def test_rectify_iv_curve(ivcurve):
voltage, current = ivcurve
vexp_no_dec = np.array([0., 1., 5., 10., 25., 25.00001, 28., 30., 47.,
51.])
iexp_no_dec = np.array([7., 6., 6., 5., 4., 3., 2.5, 2.7, 0.5, 0.])
v, i = rectify_iv_curve(voltage, current)
np.testing.assert_allclose(v, vexp_no_dec, atol=.0001)
np.testing.assert_allclose(i, iexp_no_dec, atol=.0001)
vexp = np.array([0., 1., 5., 10., 25., 28., 30., 47., 51.])
iexp = np.array([7., 6., 6., 5., 3.5, 2.5, 2.7, 0.5, 0.])
v, i = rectify_iv_curve(voltage, current, decimals=4)
np.testing.assert_allclose(v, vexp, atol=.0001)
np.testing.assert_allclose(i, iexp, atol=.0001)
def _initial_iv_params(ivcurves, ee, voc, isc, rsh, nnsvth):
# sets initial values for iph, io, rs and quality filter u.
# Helper function for fit_<model>_sandia.
n = len(ivcurves['v_oc'])
io = np.ones(n)
iph = np.ones(n)
rs = np.ones(n)
for j in range(n):
if rsh[j] > 0:
volt, curr = rectify_iv_curve(ivcurves['v'][j],
ivcurves['i'][j])
# Initial estimate of Io, evaluate the single diode model at
# voc and approximate Iph + Io = Isc [5] Step 3a; [6] Step 3b
io[j] = (isc[j] - voc[j] / rsh[j]) * np.exp(-voc[j] /
nnsvth[j])
# initial estimate of rs from dI/dV near Voc
# [5] Step 3a; [6] Step 3c
[didv, d2id2v] = _numdiff(volt, curr)
t3 = volt > .5 * voc[j]
t4 = volt < .9 * voc[j]
tmp = -rsh[j] * didv - 1.
with np.errstate(invalid="ignore"): # expect nan in didv
v = np.logical_and.reduce(np.array([t3, t4, ~np.isnan(tmp),
np.greater(tmp, 0)]))
if np.any(v):
vtrs = (nnsvth[j] / isc[j] * (
np.log(tmp[v] * nnsvth[j] / (rsh[j] * io[j]))
- volt[v] / nnsvth[j]))
rs[j] = np.mean(vtrs[vtrs > 0], axis=0)
else:
rs[j] = 0.
# Initial estimate of Iph, evaluate the single diode model at
# Isc [5] Step 3a; [6] Step 3d
iph[j] = isc[j] + io[j] * np.expm1(isc[j] / nnsvth[j]) \
+ isc[j] * rs[j] / rsh[j]
else:
io[j] = np.nan
rs[j] = np.nan
iph[j] = np.nan
# Filter IV curves for good initial values
# [5] Step 3b
u = _filter_params(ee, isc, io, rs, rsh)
# [5] Step 3c
# Refine Io to match Voc
io[u] = _update_io(voc[u], iph[u], io[u], rs[u], rsh[u], nnsvth[u])
# parameters [6], Step 3c
# Calculate Iph to be consistent with Isc and current values of other
iph = isc + io * np.expm1(rs * isc / nnsvth) + isc * rs / rsh
return iph, io, rs, u
def fit_desoto_sandia(ivcurves, specs, const=None, maxiter=5, eps1=1.e-3):
"""
Estimate parameters for the De Soto module performance model.
Parameters
----------
ivcurves : dict
i : array
One array element for each IV curve. The jth element is itself an
array of current for jth IV curve (same length as v[j]) [A]
v : array
One array element for each IV curve. The jth element is itself an
array of voltage for jth IV curve (same length as i[j]) [V]
ee : array
effective irradiance for each IV curve, i.e., POA broadband
irradiance adjusted by solar spectrum modifier [W / m^2]
tc : array
cell temperature for each IV curve [C]
i_sc : array
short circuit current for each IV curve [A]
v_oc : array
open circuit voltage for each IV curve [V]
i_mp : array
current at max power point for each IV curve [A]
v_mp : array
voltage at max power point for each IV curve [V]
specs : dict
cells_in_series : int
number of cells in series
alpha_sc : float
temperature coefficient of Isc [A/C]
beta_voc : float
temperature coefficient of Voc [V/C]
const : dict
E0 : float
effective irradiance at STC, default 1000 [W/m^2]
T0 : float
cell temperature at STC, default 25 [C]
k : float
1.38066E-23 J/K (Boltzmann's constant)
q : float
1.60218E-19 Coulomb (elementary charge)
maxiter : int, default 5
input that sets the maximum number of iterations for the parameter
updating part of the algorithm.
eps1: float, default 1e-3
Tolerance for the IV curve fitting. The parameter updating stops when
absolute values of the percent change in mean, max and standard
deviation of Imp, Vmp and Pmp between iterations are all less than
eps1, or when the number of iterations exceeds maxiter.
Returns
-------
dict
I_L_ref : float
light current at STC [A]
I_o_ref : float
dark current at STC [A]
EgRef : float
effective band gap at STC [eV]
R_s : float
series resistance at STC [ohm]
R_sh_ref : float
shunt resistance at STC [ohm]
cells_in_series : int
number of cells in series
iph : array
light current for each IV curve [A]
io : array
dark current for each IV curve [A]
rs : array
series resistance for each IV curve [ohm]
rsh : array
shunt resistance for each IV curve [ohm]
u : array
boolean for each IV curve indicating that the parameter values
are deemed reasonable by the private function ``_filter_params``
Notes
-----
The De Soto module performance model is described in [1]_. The fitting
method is documented in [2]_, [3]_. Ported from PVLib Matlab [4]_.
References
----------
.. [1] W. De Soto et al., "Improvement and validation of a model for
photovoltaic array performance", Solar Energy, vol 80, pp. 78-88,
2006.
.. [2] C. Hansen, Parameter Estimation for Single Diode Models of
Photovoltaic Modules, Sandia National Laboratories Report SAND2015-2065
.. [3] C. Hansen, Estimation of Parameters for Single Diode Models using
Measured IV Curves, Proc. of the 39th IEEE PVSC, June 2013.
.. [4] PVLib MATLAB https://github.com/sandialabs/MATLAB_PV_LIB
"""
if const is None:
const = {'E0': 1000.0, 'T0': 25.0, 'k': 1.38066e-23, 'q': 1.60218e-19}
ee = ivcurves['ee']
tc = ivcurves['tc']
tck = tc + 273.15
isc = ivcurves['i_sc']
voc = ivcurves['v_oc']
imp = ivcurves['i_mp']
vmp = ivcurves['v_mp']
# Cell Thermal Voltage
vth = const['k'] / const['q'] * tck
n = len(voc)
# Initial estimate of Rsh used to obtain the diode factor gamma0 and diode
# temperature coefficient mu_gamma. Rsh is estimated using the co-content
# integral method.
rsh = np.ones(n)
for j in range(n):
voltage, current = rectify_iv_curve(ivcurves['v'][j], ivcurves['i'][j])
# initial estimate of Rsh, from integral over voltage regression
# [5] Step 3a; [6] Step 3a
_, _, _, rsh[j], _ = _fit_sandia_cocontent(
voltage, current, vth[j] * specs['cells_in_series'])
n0 = _fit_desoto_sandia_diode(ee, voc, vth, tc, specs, const)
bad_n = np.isnan(n0) or not np.isreal(n0)
if bad_n:
raise RuntimeError(
"Failed to estimate the diode (ideality) factor parameter;"
" aborting parameter estimation.")
nnsvth = n0 * specs['cells_in_series'] * vth
# For each IV curve, sequentially determine initial values for Io, Rs,
# and Iph [5] Step 3a; [6] Step 3
iph, io, rs, u = _initial_iv_params(ivcurves, ee, voc, isc, rsh,
nnsvth)
# Update values for each IV curve to converge at vmp, imp, voc and isc
iph, io, rs, rsh, u = _update_iv_params(voc, isc, vmp, imp, ee,
iph, io, rs, rsh, nnsvth, u,
maxiter, eps1)
# get single diode models from converged values for each IV curve
desoto = _extract_sdm_params(ee, tc, iph, io, rs, rsh, n0, u,
specs, const, model='desoto')
# Add parameters estimated in this function
desoto['a_ref'] = n0 * specs['cells_in_series'] * const['k'] / \
const['q'] * (const['T0'] + 273.15)
desoto['cells_in_series'] = specs['cells_in_series']
return desoto
def fit_pvsyst_sandia(ivcurves, specs, const=None, maxiter=5, eps1=1.e-3):
"""
Estimate parameters for the PVsyst module performance model.
Parameters
----------
ivcurves : dict
i : array
One array element for each IV curve. The jth element is itself an
array of current for jth IV curve (same length as v[j]) [A]
v : array
One array element for each IV curve. The jth element is itself an
array of voltage for jth IV curve (same length as i[j]) [V]
ee : array
effective irradiance for each IV curve, i.e., POA broadband
irradiance adjusted by solar spectrum modifier [W / m^2]
tc : array
cell temperature for each IV curve [C]
i_sc : array
short circuit current for each IV curve [A]
v_oc : array
open circuit voltage for each IV curve [V]
i_mp : array
current at max power point for each IV curve [A]
v_mp : array
voltage at max power point for each IV curve [V]
specs : dict
cells_in_series : int
number of cells in series
alpha_sc : float
temperature coefficient of isc [A/C]
const : dict
E0 : float
effective irradiance at STC, default 1000 [W/m^2]
T0 : float
cell temperature at STC, default 25 [C]
k : float
1.38066E-23 J/K (Boltzmann's constant)
q : float
1.60218E-19 Coulomb (elementary charge)
maxiter : int, default 5
input that sets the maximum number of iterations for the parameter
updating part of the algorithm.
eps1: float, default 1e-3
Tolerance for the IV curve fitting. The parameter updating stops when
absolute values of the percent change in mean, max and standard
deviation of Imp, Vmp and Pmp between iterations are all less than
eps1, or when the number of iterations exceeds maxiter.
Returns
-------
dict
I_L_ref : float
light current at STC [A]
I_o_ref : float
dark current at STC [A]
EgRef : float
effective band gap at STC [eV]
R_s : float
series resistance at STC [ohm]
R_sh_ref : float
shunt resistance at STC [ohm]
R_sh_0 : float
shunt resistance at zero irradiance [ohm]
R_sh_exp : float
exponential factor defining decrease in shunt resistance with
increasing effective irradiance
gamma_ref : float
diode (ideality) factor at STC [unitless]
mu_gamma : float
temperature coefficient for diode (ideality) factor [1/K]
cells_in_series : int
number of cells in series
iph : array
light current for each IV curve [A]
io : array
dark current for each IV curve [A]
rs : array
series resistance for each IV curve [ohm]
rsh : array
shunt resistance for each IV curve [ohm]
u : array
boolean for each IV curve indicating that the parameter values
are deemed reasonable by the private function ``_filter_params``
Notes
-----
The PVsyst module performance model is described in [1]_, [2]_, and [3]_.
The fitting method is documented in [4]_, [5]_, and [6]_.
Ported from PVLib Matlab [7]_.
References
----------
.. [1] K. Sauer, T. Roessler, C. W. Hansen, Modeling the Irradiance and
Temperature Dependence of Photovoltaic Modules in PVsyst, IEEE Journal
of Photovoltaics v5(1), January 2015.
.. [2] A. Mermoud, PV Modules modeling, Presentation at the 2nd PV
Performance Modeling Workshop, Santa Clara, CA, May 2013
.. [3] A. Mermoud, T. Lejeuene, Performance Assessment of a Simulation
Model for PV modules of any available technology, 25th European
Photovoltaic Solar Energy Conference, Valencia, Spain, Sept. 2010
.. [4] C. Hansen, Estimating Parameters for the PVsyst Version 6
Photovoltaic Module Performance Model, Sandia National Laboratories
Report SAND2015-8598
.. [5] C. Hansen, Parameter Estimation for Single Diode Models of
Photovoltaic Modules, Sandia National Laboratories Report SAND2015-2065
.. [6] C. Hansen, Estimation of Parameters for Single Diode Models using
Measured IV Curves, Proc. of the 39th IEEE PVSC, June 2013.
.. [7] PVLib MATLAB https://github.com/sandialabs/MATLAB_PV_LIB
"""
if const is None:
const = {'E0': 1000.0, 'T0': 25.0, 'k': 1.38066e-23, 'q': 1.60218e-19}
ee = ivcurves['ee']
tc = ivcurves['tc']
tck = tc + 273.15
isc = ivcurves['i_sc']
voc = ivcurves['v_oc']
imp = ivcurves['i_mp']
vmp = ivcurves['v_mp']
# Cell Thermal Voltage
vth = const['k'] / const['q'] * tck
n = len(ivcurves['v_oc'])
# Initial estimate of Rsh used to obtain the diode factor gamma0 and diode
# temperature coefficient mu_gamma. Rsh is estimated using the co-content
# integral method.
rsh = np.ones(n)
for j in range(n):
voltage, current = rectify_iv_curve(ivcurves['v'][j], ivcurves['i'][j])
# initial estimate of Rsh, from integral over voltage regression
# [5] Step 3a; [6] Step 3a
_, _, _, rsh[j], _ = _fit_sandia_cocontent(
voltage, current, vth[j] * specs['cells_in_series'])
gamma_ref, mu_gamma = _fit_pvsyst_sandia_gamma(voc, isc, rsh, vth, tck,
specs, const)
badgamma = np.isnan(gamma_ref) or np.isnan(mu_gamma) \
or not np.isreal(gamma_ref) or not np.isreal(mu_gamma)
if badgamma:
raise RuntimeError(
"Failed to estimate the diode (ideality) factor parameter;"
" aborting parameter estimation.")
gamma = gamma_ref + mu_gamma * (tc - const['T0'])
nnsvth = gamma * (vth * specs['cells_in_series'])
# For each IV curve, sequentially determine initial values for Io, Rs,
# and Iph [5] Step 3a; [6] Step 3
iph, io, rs, u = _initial_iv_params(ivcurves, ee, voc, isc, rsh,
nnsvth)
# Update values for each IV curve to converge at vmp, imp, voc and isc
iph, io, rs, rsh, u = _update_iv_params(voc, isc, vmp, imp, ee,
iph, io, rs, rsh, nnsvth, u,
maxiter, eps1)
# get single diode models from converged values for each IV curve
pvsyst = _extract_sdm_params(ee, tc, iph, io, rs, rsh, gamma, u,
specs, const, model='pvsyst')
# Add parameters estimated in this function
pvsyst['gamma_ref'] = gamma_ref
pvsyst['mu_gamma'] = mu_gamma
pvsyst['cells_in_series'] = specs['cells_in_series']
return pvsyst