.51


gamma = [R*Se’*cos(tilt)]/[(H2 – Se’2)/2*tan(P)]

S_prev = np.roll(S,1)
N_prev = np.roll(N,1)

Se = townsend_Se(S, N)
Se_prev = townsend_Se(S_prev, N_prev)

Se_weighted = 1/3 * Se_prev + 2/3 * Se
gamma = (R * 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)
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I'd also change this to ground_interference_term and use more lines in the equation below.

loss = C1 * Se_ * (np.cos(tilt))**2 * GIT * RH / T_air**2 / POA**0.67
loss = C1 * Se_weighted * (np.cos(np.deg2rad(tilt)))**2 * GIT * RH / (T_air+273.15)**2 / POA**0.67

return x**2
return (np.round(loss,2))
23 changes: 23 additions & 0 deletions pvlib/tests/test_snow.py
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Expand Up @@ -95,3 +95,26 @@ 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_townsend_snow_loss_model():
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])
tilt = 20
RH = np.array([80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80])
T_air = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
POA = np.array([350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350, 350])
P = 40
R = 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.townsend_snow_loss_model(S,N,tilt,RH,T_air,POA,R,
H,P)
np.testing.assert_allclose(expected, actual, rtol=1e-07)

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