Single Array PV System

This tutorial explores the pvlib.pvsystem module. The module has functions for importing PV module and inverter data and functions for modeling module and inverter performance.

  1. systemdef
  2. Angle of Incidence Modifiers
  3. Sandia Cell Temp correction
  4. Sandia Inverter Model
  5. Sandia Array Performance Model
    1. SAPM IV curves
  6. DeSoto Model
  7. Single Diode Model

This tutorial has been tested against the following package versions: * pvlib 0.3.0 * Python 3.5.1 * IPython 3.2 * Pandas 0.18.0

It should work with other Python and Pandas versions. It requires pvlib >= 0.3.0 and IPython >= 3.0.

Authors: * Will Holmgren (@wholmgren), University of Arizona. 2015, March 2016.

# built-in python modules
import os
import inspect
import datetime

# scientific python add-ons
import numpy as np
import pandas as pd

# plotting stuff
# first line makes the plots appear in the notebook
%matplotlib inline
import matplotlib.pyplot as plt
# seaborn makes your plots look better
try:
    import seaborn as sns
    sns.set(rc={"figure.figsize": (12, 6)})
except ImportError:
    print('We suggest you install seaborn using conda or pip and rerun this cell')

# finally, we import the pvlib library
import pvlib

import pvlib
from pvlib import pvsystem

systemdef

pvlib can import TMY2 and TMY3 data. Here, we import the example files.

pvlib_abspath = os.path.dirname(os.path.abspath(inspect.getfile(pvlib)))

tmy3_data, tmy3_metadata = pvlib.tmy.readtmy3(os.path.join(pvlib_abspath, 'data', '703165TY.csv'))
tmy2_data, tmy2_metadata = pvlib.tmy.readtmy2(os.path.join(pvlib_abspath, 'data', '12839.tm2'))

pvlib.pvsystem.systemdef(tmy3_metadata, 0, 0, .1, 5, 5)

{'albedo': 0.1,
 'altitude': 7.0,
 'latitude': 55.317,
 'longitude': -160.517,
 'name': '"SAND POINT"',
 'strings_per_inverter': 5,
 'modules_per_string': 5,
 'surface_azimuth': 0,
 'surface_tilt': 0,
 'tz': -9.0}

pvlib.pvsystem.systemdef(tmy2_metadata, 0, 0, .1, 5, 5)

{'albedo': 0.1,
 'altitude': 2.0,
 'latitude': 25.8,
 'longitude': -80.26666666666667,
 'name': 'MIAMI',
 'strings_per_inverter': 5,
 'modules_per_string': 5,
 'surface_azimuth': 0,
 'surface_tilt': 0,
 'tz': -5}

Angle of Incidence Modifiers

angles = np.linspace(-180,180,3601)
ashraeiam = pd.Series(pvsystem.ashraeiam(.05, angles), index=angles)

ashraeiam.plot()
plt.ylabel('ASHRAE modifier')
plt.xlabel('input angle (deg)')

<matplotlib.text.Text at 0x1112e4828>
_images/pvsystem_files/pvsystem_10_1.png 
angles = np.linspace(-180,180,3601)
physicaliam = pd.Series(pvsystem.physicaliam(4, 0.002, 1.526, angles), index=angles)

physicaliam.plot()
plt.ylabel('physical modifier')
plt.xlabel('input index')

<matplotlib.text.Text at 0x10fdcd240>
_images/pvsystem_files/pvsystem_11_1.png 
plt.figure()
ashraeiam.plot(label='ASHRAE')
physicaliam.plot(label='physical')
plt.ylabel('modifier')
plt.xlabel('input angle (deg)')
plt.legend()

<matplotlib.legend.Legend at 0x10434b2b0>
_images/pvsystem_files/pvsystem_12_1.png

Sandia Cell Temp correction

PV system efficiency can vary by up to 0.5% per degree C, so it’s important to accurately model cell and module temperature. The sapm_celltemp function uses plane of array irradiance, ambient temperature, wind speed, and module and racking type to calculate cell and module temperatures. From King et. al. (2004):

\[T_m = E e^{a+b*WS} + T_a\]
\[T_c = T_m + \frac{E}{E_0} \Delta T\]

The \(a\), \(b\), and \(\Delta T\) parameters depend on the module and racking type. The default parameter set is open_rack_cell_glassback.

sapm_celltemp works with either scalar or vector inputs, but always returns a pandas DataFrame.

# scalar inputs
pvsystem.sapm_celltemp(900, 5, 20) # irrad, wind, temp
temp_cell temp_module
0 43.509191 40.809191 
# vector inputs
times = pd.DatetimeIndex(start='2015-01-01', end='2015-01-02', freq='12H')
temps = pd.Series([0, 10, 5], index=times)
irrads = pd.Series([0, 500, 0], index=times)
winds = pd.Series([10, 5, 0], index=times)

pvtemps = pvsystem.sapm_celltemp(irrads, winds, temps)
pvtemps.plot()

<matplotlib.axes._subplots.AxesSubplot at 0x10f9bbcc0>
_images/pvsystem_files/pvsystem_17_1.png

Cell and module temperature as a function of wind speed.

wind = np.linspace(0,20,21)
temps = pd.DataFrame(pvsystem.sapm_celltemp(900, wind, 20), index=wind)

temps.plot()
plt.legend()
plt.xlabel('wind speed (m/s)')
plt.ylabel('temperature (deg C)')

<matplotlib.text.Text at 0x110799828>
_images/pvsystem_files/pvsystem_19_1.png

Cell and module temperature as a function of ambient temperature.

atemp = np.linspace(-20,50,71)
temps = pvsystem.sapm_celltemp(900, 2, atemp).set_index(atemp)

temps.plot()
plt.legend()
plt.xlabel('ambient temperature (deg C)')
plt.ylabel('temperature (deg C)')

<matplotlib.text.Text at 0x11078d4e0>
_images/pvsystem_files/pvsystem_21_1.png

Cell and module temperature as a function of incident irradiance.

irrad = np.linspace(0,1000,101)
temps = pvsystem.sapm_celltemp(irrad, 2, 20).set_index(irrad)

temps.plot()
plt.legend()
plt.xlabel('incident irradiance (W/m**2)')
plt.ylabel('temperature (deg C)')

<matplotlib.text.Text at 0x1108734e0>
_images/pvsystem_files/pvsystem_23_1.png

Cell and module temperature for different module and racking types.

models = ['open_rack_cell_glassback',
          'roof_mount_cell_glassback',
          'open_rack_cell_polymerback',
          'insulated_back_polymerback',
          'open_rack_polymer_thinfilm_steel',
          '22x_concentrator_tracker']

temps = pd.DataFrame(index=['temp_cell','temp_module'])

for model in models:
    temps[model] = pd.Series(pvsystem.sapm_celltemp(1000, 5, 20, model=model).ix[0])

temps.T.plot(kind='bar') # try removing the transpose operation and replotting
plt.legend()
plt.ylabel('temperature (deg C)')

<matplotlib.text.Text at 0x1108afa20>
_images/pvsystem_files/pvsystem_25_1.png

snlinverter

inverters = pvsystem.retrieve_sam('sandiainverter')
inverters
ABB__MICRO_0_25_I_OUTD_US_208_208V__CEC_2014_ ABB__MICRO_0_25_I_OUTD_US_240_240V__CEC_2014_ ABB__MICRO_0_3HV_I_OUTD_US_208_208V__CEC_2014_ ABB__MICRO_0_3HV_I_OUTD_US_240_240V__CEC_2014_ ABB__MICRO_0_3_I_OUTD_US_208_208V__CEC_2014_ ABB__MICRO_0_3_I_OUTD_US_240_240V__CEC_2014_ ABB__PVI_3_0_OUTD_S_US_Z_M_A__208_V__208V__CEC_2014_ ABB__PVI_3_0_OUTD_S_US_Z_M_A__240_V__240V__CEC_2014_ ABB__PVI_3_0_OUTD_S_US_Z_M_A__277_V__277V__CEC_2014_ ABB__PVI_3_6_OUTD_S_US_Z_M__208_V__208V__CEC_2014_ ... Yes!_Solar_Inc___ES5000__240V__240V__CEC_2009_ Yes!_Solar_Inc___ES5300__208V__208V__CEC_2009_ Yes!_Solar_Inc___ES5300__240V__240V__CEC_2009_ Zhejiang_Yuhui_Solar_Energy_Source__Replus_250A_240V__CEC_2012_ Zhejiang_Yuhui_Solar_Energy_Source__Replus_250B_208V__CEC_2012_ Zigor__Sunzet_2_TL_US_240V__CEC_2011_ Zigor__Sunzet_3_TL_US_240V__CEC_2011_ Zigor__Sunzet_4_TL_US_240V__CEC_2011_ Zigor__Sunzet_5_TL_US_240V__CEC_2011_ Zigor__SUNZET4_USA_240V__CEC_2011_
Vac 208.000000 240.000000 208.000000 240.000000 208.000000 240.000000 208.000000 240.000000 277.000000 208.000000 ... 240.000000 208.000000 240.000000 2.400000e+02 208.000000 240.000000 240.000000 240.000000 240.000000 240.000000
Paco 250.000000 250.000000 300.000000 300.000000 300.000000 300.000000 3000.000000 3000.000000 3000.000000 3600.000000 ... 4900.000000 4600.000000 5300.000000 2.251900e+02 213.830000 2110.000000 3180.000000 4160.000000 5240.000000 4030.000000
Pdco 259.522050 259.552697 312.523347 312.022059 311.714554 311.504961 3147.009528 3125.758222 3110.342942 3759.288140 ... 5135.584132 4829.422409 5571.180956 2.348419e+02 225.563055 2191.825129 3313.675805 4342.409314 5495.829926 4267.477069
Vdco 40.242603 39.982246 45.259429 45.495009 40.227111 40.136095 313.429286 340.842937 389.986270 309.948254 ... 275.000000 275.000000 274.900000 2.846843e+01 28.632617 399.207333 389.513254 388.562050 386.082539 302.851707
Pso 1.771614 1.931194 1.882620 1.928591 1.971053 1.991342 18.104122 19.866112 22.720135 24.202212 ... 29.358943 26.071506 28.519033 1.646711e+00 1.845029 30.843703 31.265046 31.601704 32.450808 37.372766
C0 -0.000025 -0.000027 -0.000049 -0.000035 -0.000036 -0.000031 -0.000009 -0.000007 -0.000006 -0.000005 ... -0.000006 -0.000006 -0.000006 -3.860000e-07 -0.000121 -0.000004 -0.000006 -0.000004 -0.000005 -0.000009
C1 -0.000090 -0.000158 -0.000241 -0.000228 -0.000256 -0.000289 -0.000012 -0.000025 -0.000044 0.000002 ... 0.000020 0.000024 0.000019 -3.580000e-04 -0.000533 -0.000077 -0.000095 -0.000079 -0.000097 -0.000029
C2 0.000669 0.001480 0.000975 -0.000224 -0.000833 -0.002110 0.001620 0.001050 0.000036 0.001730 ... 0.001870 0.002620 0.001630 -1.350000e-02 0.025900 0.000502 0.000261 0.000213 -0.000251 0.002150
C3 -0.018900 -0.034600 -0.027600 -0.039600 -0.039100 -0.049500 -0.000217 -0.000471 -0.001550 0.001140 ... -0.000276 0.000468 -0.000371 -3.350684e+01 -0.066800 -0.003260 -0.001960 -0.001870 -0.002340 -0.001900
Pnt 0.020000 0.050000 0.060000 0.060000 0.020000 0.050000 0.100000 0.100000 0.200000 0.100000 ... 0.500000 0.500000 0.500000 1.700000e-01 0.170000 0.250000 0.250000 0.200000 0.200000 0.190000
Vdcmax 65.000000 65.000000 79.000000 79.000000 65.000000 65.000000 600.000000 600.000000 600.000000 600.000000 ... 600.000000 600.000000 600.000000 5.500000e+01 55.000000 500.000000 500.000000 500.000000 500.000000 600.000000
Idcmax 10.000000 10.000000 10.500000 10.500000 10.000000 10.000000 20.000000 20.000000 20.000000 32.000000 ... 25.000000 25.000000 25.000000 1.400000e+01 14.000000 14.600000 22.000000 28.000000 35.300000 20.000000
Mppt_low 20.000000 20.000000 30.000000 30.000000 30.000000 30.000000 160.000000 160.000000 160.000000 120.000000 ... 200.000000 200.000000 200.000000 2.200000e+01 22.000000 150.000000 150.000000 150.000000 150.000000 240.000000
Mppt_high 50.000000 50.000000 75.000000 75.000000 50.000000 50.000000 530.000000 530.000000 530.000000 530.000000 ... 550.000000 550.000000 550.000000 4.500000e+01 45.000000 450.000000 450.000000 450.000000 450.000000 480.000000

14 rows × 1799 columns

vdcs = pd.Series(np.linspace(0,50,51))
idcs = pd.Series(np.linspace(0,11,110))
pdcs = idcs * vdcs

pacs = pvsystem.snlinverter(inverters['ABB__MICRO_0_25_I_OUTD_US_208_208V__CEC_2014_'], vdcs, pdcs)
#pacs.plot()
plt.plot(pacs, pdcs)
plt.ylabel('ac power')
plt.xlabel('dc power')

<matplotlib.text.Text at 0x10f87e8d0>
_images/pvsystem_files/pvsystem_28_1.png

Need to put more effort into describing this function.

SAPM

The CEC module database.

cec_modules = pvsystem.retrieve_sam('cecmod')
cec_modules
BEoptCA_Default_Module Example_Module 1Soltech_1STH_215_P 1Soltech_1STH_220_P 1Soltech_1STH_225_P 1Soltech_1STH_230_P 1Soltech_1STH_235_WH 1Soltech_1STH_240_WH 1Soltech_1STH_245_WH 1Soltech_1STH_FRL_4H_245_M60_BLK ... Zytech_Solar_ZT275P Zytech_Solar_ZT280P Zytech_Solar_ZT285P Zytech_Solar_ZT290P Zytech_Solar_ZT295P Zytech_Solar_ZT300P Zytech_Solar_ZT305P Zytech_Solar_ZT310P Zytech_Solar_ZT315P Zytech_Solar_ZT320P
BIPV Y Y N N N N N N N N ... N N N N N N N N N N
Date 12/17/2008 4/28/2008 10/7/2010 10/4/2010 10/4/2010 10/4/2010 3/4/2010 3/4/2010 3/4/2010 1/14/2013 ... 12/23/2014 12/23/2014 12/23/2014 12/23/2014 12/23/2014 12/23/2014 12/23/2014 12/23/2014 12/23/2014 12/23/2014
T_NOCT 65 65 47.4 47.4 47.4 47.4 49.9 49.9 49.9 48.3 ... 46.4 46.4 46.4 46.4 46.4 46.4 46.4 46.4 46.4 46.4
A_c 0.67 0.67 1.567 1.567 1.567 1.567 1.635 1.635 1.635 1.668 ... 1.931 1.931 1.931 1.931 1.931 1.931 1.931 1.931 1.931 1.931
N_s 18 18 60 60 60 60 60 60 60 60 ... 72 72 72 72 72 72 72 72 72 72
I_sc_ref 7.5 7.5 7.84 7.97 8.09 8.18 8.54 8.58 8.62 8.81 ... 8.31 8.4 8.48 8.55 8.64 8.71 8.87 8.9 9.01 9.12
V_oc_ref 10.4 10.4 36.3 36.6 36.9 37.1 37 37.1 37.2 38.3 ... 45.1 45.25 45.43 45.59 45.75 45.96 46.12 46.28 46.44 46.6
I_mp_ref 6.6 6.6 7.35 7.47 7.58 7.65 8.02 8.07 8.1 8.06 ... 7.76 7.87 7.97 8.07 8.16 8.26 8.36 8.46 8.56 8.66
V_mp_ref 8.4 8.4 29 29.3 29.6 29.9 29.3 29.7 30.2 30.2 ... 35.44 35.62 35.8 35.94 36.16 36.32 36.49 36.66 36.81 37
alpha_sc 0.003 0.003 0.007997 0.008129 0.008252 0.008344 0.00743 0.007465 0.007499 0.006167 ... 0.004014 0.004057 0.004096 0.00413 0.004173 0.004207 0.004284 0.004299 0.004352 0.004405
beta_oc -0.04 -0.04 -0.13104 -0.13213 -0.13321 -0.13393 -0.13653 -0.1369 -0.13727 -0.13635 ... -0.14428 -0.14476 -0.14533 -0.14584 -0.14635 -0.14703 -0.14754 -0.14805 -0.14856 -0.14907
a_ref 0.473 0.473 1.6413 1.6572 1.6732 1.6888 1.6292 1.6425 1.6617 1.6351 ... 1.8102 1.8147 1.82 1.8227 1.8311 1.8443 1.849 1.8573 1.8649 1.8737
I_L_ref 7.545 7.545 7.843 7.974 8.094 8.185 8.543 8.582 8.623 8.844 ... 8.324 8.41 8.487 8.552 8.642 8.805 8.874 8.995 9.107 9.218
I_o_ref 1.943e-09 1.943e-09 1.936e-09 2.03e-09 2.126e-09 2.332e-09 1.166e-09 1.325e-09 1.623e-09 5.7e-10 ... 1.24e-10 1.23e-10 1.22e-10 1.17e-10 1.22e-10 1.31e-10 1.3e-10 1.35e-10 1.38e-10 1.44e-10
R_s 0.094 0.094 0.359 0.346 0.334 0.311 0.383 0.335 0.272 0.421 ... 0.567 0.553 0.544 0.539 0.521 0.516 0.507 0.496 0.488 0.476
R_sh_ref 15.72 15.72 839.4 751.03 670.65 462.56 1257.84 1463.82 724.06 109.31 ... 341.66 457.29 687.16 2344.16 2910.76 552.2 1118.01 767.45 681.89 603.91
Adjust 10.6 10.6 16.5 16.8 17.1 17.9 8.7 9.8 11.6 6.502 ... 5.554 5.406 5.197 4.792 5.033 5.548 5.373 5.578 5.711 5.971
gamma_r -0.5 -0.5 -0.495 -0.495 -0.495 -0.495 -0.482 -0.482 -0.482 -0.453 ... -0.431 -0.431 -0.431 -0.431 -0.431 -0.431 -0.431 -0.431 -0.431 -0.431
Version MM106 MM105 MM107 MM107 MM107 MM107 MM107 MM107 MM107 NRELv1 ... NRELv1 NRELv1 NRELv1 NRELv1 NRELv1 NRELv1 NRELv1 NRELv1 NRELv1 NRELv1
PTC 48.9 48.9 189.4 194 198.5 203.1 205.1 209.6 214.1 217.7 ... 248 252.6 257.3 261.9 266.5 271.2 275.8 280.5 285.1 289.8
Technology Multi-c-Si Multi-c-Si Multi-c-Si Multi-c-Si Multi-c-Si Multi-c-Si Mono-c-Si Mono-c-Si Mono-c-Si Mono-c-Si ... Multi-c-Si Multi-c-Si Multi-c-Si Multi-c-Si Multi-c-Si Multi-c-Si Multi-c-Si Multi-c-Si Multi-c-Si Multi-c-Si

21 rows × 13953 columns

cecmodule = cec_modules.Example_Module
cecmodule

BIPV                   Y
Date           4/28/2008
T_NOCT                65
A_c                 0.67
N_s                   18
I_sc_ref             7.5
V_oc_ref            10.4
I_mp_ref             6.6
V_mp_ref             8.4
alpha_sc           0.003
beta_oc            -0.04
a_ref              0.473
I_L_ref            7.545
I_o_ref        1.943e-09
R_s                0.094
R_sh_ref           15.72
Adjust              10.6
gamma_r             -0.5
Version            MM105
PTC                 48.9
Technology    Multi-c-Si
Name: Example_Module, dtype: object

The Sandia module database.

sandia_modules = pvsystem.retrieve_sam(name='SandiaMod')
sandia_modules
Advent_Solar_AS160___2006_ Advent_Solar_Ventura_210___2008_ Advent_Solar_Ventura_215___2009_ Aleo_S03_160__2007__E__ Aleo_S03_165__2007__E__ Aleo_S16_165__2007__E__ Aleo_S16_170__2007__E__ Aleo_S16_175__2007__E__ Aleo_S16_180__2007__E__ Aleo_S16_185__2007__E__ ... Panasonic_VBHN235SA06B__2013_ Trina_TSM_240PA05__2013_ Hanwha_HSL60P6_PA_4_250T__2013_ Suniva_OPT300_72_4_100__2013_ Canadian_Solar_CS6X_300M__2013_ LG_LG290N1C_G3__2013_ Sharp_NDQ235F4__2013_ Solar_Frontier_SF_160S__2013_ SolarWorld_Sunmodule_250_Poly__2013_ Silevo_Triex_U300_Black__2014_
Vintage 2006 2008 2009 2007 (E) 2007 (E) 2007 (E) 2007 (E) 2007 (E) 2007 (E) 2007 (E) ... 2013 2013 2013 2013 2013 2013 2013 2013 2013 2014
Area 1.312 1.646 1.646 1.28 1.28 1.378 1.378 1.378 1.378 1.378 ... 1.26 1.63 1.65 1.93 1.91 1.64 1.56 1.22 1.68 1.68
Material mc-Si mc-Si mc-Si c-Si c-Si mc-Si mc-Si mc-Si mc-Si mc-Si ... a-Si / mono-Si mc-Si mc-Si c-Si c-Si c-Si mc-Si CIS mc-Si c-Si
Cells_in_Series 72 60 60 72 72 50 50 50 50 50 ... 72 60 60 72 72 60 60 172 60 96
Parallel_Strings 1 1 1 1 1 1 1 1 1 1 ... 1 1 1 1 1 1 1 1 1 1
Isco 5.564 8.34 8.49 5.1 5.2 7.9 7.95 8.1 8.15 8.2 ... 5.8738 8.8449 8.5935 8.5753 8.6388 9.8525 8.6739 2.0259 8.3768 5.771
Voco 42.832 35.31 35.92 43.5 43.6 30 30.1 30.2 30.3 30.5 ... 52.0042 36.8926 36.8075 44.2921 43.5918 39.6117 36.8276 112.505 36.3806 68.5983
Impo 5.028 7.49 7.74 4.55 4.65 7.08 7.23 7.38 7.53 7.67 ... 5.5383 8.2955 8.0822 7.963 8.1359 9.2473 8.1243 1.8356 7.6921 5.383
Vmpo 32.41 27.61 27.92 35.6 35.8 23.3 23.5 23.7 23.9 24.1 ... 43.1204 29.066 29.2011 35.0837 34.9531 31.2921 29.1988 86.6752 28.348 55.4547
Aisc 0.000537 0.00077 0.00082 0.0003 0.0003 0.0008 0.0008 0.0008 0.0008 0.0008 ... 0.0005 0.0004 0.0004 0.0006 0.0005 0.0002 0.0006 0.0001 0.0006 0.0003
Aimp -0.000491 -0.00015 -0.00013 -0.00025 -0.00025 -0.0003 -0.0003 -0.0003 -0.0003 -0.0003 ... -0.0001 -0.0003 -0.0003 -0.0002 -0.0001 -0.0004 -0.0002 -0.0003 -0.0001 -0.0003
C0 1.0233 0.937 1.015 0.99 0.99 0.99 0.99 0.99 0.99 0.99 ... 1.0015 1.0116 1.0061 0.999 1.0121 1.0145 1.0049 1.0096 1.0158 0.995
C1 -0.0233 0.063 -0.015 0.01 0.01 0.01 0.01 0.01 0.01 0.01 ... -0.0015 -0.0116 -0.0061 0.001 -0.0121 -0.0145 -0.0049 -0.0096 -0.0158 0.005
Bvoco -0.1703 -0.133 -0.135 -0.152 -0.152 -0.11 -0.11 -0.11 -0.11 -0.11 ... -0.1411 -0.137 -0.1263 -0.155 -0.1532 -0.1205 -0.1279 -0.3044 -0.1393 -0.1913
Mbvoc 0 0 0 0 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 0 0
Bvmpo -0.1731 -0.135 -0.136 -0.158 -0.158 -0.115 -0.115 -0.115 -0.115 -0.115 ... -0.1366 -0.1441 -0.1314 -0.1669 -0.1634 -0.1337 -0.1348 -0.2339 -0.1449 -0.184
Mbvmp 0 0 0 0 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 0 0
N 1.174 1.495 1.373 1.25 1.25 1.35 1.35 1.35 1.35 1.35 ... 1.029 1.2073 1.0686 1.0771 1.0025 1.0925 1.0695 1.2066 1.226 1.345
C2 -0.76444 0.0182 0.0036 -0.15 -0.15 -0.12 -0.12 -0.12 -0.12 -0.12 ... 0.2859 -0.07993 -0.2585 -0.355 -0.171 -0.4647 -0.2718 -0.5426 -0.09677 0.3221
C3 -15.5087 -10.758 -7.2509 -8.96 -8.96 -11.08 -11.08 -11.08 -11.08 -11.08 ... -5.48455 -7.27624 -9.85905 -13.0643 -9.39745 -11.9008 -11.4033 -15.2598 -8.51148 -6.7178
A0 0.9281 0.9067 0.9323 0.938 0.938 0.924 0.924 0.924 0.924 0.924 ... 0.9161 0.9645 0.9428 0.9327 0.9371 0.9731 0.9436 0.9354 0.9288 0.9191
A1 0.06615 0.09573 0.06526 0.05422 0.05422 0.06749 0.06749 0.06749 0.06749 0.06749 ... 0.07968 0.02753 0.0536 0.07283 0.06262 0.02966 0.04765 0.06809 0.07201 0.09988
A2 -0.01384 -0.0266 -0.01567 -0.009903 -0.009903 -0.012549 -0.012549 -0.012549 -0.012549 -0.012549 ... -0.01866 -0.002848 -0.01281 -0.02402 -0.01667 -0.01024 -0.007405 -0.02094 -0.02065 -0.04273
A3 0.001298 0.00343 0.00193 0.0007297 0.0007297 0.0010049 0.0010049 0.0010049 0.0010049 0.0010049 ... 0.002278 -0.0001439 0.001826 0.003819 0.002168 0.001793 0.0003818 0.00293 0.002862 0.00937
A4 -4.6e-05 -0.0001794 -9.81e-05 -1.907e-05 -1.907e-05 -2.8797e-05 -2.8797e-05 -2.8797e-05 -2.8797e-05 -2.8797e-05 ... -0.0001118 2.219e-05 -0.0001048 -0.000235 -0.0001087 -0.0001286 -1.101e-05 -0.0001564 -0.0001544 -0.0007643
B0 1 1 1 1 1 1 1 1 1 1 ... 1 1 1 1 1 1 1 1 1 1
B1 -0.002438 -0.002438 -0.002438 -0.002438 -0.002438 -0.002438 -0.002438 -0.002438 -0.002438 -0.002438 ... -0.01053 -0.00261 -0.007861 -0.006801 -0.00789 -0.0154 -0.00464 -0.0152 -0.00308 -0.006498
B2 0.0003103 0.00031 0.00031 0.0003103 0.0003103 0.0003103 0.0003103 0.0003103 0.0003103 0.0003103 ... 0.001149 0.0003279 0.0009058 0.0007968 0.0008656 0.001572 0.000559 0.001598 0.0004053 0.0006908
B3 -1.246e-05 -1.246e-05 -1.246e-05 -1.246e-05 -1.246e-05 -1.246e-05 -1.246e-05 -1.246e-05 -1.246e-05 -1.246e-05 ... -4.268e-05 -1.458e-05 -3.496e-05 -3.095e-05 -3.298e-05 -5.525e-05 -2.249e-05 -5.682e-05 -1.729e-05 -2.678e-05
B4 2.11e-07 2.11e-07 2.11e-07 2.11e-07 2.11e-07 2.11e-07 2.11e-07 2.11e-07 2.11e-07 2.11e-07 ... 6.517e-07 2.654e-07 5.473e-07 4.896e-07 5.178e-07 8.04e-07 3.673e-07 8.326e-07 2.997e-07 4.322e-07
B5 -1.36e-09 -1.36e-09 -1.36e-09 -1.36e-09 -1.36e-09 -1.36e-09 -1.36e-09 -1.36e-09 -1.36e-09 -1.36e-09 ... -3.556e-09 -1.732e-09 -3.058e-09 -2.78e-09 -2.918e-09 -4.202e-09 -2.144e-09 -4.363e-09 -1.878e-09 -2.508e-09
DTC 3 3 3 3 3 3 3 3 3 3 ... 2.03 3.03 2.55 2.58 3.2 3.05 3.27 3.29 3.19 3.13
FD 1 1 1 1 1 1 1 1 1 1 ... 1 1 1 1 1 1 1 1 1 1
A -3.35 -3.45 -3.47 -3.56 -3.56 -3.56 -3.56 -3.56 -3.56 -3.56 ... -3.7489 -3.5924 -3.5578 -3.7566 -3.6024 -3.4247 -3.7445 -3.6836 -3.73 -3.6866
B -0.1161 -0.077 -0.087 -0.075 -0.075 -0.075 -0.075 -0.075 -0.075 -0.075 ... -0.1287 -0.1319 -0.1766 -0.156 -0.2106 -0.0951 -0.149 -0.1483 -0.1483 -0.104
C4 0.9974 0.972 0.989 0.995 0.995 0.995 0.995 0.995 0.995 0.995 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
C5 0.0026 0.028 0.012 0.005 0.005 0.005 0.005 0.005 0.005 0.005 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
IXO 5.54 8.25 8.49 5.04 5.14 7.8 7.85 8 8.05 8.1 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
IXXO 3.56 5.2 5.45 3.16 3.25 4.92 5.08 5.18 5.39 5.54 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
C6 1.173 1.067 1.137 1.15 1.15 1.15 1.15 1.15 1.15 1.15 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
C7 -0.173 -0.067 -0.137 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
Notes Source: Sandia National Laboratories Updated 9... Source: Sandia National Laboratories Updated 9... Source: Sandia National Laboratories Updated 9... Source: Sandia National Laboratories Updated 9... Source: Sandia National Laboratories Updated 9... Source: Sandia National Laboratories Updated 9... Source: Sandia National Laboratories Updated 9... Source: Sandia National Laboratories Updated 9... Source: Sandia National Laboratories Updated 9... Source: Sandia National Laboratories Updated 9... ... Source: CFV Solar Test Lab. Tested 2013. Mo... Source: CFV Solar Test Lab. Tested 2013. Mo... Source: CFV Solar Test Lab. Tested 2013. Mo... Source: CFV Solar Test Lab. Tested 2013. Mo... Source: CFV Solar Test Lab. Tested 2013. Mo... Source: CFV Solar Test Lab. Tested 2013. Mo... Source: CFV Solar Test Lab. Tested 2013. Mo... Source: CFV Solar Test Lab. Tested 2013. Mo... Source: CFV Solar Test Lab. Tested 2013. Mo... Source: CFV Solar Test Lab. Tested 2014. Mo...

42 rows × 523 columns

sandia_module = sandia_modules.Canadian_Solar_CS5P_220M___2009_
sandia_module

Vintage                                                          2009
Area                                                            1.701
Material                                                         c-Si
Cells_in_Series                                                    96
Parallel_Strings                                                    1
Isco                                                          5.09115
Voco                                                          59.2608
Impo                                                          4.54629
Vmpo                                                          48.3156
Aisc                                                         0.000397
Aimp                                                         0.000181
C0                                                            1.01284
C1                                                         -0.0128398
Bvoco                                                        -0.21696
Mbvoc                                                               0
Bvmpo                                                       -0.235488
Mbvmp                                                               0
N                                                              1.4032
C2                                                           0.279317
C3                                                           -7.24463
A0                                                           0.928385
A1                                                           0.068093
A2                                                         -0.0157738
A3                                                          0.0016606
A4                                                          -6.93e-05
B0                                                                  1
B1                                                          -0.002438
B2                                                          0.0003103
B3                                                         -1.246e-05
B4                                                           2.11e-07
B5                                                          -1.36e-09
DTC                                                                 3
FD                                                                  1
A                                                            -3.40641
B                                                          -0.0842075
C4                                                           0.996446
C5                                                           0.003554
IXO                                                           4.97599
IXXO                                                          3.18803
C6                                                            1.15535
C7                                                          -0.155353
Notes               Source: Sandia National Laboratories Updated 9...
Name: Canadian_Solar_CS5P_220M___2009_, dtype: object

Generate some irradiance data for modeling.

from pvlib import clearsky
from pvlib import irradiance
from pvlib import atmosphere
from pvlib.location import Location

tus = Location(32.2, -111, 'US/Arizona', 700, 'Tucson')
times_loc = pd.date_range(start=datetime.datetime(2014,4,1), end=datetime.datetime(2014,4,2), freq='30s', tz=tus.tz)
ephem_data = pvlib.solarposition.get_solarposition(times_loc, tus.latitude, tus.longitude)
irrad_data = clearsky.ineichen(times_loc, tus.latitude, tus.longitude)
#irrad_data.plot()

aoi = irradiance.aoi(0, 0, ephem_data['apparent_zenith'], ephem_data['azimuth'])
#plt.figure()
#aoi.plot()

am = atmosphere.relativeairmass(ephem_data['apparent_zenith'])

# a hot, sunny spring day in the desert.
temps = pvsystem.sapm_celltemp(irrad_data['ghi'], 0, 30)

Now we can run the module parameters and the irradiance data through the SAPM function.

sapm_1 = pvsystem.sapm(sandia_module, irrad_data['dni']*np.cos(np.radians(aoi)),
                     irrad_data['dhi'], temps['temp_cell'], am, aoi)
sapm_1.head()
i_sc i_mp v_oc v_mp p_mp i_x i_xx effective_irradiance
2014-04-01 00:00:00-07:00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2014-04-01 00:00:30-07:00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2014-04-01 00:01:00-07:00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2014-04-01 00:01:30-07:00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2014-04-01 00:02:00-07:00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 
def plot_sapm(sapm_data):
    """
    Makes a nice figure with the SAPM data.

    Parameters
    ----------
    sapm_data : DataFrame
        The output of ``pvsystem.sapm``
    """
    fig, axes = plt.subplots(2, 3, figsize=(16,10), sharex=False, sharey=False, squeeze=False)
    plt.subplots_adjust(wspace=.2, hspace=.3)

    ax = axes[0,0]
    sapm_data.filter(like='i_').plot(ax=ax)
    ax.set_ylabel('Current (A)')

    ax = axes[0,1]
    sapm_data.filter(like='v_').plot(ax=ax)
    ax.set_ylabel('Voltage (V)')

    ax = axes[0,2]
    sapm_data.filter(like='p_').plot(ax=ax)
    ax.set_ylabel('Power (W)')

    ax = axes[1,0]
    [ax.plot(sapm_data['effective_irradiance'], current, label=name) for name, current in
     sapm_data.filter(like='i_').iteritems()]
    ax.set_ylabel('Current (A)')
    ax.set_xlabel('Effective Irradiance')
    ax.legend(loc=2)

    ax = axes[1,1]
    [ax.plot(sapm_data['effective_irradiance'], voltage, label=name) for name, voltage in
     sapm_data.filter(like='v_').iteritems()]
    ax.set_ylabel('Voltage (V)')
    ax.set_xlabel('Effective Irradiance')
    ax.legend(loc=4)

    ax = axes[1,2]
    ax.plot(sapm_data['effective_irradiance'], sapm_data['p_mp'], label='p_mp')
    ax.set_ylabel('Power (W)')
    ax.set_xlabel('Effective Irradiance')
    ax.legend(loc=2)

    # needed to show the time ticks
    for ax in axes.flatten():
        for tk in ax.get_xticklabels():
            tk.set_visible(True)

plot_sapm(sapm_1)
_images/pvsystem_files/pvsystem_42_0.png

For comparison, here’s the SAPM for a sunny, windy, cold version of the same day.

temps = pvsystem.sapm_celltemp(irrad_data['ghi'], 10, 5)

sapm_2 = pvsystem.sapm(sandia_module, irrad_data['dni']*np.cos(np.radians(aoi)),
                     irrad_data['dhi'], temps['temp_cell'], am, aoi)

plot_sapm(sapm_2)
_images/pvsystem_files/pvsystem_44_0.png 
sapm_1['p_mp'].plot(label='30 C,  0 m/s')
sapm_2['p_mp'].plot(label=' 5 C, 10 m/s')
plt.legend()
plt.ylabel('Pmp')
plt.title('Comparison of a hot, calm day and a cold, windy day')

<matplotlib.text.Text at 0x10febe828>
_images/pvsystem_files/pvsystem_45_1.png

SAPM IV curves

The IV curve function only calculates the 5 points of the SAPM. We will add arbitrary points in a future release, but for now we just interpolate between the 5 SAPM points.

import warnings
warnings.simplefilter('ignore', np.RankWarning)

def sapm_to_ivframe(sapm_row):
    pnt = sapm_row.T.ix[:,0]

    ivframe = {'Isc': (pnt['i_sc'], 0),
              'Pmp': (pnt['i_mp'], pnt['v_mp']),
              'Ix': (pnt['i_x'], 0.5*pnt['v_oc']),
              'Ixx': (pnt['i_xx'], 0.5*(pnt['v_oc']+pnt['v_mp'])),
              'Voc': (0, pnt['v_oc'])}
    ivframe = pd.DataFrame(ivframe, index=['current', 'voltage']).T
    ivframe = ivframe.sort_values(by='voltage')

    return ivframe

def ivframe_to_ivcurve(ivframe, points=100):
    ivfit_coefs = np.polyfit(ivframe['voltage'], ivframe['current'], 30)
    fit_voltages = np.linspace(0, ivframe.ix['Voc', 'voltage'], points)
    fit_currents = np.polyval(ivfit_coefs, fit_voltages)

    return fit_voltages, fit_currents

sapm_to_ivframe(sapm_1['2014-04-01 10:00:00'])
current voltage
Isc 3.848214 0.000000
Ix 3.757784 25.754530
Pmp 3.425038 40.706316
Ixx 2.504497 46.107688
Voc 0.000000 51.509060 
times = ['2014-04-01 07:00:00', '2014-04-01 08:00:00', '2014-04-01 09:00:00',
         '2014-04-01 10:00:00', '2014-04-01 11:00:00', '2014-04-01 12:00:00']
times.reverse()

fig, ax = plt.subplots(1, 1, figsize=(12,8))

for time in times:
    ivframe = sapm_to_ivframe(sapm_1[time])

    fit_voltages, fit_currents = ivframe_to_ivcurve(ivframe)

    ax.plot(fit_voltages, fit_currents, label=time)
    ax.plot(ivframe['voltage'], ivframe['current'], 'ko')

ax.set_xlabel('Voltage (V)')
ax.set_ylabel('Current (A)')
ax.set_ylim(0, None)
ax.set_title('IV curves at multiple times')
ax.legend()

<matplotlib.legend.Legend at 0x11123b908>
_images/pvsystem_files/pvsystem_51_1.png

desoto

The same data run through the desoto model.

photocurrent, saturation_current, resistance_series, resistance_shunt, nNsVth = (
    pvsystem.calcparams_desoto(irrad_data.ghi,
                                 temp_cell=temps['temp_cell'],
                                 alpha_isc=cecmodule['alpha_sc'],
                                 module_parameters=cecmodule,
                                 EgRef=1.121,
                                 dEgdT=-0.0002677) )

photocurrent.plot()
plt.ylabel('Light current I_L (A)')

<matplotlib.text.Text at 0x117c06160>
_images/pvsystem_files/pvsystem_55_1.png 
saturation_current.plot()
plt.ylabel('Saturation current I_0 (A)')

<matplotlib.text.Text at 0x117c5aac8>
_images/pvsystem_files/pvsystem_56_1.png 
resistance_series

0.094

resistance_shunt.plot()
plt.ylabel('Shunt resistance (ohms)')
plt.ylim(0,100)

(0, 100)
_images/pvsystem_files/pvsystem_58_1.png 
nNsVth.plot()
plt.ylabel('nNsVth')

<matplotlib.text.Text at 0x117c704a8>
_images/pvsystem_files/pvsystem_59_1.png

Single diode model

single_diode_out = pvsystem.singlediode(cecmodule, photocurrent, saturation_current,
                                        resistance_series, resistance_shunt, nNsVth)
single_diode_out
i_mp i_sc i_x i_xx p_mp v_mp v_oc
2014-04-01 00:00:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:00:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:01:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:01:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:02:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:02:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:03:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:03:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:04:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:04:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:05:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:05:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:06:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:06:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:07:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:07:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:08:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:08:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:09:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:09:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:10:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:10:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:11:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:11:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:12:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:12:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:13:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:13:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:14:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 00:14:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
... ... ... ... ... ... ... ...
2014-04-01 23:45:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:46:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:46:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:47:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:47:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:48:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:48:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:49:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:49:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:50:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:50:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:51:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:51:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:52:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:52:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:53:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:53:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:54:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:54:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:55:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:55:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:56:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:56:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:57:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:57:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:58:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:58:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:59:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-01 23:59:30-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739
2014-04-02 00:00:00-07:00 NaN NaN NaN NaN NaN 0.022756 0.019739

2881 rows × 7 columns

single_diode_out['i_sc'].plot()

<matplotlib.axes._subplots.AxesSubplot at 0x117cde358>
_images/pvsystem_files/pvsystem_62_1.png 
single_diode_out['v_oc'].plot()

<matplotlib.axes._subplots.AxesSubplot at 0x10fe34908>
_images/pvsystem_files/pvsystem_63_1.png 
single_diode_out['p_mp'].plot()

<matplotlib.axes._subplots.AxesSubplot at 0x117cde080>
_images/pvsystem_files/pvsystem_64_1.png