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Apr 11, 2020
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add capability for reverse bias #948

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c95ac2a
add capability for reverse bias
cwhanse Mar 31, 2020
4f07c04
lint, correct test_pvsyst_breakdown
cwhanse Mar 31, 2020
90692a7
default value for breakdown_factor
cwhanse Apr 1, 2020
70553fa
handle recombination in breakdown test, lint
cwhanse Apr 1, 2020
4bb530c
correct parameter parsing
cwhanse Apr 1, 2020
4bcb468
whatsnew
cwhanse Apr 1, 2020
bcb93bf
Update pvlib/tests/test_singlediode.py
cwhanse Apr 6, 2020
32f8017
Update pvlib/singlediode.py
cwhanse Apr 6, 2020
9dbfdf2
Update pvlib/singlediode.py
cwhanse Apr 6, 2020
0ddde4c
fix formatting
cwhanse Apr 6, 2020
21a7edc
improve docstring
cwhanse Apr 6, 2020
9445d32
lint
cwhanse Apr 6, 2020
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4 changes: 4 additions & 0 deletions docs/sphinx/source/whatsnew/v0.7.2.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -25,6 +25,10 @@ Enhancements
* Add new module :py:mod:`pvlib.snow` to contain models related to snow coverage and effects on a PV system. (:pull:`764`)
* Add snow coverage model :py:func:`pvlib.snow.coverage_nrel` and function to identify when modules are fully covered by snow :py:func:`pvlib.snow.fully_covered_nrel`. (:issue:`577`)
* Add function :py:func:`pvlib.snow.dc_loss_nrel` for effect of snow coverage on DC output. (:pull:`764`)
* Add capability to calculate current at reverse bias using an avalanche
breakdown model, affects :py:func:`pvlib.singlediode.bishop88`,
:py:func:`pvlib.singlediode.bishop88_i_from_v`, :py:func:`pvlib.singlediode.bishop88_v_from_i`,
:py:func:`pvlib.singlediode.bishop88_mpp`. (:pull:`948`)

Bug fixes
~~~~~~~~~
Expand Down
184 changes: 132 additions & 52 deletions pvlib/singlediode.py
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Original file line number Diff line number Diff line change
Expand Up @@ -69,42 +69,65 @@ def estimate_voc(photocurrent, saturation_current, nNsVth):

def bishop88(diode_voltage, photocurrent, saturation_current,
resistance_series, resistance_shunt, nNsVth, d2mutau=0,
NsVbi=np.Inf, gradients=False):
"""
NsVbi=np.Inf, breakdown_factor=0., breakdown_voltage=-5.5,
breakdown_exp=3.28, gradients=False):
r"""
Explicit calculation of points on the IV curve described by the single
diode equation. Values are calculated as described in [1]_.

The single diode equation with recombination current and reverse bias
breakdown is

.. math::

I = I_{L} - I_{0} (\exp \frac{V_{d}}{nNsVth} - 1)
- \frac{V_{d}}{R_{sh}}
- \frac{I_{L} \frac{d^{2}}{\mu \tau}{N_{s} V_{bi} - V_{d}}
- a \frac{V_{d}{R_{sh}} (1 - \frac{V_{d}}{V_{br}})^-m

The input `diode_voltage` must be :math:`V + I R_{s}`.


.. warning::
* Usage of ``d2mutau`` is required with PVSyst
coefficients for cadmium-telluride (CdTe) and amorphous-silicon
(a:Si) PV modules only.
* Do not use ``d2mutau`` with CEC coefficients.
* Usage of ``d2mutau`` with PVSyst coefficients is required for cadmium-
telluride (CdTe) and amorphous-silicon (a:Si) PV modules only.

Parameters
----------
diode_voltage : numeric
diode voltages [V]
photocurrent : numeric
photo-generated current [A]
photo-generated current :math:`I_{L}` [A]
saturation_current : numeric
diode reverse saturation current [A]
diode reverse saturation current :math:`I_{0}` [A]
resistance_series : numeric
series resistance [ohms]
series resistance :math:`R_{s}` [ohms]
resistance_shunt: numeric
shunt resistance [ohms]
shunt resistance :math:`R_{sh}` [ohms]
nNsVth : numeric
product of thermal voltage ``Vth`` [V], diode ideality factor ``n``,
and number of series cells ``Ns``
product of thermal voltage :math:`V_{th}` [V], diode ideality factor
``n``, and number of series cells :math:`N_{s}`
d2mutau : numeric, default 0
PVsyst parameter for cadmium-telluride (CdTe) and amorphous-silicon
(a-Si) modules that accounts for recombination current in the
intrinsic layer. The value is the ratio of intrinsic layer thickness
squared :math:`d^2` to the diffusion length of charge carriers
:math:`\\mu \\tau`. [V]
:math:`\mu \tau`. [V]
NsVbi : numeric, default np.inf
PVsyst parameter for cadmium-telluride (CdTe) and amorphous-silicon
(a-Si) modules that is the product of the PV module number of series
cells ``Ns`` and the builtin voltage ``Vbi`` of the intrinsic layer.
[V].
cells :math:`N_{s}` and the builtin voltage :math:`V_{bi}` of the
intrinsic layer. [V].
breakdown_factor : numeric, default 0
fraction of ohmic current involved in avalanche breakdown :math:`a`.
Default of 0 excludes the reverse bias term from the model. [unitless]
breakdown_voltage : numeric, default -5.5
reverse breakdown voltage of the photovoltaic junction :math:`V_{br}`
[V]
breakdown_exp : numeric, default 3.28
avalanche breakdown exponent :math:`m` [unitless]
gradients : bool
False returns only I, V, and P. True also returns gradients

Expand Down Expand Up @@ -150,21 +173,39 @@ def bishop88(diode_voltage, photocurrent, saturation_current,
# calculate temporary values to simplify calculations
v_star = diode_voltage / nNsVth # non-dimensional diode voltage
g_sh = 1.0 / resistance_shunt # conductance
i = (photocurrent - saturation_current * np.expm1(v_star)
- diode_voltage * g_sh - i_recomb)
if breakdown_factor > 0: # reverse bias is considered
brk_term = 1 - diode_voltage / breakdown_voltage
brk_pwr = np.power(brk_term, -breakdown_exp)
i_breakdown = breakdown_factor * diode_voltage * g_sh * brk_pwr
else:
i_breakdown = 0.
i = (photocurrent - saturation_current * np.expm1(v_star) -
diode_voltage * g_sh - i_recomb - i_breakdown)
v = diode_voltage - i * resistance_series
retval = (i, v, i*v)
if gradients:
# calculate recombination loss current gradients where d2mutau > 0
grad_i_recomb = np.where(is_recomb, i_recomb / v_recomb, 0)
grad_2i_recomb = np.where(is_recomb, 2 * grad_i_recomb / v_recomb, 0)
g_diode = saturation_current * np.exp(v_star) / nNsVth # conductance
grad_i = -g_diode - g_sh - grad_i_recomb # di/dvd
if breakdown_factor > 0: # reverse bias is considered
brk_pwr_1 = np.power(brk_term, -breakdown_exp - 1)
brk_pwr_2 = np.power(brk_term, -breakdown_exp - 2)
brk_fctr = breakdown_factor * g_sh
grad_i_brk = brk_fctr * (brk_pwr + diode_voltage *
-breakdown_exp * brk_pwr_1)
grad2i_brk = brk_fctr * -breakdown_exp * (
2 * brk_pwr_1 + diode_voltage * (-breakdown_exp - 1) *
brk_pwr_2)
else:
grad_i_brk = 0.
grad2i_brk = 0.
grad_i = -g_diode - g_sh - grad_i_recomb - grad_i_brk # di/dvd
grad_v = 1.0 - grad_i * resistance_series # dv/dvd
# dp/dv = d(iv)/dv = v * di/dv + i
grad = grad_i / grad_v # di/dv
grad_p = v * grad + i # dp/dv
grad2i = -g_diode / nNsVth - grad_2i_recomb # d2i/dvd
grad2i = -g_diode / nNsVth - grad_2i_recomb - grad2i_brk # d2i/dvd
grad2v = -grad2i * resistance_series # d2v/dvd
grad2p = (
grad_v * grad + v * (grad2i/grad_v - grad_i*grad2v/grad_v**2)
Expand All @@ -176,7 +217,9 @@ def bishop88(diode_voltage, photocurrent, saturation_current,

def bishop88_i_from_v(voltage, photocurrent, saturation_current,
resistance_series, resistance_shunt, nNsVth,
d2mutau=0, NsVbi=np.Inf, method='newton'):
d2mutau=0, NsVbi=np.Inf, breakdown_factor=0.,
breakdown_voltage=-5.5, breakdown_exp=3.28,
method='newton'):
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As a convention, is it better to add new kwargs at the end, E.g. after method='newton', so it doesn't break code that relies on position than explicit kwarg= usage?

I'm half asking if that's something that's been historically done.

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I agree, but would like to keep like arguments grouped together in general order of decreasing interest: required module parameters first, then optional thin-film parameters, reverse bias parameters third, numerical control last.

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I think it's bad form to rely on the position of a keyword argument. Don't worry about it.

"""
Find current given any voltage.

Expand All @@ -185,13 +228,13 @@ def bishop88_i_from_v(voltage, photocurrent, saturation_current,
voltage : numeric
voltage (V) in volts [V]
photocurrent : numeric
photogenerated current (Iph or IL) in amperes [A]
photogenerated current (Iph or IL) [A]
saturation_current : numeric
diode dark or saturation current (Io or Isat) in amperes [A]
diode dark or saturation current (Io or Isat) [A]
resistance_series : numeric
series resistance (Rs) in ohms
series resistance (Rs) in [Ohm]
resistance_shunt : numeric
shunt resistance (Rsh) in ohms
shunt resistance (Rsh) [Ohm]
nNsVth : numeric
product of diode ideality factor (n), number of series cells (Ns), and
thermal voltage (Vth = k_b * T / q_e) in volts [V]
Expand All @@ -206,18 +249,27 @@ def bishop88_i_from_v(voltage, photocurrent, saturation_current,
(a-Si) modules that is the product of the PV module number of series
cells ``Ns`` and the builtin voltage ``Vbi`` of the intrinsic layer.
[V].
method : str
one of two optional search methods: either ``'brentq'``, a reliable and
bounded method or ``'newton'`` which is the default.
breakdown_factor : numeric, default 0
fraction of ohmic current involved in avalanche breakdown :math:`a`.
Default of 0 excludes the reverse bias term from the model. [unitless]
breakdown_voltage : numeric, default -5.5
reverse breakdown voltage of the photovoltaic junction :math:`V_{br}`
[V]
breakdown_exp : numeric, default 3.28
avalanche breakdown exponent :math:`m` [unitless]
method : str, default 'newton'
must be either ``'newton'`` or ``'brentq'``. If ``'breakdown_factor'``
is not 0, must be ``'newton'``.

Returns
-------
current : numeric
current (I) at the specified voltage (V) in amperes [A]
current (I) at the specified voltage (V). [A]
"""
# collect args
args = (photocurrent, saturation_current, resistance_series,
resistance_shunt, nNsVth, d2mutau, NsVbi)
resistance_shunt, nNsVth, d2mutau, NsVbi,
breakdown_factor, breakdown_voltage, breakdown_exp)

def fv(x, v, *a):
# calculate voltage residual given diode voltage "x"
Expand All @@ -230,9 +282,12 @@ def fv(x, v, *a):
# brentq only works with scalar inputs, so we need a set up function
# and np.vectorize to repeatedly call the optimizer with the right
# arguments for possible array input
def vd_from_brent(voc, v, iph, isat, rs, rsh, gamma, d2mutau, NsVbi):
def vd_from_brent(voc, v, iph, isat, rs, rsh, gamma, d2mutau, NsVbi,
breakdown_factor, breakdown_voltage, breakdown_exp):
return brentq(fv, 0.0, voc,
args=(v, iph, isat, rs, rsh, gamma, d2mutau, NsVbi))
args=(v, iph, isat, rs, rsh, gamma, d2mutau, NsVbi,
breakdown_factor, breakdown_voltage,
breakdown_exp))

vd_from_brent_vectorized = np.vectorize(vd_from_brent)
vd = vd_from_brent_vectorized(voc_est, voltage, *args)
Expand All @@ -250,7 +305,9 @@ def vd_from_brent(voc, v, iph, isat, rs, rsh, gamma, d2mutau, NsVbi):

def bishop88_v_from_i(current, photocurrent, saturation_current,
resistance_series, resistance_shunt, nNsVth,
d2mutau=0, NsVbi=np.Inf, method='newton'):
d2mutau=0, NsVbi=np.Inf, breakdown_factor=0.,
breakdown_voltage=-5.5, breakdown_exp=3.28,
method='newton'):
"""
Find voltage given any current.

Expand All @@ -259,13 +316,13 @@ def bishop88_v_from_i(current, photocurrent, saturation_current,
current : numeric
current (I) in amperes [A]
photocurrent : numeric
photogenerated current (Iph or IL) in amperes [A]
photogenerated current (Iph or IL) [A]
saturation_current : numeric
diode dark or saturation current (Io or Isat) in amperes [A]
diode dark or saturation current (Io or Isat) [A]
resistance_series : numeric
series resistance (Rs) in ohms
series resistance (Rs) in [Ohm]
resistance_shunt : numeric
shunt resistance (Rsh) in ohms
shunt resistance (Rsh) [Ohm]
nNsVth : numeric
product of diode ideality factor (n), number of series cells (Ns), and
thermal voltage (Vth = k_b * T / q_e) in volts [V]
Expand All @@ -280,9 +337,17 @@ def bishop88_v_from_i(current, photocurrent, saturation_current,
(a-Si) modules that is the product of the PV module number of series
cells ``Ns`` and the builtin voltage ``Vbi`` of the intrinsic layer.
[V].
method : str
one of two optional search methods: either ``'brentq'``, a reliable and
bounded method or ``'newton'`` which is the default.
breakdown_factor : numeric, default 0
fraction of ohmic current involved in avalanche breakdown :math:`a`.
Default of 0 excludes the reverse bias term from the model. [unitless]
breakdown_voltage : numeric, default -5.5
reverse breakdown voltage of the photovoltaic junction :math:`V_{br}`
[V]
breakdown_exp : numeric, default 3.28
avalanche breakdown exponent :math:`m` [unitless]
method : str, default 'newton'
must be either ``'newton'`` or ``'brentq'``. If ``'breakdown_factor'``
is not 0, must be ``'newton'``.

Returns
-------
Expand All @@ -291,7 +356,8 @@ def bishop88_v_from_i(current, photocurrent, saturation_current,
"""
# collect args
args = (photocurrent, saturation_current, resistance_series,
resistance_shunt, nNsVth, d2mutau, NsVbi)
resistance_shunt, nNsVth, d2mutau, NsVbi, breakdown_factor,
breakdown_voltage, breakdown_exp)
# first bound the search using voc
voc_est = estimate_voc(photocurrent, saturation_current, nNsVth)

Expand All @@ -303,9 +369,12 @@ def fi(x, i, *a):
# brentq only works with scalar inputs, so we need a set up function
# and np.vectorize to repeatedly call the optimizer with the right
# arguments for possible array input
def vd_from_brent(voc, i, iph, isat, rs, rsh, gamma, d2mutau, NsVbi):
def vd_from_brent(voc, i, iph, isat, rs, rsh, gamma, d2mutau, NsVbi,
breakdown_factor, breakdown_voltage, breakdown_exp):
return brentq(fi, 0.0, voc,
args=(i, iph, isat, rs, rsh, gamma, d2mutau, NsVbi))
args=(i, iph, isat, rs, rsh, gamma, d2mutau, NsVbi,
breakdown_factor, breakdown_voltage,
breakdown_exp))

vd_from_brent_vectorized = np.vectorize(vd_from_brent)
vd = vd_from_brent_vectorized(voc_est, current, *args)
Expand All @@ -323,20 +392,21 @@ def vd_from_brent(voc, i, iph, isat, rs, rsh, gamma, d2mutau, NsVbi):

def bishop88_mpp(photocurrent, saturation_current, resistance_series,
resistance_shunt, nNsVth, d2mutau=0, NsVbi=np.Inf,
method='newton'):
breakdown_factor=0., breakdown_voltage=-5.5,
breakdown_exp=3.28, method='newton'):
"""
Find max power point.

Parameters
----------
photocurrent : numeric
photogenerated current (Iph or IL) in amperes [A]
photogenerated current (Iph or IL) [A]
saturation_current : numeric
diode dark or saturation current (Io or Isat) in amperes [A]
diode dark or saturation current (Io or Isat) [A]
resistance_series : numeric
series resistance (Rs) in ohms
series resistance (Rs) in [Ohm]
resistance_shunt : numeric
shunt resistance (Rsh) in ohms
shunt resistance (Rsh) [Ohm]
nNsVth : numeric
product of diode ideality factor (n), number of series cells (Ns), and
thermal voltage (Vth = k_b * T / q_e) in volts [V]
Expand All @@ -351,9 +421,17 @@ def bishop88_mpp(photocurrent, saturation_current, resistance_series,
(a-Si) modules that is the product of the PV module number of series
cells ``Ns`` and the builtin voltage ``Vbi`` of the intrinsic layer.
[V].
method : str
one of two optional search methods: either ``'brentq'``, a reliable and
bounded method or ``'newton'`` which is the default.
breakdown_factor : numeric, default 0
fraction of ohmic current involved in avalanche breakdown :math:`a`.
Default of 0 excludes the reverse bias term from the model. [unitless]
breakdown_voltage : numeric, default -5.5
reverse breakdown voltage of the photovoltaic junction :math:`V_{br}`
[V]
breakdown_exp : numeric, default 3.28
avalanche breakdown exponent :math:`m` [unitless]
method : str, default 'newton'
must be either ``'newton'`` or ``'brentq'``. If ``'breakdown_factor'``
is not 0, must be ``'newton'``.

Returns
-------
Expand All @@ -363,7 +441,8 @@ def bishop88_mpp(photocurrent, saturation_current, resistance_series,
"""
# collect args
args = (photocurrent, saturation_current, resistance_series,
resistance_shunt, nNsVth, d2mutau, NsVbi)
resistance_shunt, nNsVth, d2mutau, NsVbi, breakdown_factor,
breakdown_voltage, breakdown_exp)
# first bound the search using voc
voc_est = estimate_voc(photocurrent, saturation_current, nNsVth)

Expand All @@ -373,9 +452,10 @@ def fmpp(x, *a):
if method.lower() == 'brentq':
# break out arguments for numpy.vectorize to handle broadcasting
vec_fun = np.vectorize(
lambda voc, iph, isat, rs, rsh, gamma, d2mutau, NsVbi:
brentq(fmpp, 0.0, voc,
args=(iph, isat, rs, rsh, gamma, d2mutau, NsVbi))
lambda voc, iph, isat, rs, rsh, gamma, d2mutau, NsVbi, vbr_a, vbr,
vbr_exp: brentq(fmpp, 0.0, voc,
args=(iph, isat, rs, rsh, gamma, d2mutau, NsVbi,
vbr_a, vbr, vbr_exp))
)
vd = vec_fun(voc_est, *args)
elif method.lower() == 'newton':
Expand Down
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