def test_newton_fs_495(method, cec_module_fs_495):
"""test pvsystem.singlediode with different methods on FS495"""
fs_495 = cec_module_fs_495
x = pvsystem.calcparams_desoto(
effective_irradiance=POA, temp_cell=TCELL,
alpha_sc=fs_495['alpha_sc'], a_ref=fs_495['a_ref'],
I_L_ref=fs_495['I_L_ref'], I_o_ref=fs_495['I_o_ref'],
R_sh_ref=fs_495['R_sh_ref'], R_s=fs_495['R_s'],
EgRef=1.475, dEgdT=-0.0003)
il, io, rs, rsh, nnsvt = x
x += (101, )
pvs = pvsystem.singlediode(*x, method='lambertw')
out = pvsystem.singlediode(*x, method=method)
isc, voc, imp, vmp, pmp, ix, ixx, i, v = out.values()
assert np.isclose(pvs['i_sc'], isc)
assert np.isclose(pvs['v_oc'], voc)
# the singlediode method doesn't actually get the MPP correct
pvs_imp = pvsystem.i_from_v(rsh, rs, nnsvt, vmp, io, il, method='lambertw')
pvs_vmp = pvsystem.v_from_i(rsh, rs, nnsvt, imp, io, il, method='lambertw')
assert np.isclose(pvs_imp, imp)
assert np.isclose(pvs_vmp, vmp)
assert np.isclose(pvs['p_mp'], pmp)
assert np.isclose(pvs['i_x'], ix)
pvs_ixx = pvsystem.i_from_v(rsh, rs, nnsvt, (voc + vmp)/2, io, il,
method='lambertw')
assert np.isclose(pvs_ixx, ixx)
def test_newton_fs_495():
"""test pvsystem.singlediode with Newton method on FS495"""
fs_495 = CECMOD.First_Solar_FS_495
x = pvsystem.calcparams_desoto(effective_irradiance=POA,
temp_cell=TCELL,
alpha_sc=fs_495.alpha_sc,
a_ref=fs_495.a_ref,
I_L_ref=fs_495.I_L_ref,
I_o_ref=fs_495.I_o_ref,
R_sh_ref=fs_495.R_sh_ref,
R_s=fs_495.R_s,
EgRef=1.475,
dEgdT=-0.0003)
il, io, rs, rsh, nnsvt = x
x += (101, )
pvs = pvsystem.singlediode(*x, method='lambertw')
out = pvsystem.singlediode(*x, method='newton')
isc, voc, imp, vmp, pmp, ix, ixx, i, v = out.values()
assert np.isclose(pvs['i_sc'], isc)
assert np.isclose(pvs['v_oc'], voc)
# the singlediode method doesn't actually get the MPP correct
pvs_imp = pvsystem.i_from_v(rsh, rs, nnsvt, vmp, io, il, method='lambertw')
pvs_vmp = pvsystem.v_from_i(rsh, rs, nnsvt, imp, io, il, method='lambertw')
assert np.isclose(pvs_imp, imp)
assert np.isclose(pvs_vmp, vmp)
assert np.isclose(pvs['p_mp'], pmp)
assert np.isclose(pvs['i_x'], ix)
pvs_ixx = pvsystem.i_from_v(rsh,
rs,
nnsvt, (voc + vmp) / 2,
io,
il,
method='lambertw')
assert np.isclose(pvs_ixx, ixx)
return isc, voc, imp, vmp, pmp, i, v, pvs
def test_newton_fs_495():
"""test pvsystem.singlediode with Newton method on FS495"""
fs_495 = CECMOD.First_Solar_FS_495
x = pvsystem.calcparams_desoto(
effective_irradiance=POA, temp_cell=TCELL,
alpha_sc=fs_495.alpha_sc, a_ref=fs_495.a_ref, I_L_ref=fs_495.I_L_ref,
I_o_ref=fs_495.I_o_ref, R_sh_ref=fs_495.R_sh_ref, R_s=fs_495.R_s,
EgRef=1.475, dEgdT=-0.0003)
il, io, rs, rsh, nnsvt = x
x += (101, )
pvs = pvsystem.singlediode(*x, method='lambertw')
out = pvsystem.singlediode(*x, method='newton')
isc, voc, imp, vmp, pmp, ix, ixx, i, v = out.values()
assert np.isclose(pvs['i_sc'], isc)
assert np.isclose(pvs['v_oc'], voc)
# the singlediode method doesn't actually get the MPP correct
pvs_imp = pvsystem.i_from_v(rsh, rs, nnsvt, vmp, io, il, method='lambertw')
pvs_vmp = pvsystem.v_from_i(rsh, rs, nnsvt, imp, io, il, method='lambertw')
assert np.isclose(pvs_imp, imp)
assert np.isclose(pvs_vmp, vmp)
assert np.isclose(pvs['p_mp'], pmp)
assert np.isclose(pvs['i_x'], ix)
pvs_ixx = pvsystem.i_from_v(rsh, rs, nnsvt, (voc + vmp)/2, io, il,
method='lambertw')
assert np.isclose(pvs_ixx, ixx)
return isc, voc, imp, vmp, pmp, i, v, pvs
def test_brentq_spr_e20_327():
"""test pvsystem.singlediode with Brent method on SPR-E20-327"""
spr_e20_327 = CECMOD.SunPower_SPR_E20_327
x = pvsystem.calcparams_desoto(
effective_irradiance=POA, temp_cell=TCELL,
alpha_sc=spr_e20_327.alpha_sc, a_ref=spr_e20_327.a_ref,
I_L_ref=spr_e20_327.I_L_ref, I_o_ref=spr_e20_327.I_o_ref,
R_sh_ref=spr_e20_327.R_sh_ref, R_s=spr_e20_327.R_s,
EgRef=1.121, dEgdT=-0.0002677)
il, io, rs, rsh, nnsvt = x
pvs = pvsystem.singlediode(*x, method='lambertw')
out = pvsystem.singlediode(*x, method='brentq')
isc, voc, imp, vmp, pmp, ix, ixx = out.values()
assert np.isclose(pvs['i_sc'], isc)
assert np.isclose(pvs['v_oc'], voc)
# the singlediode method doesn't actually get the MPP correct
pvs_imp = pvsystem.i_from_v(rsh, rs, nnsvt, vmp, io, il, method='lambertw')
pvs_vmp = pvsystem.v_from_i(rsh, rs, nnsvt, imp, io, il, method='lambertw')
assert np.isclose(pvs_imp, imp)
assert np.isclose(pvs_vmp, vmp)
assert np.isclose(pvs['p_mp'], pmp)
assert np.isclose(pvs['i_x'], ix)
pvs_ixx = pvsystem.i_from_v(rsh, rs, nnsvt, (voc + vmp)/2, io, il,
method='lambertw')
assert np.isclose(pvs_ixx, ixx)
return isc, voc, imp, vmp, pmp, pvs
def test_method_spr_e20_327(method, cec_module_spr_e20_327):
"""test pvsystem.singlediode with different methods on SPR-E20-327"""
spr_e20_327 = cec_module_spr_e20_327
x = pvsystem.calcparams_desoto(
effective_irradiance=POA, temp_cell=TCELL,
alpha_sc=spr_e20_327['alpha_sc'], a_ref=spr_e20_327['a_ref'],
I_L_ref=spr_e20_327['I_L_ref'], I_o_ref=spr_e20_327['I_o_ref'],
R_sh_ref=spr_e20_327['R_sh_ref'], R_s=spr_e20_327['R_s'],
EgRef=1.121, dEgdT=-0.0002677)
il, io, rs, rsh, nnsvt = x
pvs = pvsystem.singlediode(*x, method='lambertw')
out = pvsystem.singlediode(*x, method=method)
isc, voc, imp, vmp, pmp, ix, ixx = out.values()
assert np.isclose(pvs['i_sc'], isc)
assert np.isclose(pvs['v_oc'], voc)
# the singlediode method doesn't actually get the MPP correct
pvs_imp = pvsystem.i_from_v(rsh, rs, nnsvt, vmp, io, il, method='lambertw')
pvs_vmp = pvsystem.v_from_i(rsh, rs, nnsvt, imp, io, il, method='lambertw')
assert np.isclose(pvs_imp, imp)
assert np.isclose(pvs_vmp, vmp)
assert np.isclose(pvs['p_mp'], pmp)
assert np.isclose(pvs['i_x'], ix)
pvs_ixx = pvsystem.i_from_v(rsh, rs, nnsvt, (voc + vmp)/2, io, il,
method='lambertw')
assert np.isclose(pvs_ixx, ixx)
def _update_io(voc, iph, io, rs, rsh, nnsvth):
"""
Adjusts Io to match Voc using other parameter values.
Helper function for fit_pvsyst_sandia, fit_desoto_sandia
Description
-----------
Io is updated iteratively 10 times or until successive
values are less than 0.000001 % different. The updating is similar to
Newton's method.
Parameters
----------
voc: a numpy array of length N of values for Voc (V)
iph: a numpy array of length N of values for lighbt current IL (A)
io: a numpy array of length N of initial values for Io (A)
rs: a numpy array of length N of values for the series resistance (ohm)
rsh: a numpy array of length N of values for the shunt resistance (ohm)
nnsvth: a numpy array of length N of values for the diode factor x thermal
voltage for the module, equal to Ns (number of cells in series) x
Vth (thermal voltage per cell).
Returns
-------
new_io - a numpy array of length N of updated values for io
References
----------
.. [1] PVLib MATLAB https://github.com/sandialabs/MATLAB_PV_LIB
.. [2] C. Hansen, Parameter Estimation for Single Diode Models of
Photovoltaic Modules, Sandia National Laboratories Report SAND2015-2065
.. [3] C. Hansen, Estimation of Parameteres for Single Diode Models using
Measured IV Curves, Proc. of the 39th IEEE PVSC, June 2013.
"""
eps = 1e-6
niter = 10
k = 1
maxerr = 1
tio = io # Current Estimate of Io
while maxerr > eps and k < niter:
# Predict Voc
pvoc = v_from_i(rsh, rs, nnsvth, 0., tio, iph)
# Difference in Voc
dvoc = pvoc - voc
# Update Io
with np.errstate(invalid="ignore", divide="ignore"):
new_io = tio * (1. + (2. * dvoc) / (2. * nnsvth - dvoc))
# Calculate Maximum Percent Difference
maxerr = np.max(np.abs(new_io - tio) / tio) * 100.
tio = new_io
k += 1.
return new_io
def test_brentq_spr_e20_327():
"""test pvsystem.singlediode with Brent method on SPR-E20-327"""
spr_e20_327 = CECMOD.SunPower_SPR_E20_327
x = pvsystem.calcparams_desoto(effective_irradiance=POA,
temp_cell=TCELL,
alpha_sc=spr_e20_327.alpha_sc,
a_ref=spr_e20_327.a_ref,
I_L_ref=spr_e20_327.I_L_ref,
I_o_ref=spr_e20_327.I_o_ref,
R_sh_ref=spr_e20_327.R_sh_ref,
R_s=spr_e20_327.R_s,
EgRef=1.121,
dEgdT=-0.0002677)
il, io, rs, rsh, nnsvt = x
pvs = pvsystem.singlediode(*x, method='lambertw')
out = pvsystem.singlediode(*x, method='brentq')
isc, voc, imp, vmp, pmp, ix, ixx = out.values()
assert np.isclose(pvs['i_sc'], isc)
assert np.isclose(pvs['v_oc'], voc)
# the singlediode method doesn't actually get the MPP correct
pvs_imp = pvsystem.i_from_v(rsh, rs, nnsvt, vmp, io, il, method='lambertw')
pvs_vmp = pvsystem.v_from_i(rsh, rs, nnsvt, imp, io, il, method='lambertw')
assert np.isclose(pvs_imp, imp)
assert np.isclose(pvs_vmp, vmp)
assert np.isclose(pvs['p_mp'], pmp)
assert np.isclose(pvs['i_x'], ix)
pvs_ixx = pvsystem.i_from_v(rsh,
rs,
nnsvt, (voc + vmp) / 2,
io,
il,
method='lambertw')
assert np.isclose(pvs_ixx, ixx)
return isc, voc, imp, vmp, pmp, pvs
def test_v_from_i(fixture_v_from_i, method, atol):
# Solution set loaded from fixture
Rsh = fixture_v_from_i['Rsh']
Rs = fixture_v_from_i['Rs']
nNsVth = fixture_v_from_i['nNsVth']
I = fixture_v_from_i['I']
I0 = fixture_v_from_i['I0']
IL = fixture_v_from_i['IL']
V_expected = fixture_v_from_i['V_expected']
V = pvsystem.v_from_i(Rsh, Rs, nNsVth, I, I0, IL, method=method)
assert (isinstance(V, type(V_expected)))
if isinstance(V, type(np.ndarray)):
assert (isinstance(V.dtype, type(V_expected.dtype)))
assert (V.shape == V_expected.shape)
assert_allclose(V, V_expected, atol=atol)
def test_v_from_i(fixture_v_from_i):
# Solution set loaded from fixture
Rsh = fixture_v_from_i['Rsh']
Rs = fixture_v_from_i['Rs']
nNsVth = fixture_v_from_i['nNsVth']
I = fixture_v_from_i['I']
I0 = fixture_v_from_i['I0']
IL = fixture_v_from_i['IL']
V_expected = fixture_v_from_i['V_expected']
# Convergence criteria
atol = 1.e-11
V = pvsystem.v_from_i(Rsh, Rs, nNsVth, I, I0, IL)
assert(isinstance(V, type(V_expected)))
if isinstance(V, type(np.ndarray)):
assert(isinstance(V.dtype, type(V_expected.dtype)))
assert(V.shape == V_expected.shape)
assert_allclose(V, V_expected, atol=atol)
def test_v_from_i_size():
with pytest.raises(ValueError):
pvsystem.v_from_i(20, [0.1] * 2, 0.5, [3.0] * 3, 6.0e-7, 7.0)
with pytest.raises(ValueError):
pvsystem.v_from_i(20, [0.1] * 2,
0.5, [3.0] * 3,
6.0e-7,
7.0,
method='brentq')
with pytest.raises(ValueError):
pvsystem.v_from_i(20, [0.1],
0.5, [3.0] * 3,
6.0e-7,
np.array([7., 7.]),
method='newton')
def test_v_from_i():
output = pvsystem.v_from_i(20, .1, .5, 3, 6e-7, 7)
assert_allclose(7.5049875193450521, output, atol=1e-5)
def test_v_from_i_big():
output = pvsystem.v_from_i(500, 10, 4.06, 0, 6e-10, 1.2)
assert_almost_equals(86.320000493521079, output, 5)
def test_v_from_i():
output = pvsystem.v_from_i(20, .1, .5, 3, 6e-7, 7)
assert_almost_equals(7.5049875193450521, output, 5)
def update_io_known_n(rsh, rs, nnsvth, io, il, voc):
"""
update_io_known_n adjusts io to match voc using other parameter values.
Syntax
------
outio = update_io_known_n(rsh, rs, nnsvth, io, il, voc)
Description
-----------
update_io_known_n adjusts io to match voc using other parameter values,
i.e., Rsh (shunt resistance), Rs (Series Resistance), n (diode factor), and
IL (Light Current). Io is updated iteratively 10 times or until successive
values are less than 0.000001 % different. The updating is similar to
Newton's method.
Parameters
----------
rsh: a numpy array of length N of values for the shunt resistance (ohm)
rs: a numpy array of length N of values for the series resistance (ohm)
nnsvth: a numpy array of length N of values for the diode factor x thermal
voltage for the module, equal to Ns (number of cells in series) x
Vth (thermal voltage per cell).
io: a numpy array of length N of initial values for Io (A)
il: a numpy array of length N of values for lighbt current IL (A)
voc: a numpy array of length N of values for Voc (V)
Returns
-------
outio - a numpy array of lenght N of updated values for Io
References
----------
[1] PVLib MATLAB
[2] C. Hansen, Parameter Estimation for Single Diode Models of Photovoltaic
Modules, Sandia National Laboratories Report SAND2015-XXXX
[3] C. Hansen, Estimation of Parameteres for Single Diode Models using
Measured IV Curves, Proc. of the 39th IEEE PVSC, June 2013.
"""
eps = 1e-6
niter = 10
k = 1
maxerr = 1
tio = io # Current Estimate of Io
while maxerr > eps and k < niter:
# Predict Voc
pvoc = v_from_i(rsh, rs, nnsvth, 0., tio, il)
# Difference in Voc
dvoc = pvoc - voc
# Update Io
next_io = tio * (1. + (2. * dvoc) / (2. * nnsvth - dvoc))
# Calculate Maximum Percent Difference
maxerr = np.max(np.abs(next_io - tio) / tio) * 100.
tio = next_io
k += 1.
outio = tio
return outio
def test_v_from_i_bigger():
# 1000 W/m^2 on a Canadian Solar 220M with 20 C ambient temp
# github issue 225
output = pvsystem.v_from_i(190, 1.065, 2.89, 0, 7.05196029e-08, 10.491262)
assert_allclose(54.303958833791455, output, atol=1e-5)
def test_v_from_i_big():
output = pvsystem.v_from_i(500, 10, 4.06, 0, 6e-10, 1.2)
assert_allclose(86.320000493521079, output, atol=1e-5)
def test_v_from_i():
output = pvsystem.v_from_i(20, .1, .5, 3, 6e-7, 7)
assert_allclose(7.5049875193450521, output, atol=1e-5)
def test_v_from_i_big():
output = pvsystem.v_from_i(500, 10, 4.06, 0, 6e-10, 1.2)
assert_allclose(86.320000493521079, output, atol=1e-5)
def test_v_from_i_bigger():
# 1000 W/m^2 on a Canadian Solar 220M with 20 C ambient temp
# github issue 225
output = pvsystem.v_from_i(190, 1.065, 2.89, 0, 7.05196029e-08, 10.491262)
assert_allclose(54.303958833791455, output, atol=1e-5)
def test_singlediode_series_ivcurve(cec_module_params):
times = pd.date_range(start='2015-06-01', periods=3, freq='6H')
effective_irradiance = pd.Series([0.0, 400.0, 800.0], index=times)
IL, I0, Rs, Rsh, nNsVth = pvsystem.calcparams_desoto(
effective_irradiance,
temp_cell=25,
alpha_sc=cec_module_params['alpha_sc'],
a_ref=cec_module_params['a_ref'],
I_L_ref=cec_module_params['I_L_ref'],
I_o_ref=cec_module_params['I_o_ref'],
R_sh_ref=cec_module_params['R_sh_ref'],
R_s=cec_module_params['R_s'],
EgRef=1.121,
dEgdT=-0.0002677)
out = pvsystem.singlediode(IL,
I0,
Rs,
Rsh,
nNsVth,
ivcurve_pnts=3,
method='lambertw')
expected = OrderedDict([
('i_sc', array([0., 3.01054475, 6.00675648])),
('v_oc', array([0., 9.96886962, 10.29530483])),
('i_mp', array([0., 2.65191983, 5.28594672])),
('v_mp', array([0., 8.33392491, 8.4159707])),
('p_mp', array([0., 22.10090078, 44.48637274])),
('i_x', array([0., 2.88414114, 5.74622046])),
('i_xx', array([0., 2.04340914, 3.90007956])),
('v',
array([[0., 0., 0.], [0., 4.98443481, 9.96886962],
[0., 5.14765242, 10.29530483]])),
('i',
array([[0., 0., 0.], [3.01079860e+00, 2.88414114e+00, 3.10862447e-14],
[6.00726296e+00, 5.74622046e+00, 0.00000000e+00]]))
])
for k, v in out.items():
assert_allclose(v, expected[k], atol=1e-2)
out = pvsystem.singlediode(IL, I0, Rs, Rsh, nNsVth, ivcurve_pnts=3)
expected['i_mp'] = pvsystem.i_from_v(Rsh,
Rs,
nNsVth,
out['v_mp'],
I0,
IL,
method='lambertw')
expected['v_mp'] = pvsystem.v_from_i(Rsh,
Rs,
nNsVth,
out['i_mp'],
I0,
IL,
method='lambertw')
expected['i'] = pvsystem.i_from_v(Rsh,
Rs,
nNsVth,
out['v'].T,
I0,
IL,
method='lambertw').T
expected['v'] = pvsystem.v_from_i(Rsh,
Rs,
nNsVth,
out['i'].T,
I0,
IL,
method='lambertw').T
for k, v in out.items():
assert_allclose(v, expected[k], atol=1e-2)
def test_v_from_i_big():
output = pvsystem.v_from_i(500, 10, 4.06, 0, 6e-10, 1.2)
assert_almost_equals(86.320000493521079, output, 5)
def test_v_from_i():
output = pvsystem.v_from_i(20, .1, .5, 3, 6e-7, 7)
assert_almost_equals(7.5049875193450521, output, 5)
