Problem 9.12#
Fundamentals of Solar Cells and Photovoltaic Systems Engineering
Solutions Manual - Chapter 9
Problem 9.12
Use pvlib and the Typical Meteorological Year (TMY) to calculate the reference yield \(Y_R\), array yield \(Y_A\), and final yield \(Y_F\), for a small rooftop PV system installed in Cairo, Egypt (31.233\(^{\circ}\)N, 30.033\(^{\circ}\)E). The system includes one PV panel LG290N1C (oriented toward the south with inclination angle \(\beta=20^{\circ}\)) and one microinverter ABB-MICRO-0.25. For the cell temperature estimation, assume that the PV module is glass-glass and it is mounted on an open rack.
In addition, estimate the capture losses \(L_C\), the systems losses \(L_S\) and the performance ratio \(PR\).
We will use the packages pvlib, pandas and matplotlib.pyplot to plot the results. We will also use the package pytz to determine the time zone of Egypt.
import pvlib
import pandas as pd
import matplotlib.pyplot as plt
import pytz
We start by defining the location, date, and time. We also define the orientation and tilt angles.
# Cairo, Egypt
lat, lon = 31.233, 30.033
altitude = 23
tz = pytz.country_timezones('EG')[0] # timezone corresponding to country 'EG' (Egypt)
# location
location = pvlib.location.Location(lat, lon, tz=tz)
orientation = 180 # pvlib sets orientation origin at North -> South=180
tilt = 20
We retrieve typical meteorological year (TMY) data from PVGIS.
tmy, _, _, _ = pvlib.iotools.get_pvgis_tmy(latitude=lat, longitude=lon, map_variables=True)
tmy.index = tmy.index.tz_convert(tz) # use local time
We retrieve the PV modules and inverter specifications from the database at the NREL SAM (System Advisory Monitoring).
sandia_modules = pvlib.pvsystem.retrieve_sam('SandiaMod')
module = sandia_modules['LG_LG290N1C_G3__2013_'] # module LG290N1C
# Alternatively, the CEC modules database can be retrived, but this does not include all the parameters needed to use
# the SAMP (Sandia PV Array Peformance) Model
# sam_modules = pvlib.pvsystem.retrieve_sam('CECMod')
# module = sam_modules['LG_Electronics_Inc__LG345N1W_A5'] # module LG345N1W-A5
sapm_inverters = pvlib.pvsystem.retrieve_sam('cecinverter')
inverter = sapm_inverters['ABB__MICRO_0_25_I_OUTD_US_208__208V_'] # inverter ABB-MICRO-0.25
We can check the different modules and inverters included in the SAM database, as well as their properties.
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 | 30.0 | 30.1 | 30.2 | 30.3 | 30.5 | ... | 52.0042 | 36.8926 | 36.8075 | 44.2921 | 43.5918 | 39.6117 | 36.8276 | 112.5048 | 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 | ... | -5.484547 | -7.276241 | -9.859055 | -13.064291 | -9.397451 | -11.900781 | -11.403347 | -15.259846 | -8.511484 | -6.717804 |
| 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 | 0.00073 | 0.00073 | 0.001005 | 0.001005 | 0.001005 | 0.001005 | 0.001005 | ... | 0.002278 | -0.000144 | 0.001826 | 0.003819 | 0.002168 | 0.001793 | 0.000382 | 0.00293 | 0.002862 | 0.00937 |
| A4 | -0.000046 | -0.000179 | -0.000098 | -0.000019 | -0.000019 | -0.000029 | -0.000029 | -0.000029 | -0.000029 | -0.000029 | ... | -0.000112 | 0.000022 | -0.000105 | -0.000235 | -0.000109 | -0.000129 | -0.000011 | -0.000156 | -0.000154 | -0.000764 |
| 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 | 0.00031 | 0.00031 | 0.00031 | 0.00031 | 0.00031 | 0.00031 | 0.00031 | 0.00031 | 0.00031 | 0.00031 | ... | 0.001149 | 0.000328 | 0.000906 | 0.000797 | 0.000866 | 0.001572 | 0.000559 | 0.001598 | 0.000405 | 0.000691 |
| B3 | -0.000012 | -0.000012 | -0.000012 | -0.000012 | -0.000012 | -0.000012 | -0.000012 | -0.000012 | -0.000012 | -0.000012 | ... | -0.000043 | -0.000015 | -0.000035 | -0.000031 | -0.000033 | -0.000055 | -0.000022 | -0.000057 | -0.000017 | -0.000027 |
| B4 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | ... | 0.000001 | 0.0 | 0.000001 | 0.0 | 0.000001 | 0.000001 | 0.0 | 0.000001 | 0.0 | 0.0 |
| B5 | -0.0 | -0.0 | -0.0 | -0.0 | -0.0 | -0.0 | -0.0 | -0.0 | -0.0 | -0.0 | ... | -0.0 | -0.0 | -0.0 | -0.0 | -0.0 | -0.0 | -0.0 | -0.0 | -0.0 | -0.0 |
| DTC | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | ... | 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 | 8.0 | 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
sapm_inverters
| ABB__MICRO_0_25_I_OUTD_US_208__208V_ | ABB__MICRO_0_25_I_OUTD_US_240__240V_ | ABB__MICRO_0_3_I_OUTD_US_208__208V_ | ABB__MICRO_0_3_I_OUTD_US_240__240V_ | ABB__MICRO_0_3HV_I_OUTD_US_208__208V_ | ABB__MICRO_0_3HV_I_OUTD_US_240__240V_ | ABB__PVI_10_0_I_OUTD_x_US_208_y__208V_ | ABB__PVI_10_0_I_OUTD_x_US_480_y_z__480V_ | ABB__PVI_12_0_I_OUTD_x_US_480_y__480V_ | ABB__PVI_3_0_OUTD_S_US__208V_ | ... | Zigor__Sunzet_3_TL_US__240V_ | i_Energy__GT260__240V_ | iPower__SHO_1_1__120V_ | iPower__SHO_2_0__240V_ | iPower__SHO_2_5__240V_ | iPower__SHO_3_0__240V_ | iPower__SHO_3_5__240V_ | iPower__SHO_4_6__208V_ | iPower__SHO_4_8__240V_ | iPower__SHO_5_2__240V_ | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Vac | 208 | 240 | 208 | 240 | 208 | 240 | 208 | 480 | 480 | 208 | ... | 240 | 240 | 120 | 240 | 240 | 240 | 240 | 208 | 240 | 240 |
| Pso | 2.089607 | 2.240412 | 1.846506 | 1.950539 | 1.769444 | 1.843781 | 46.863808 | 67.790878 | 62.554672 | 18.166279 | ... | 36.033405 | 2.530101 | 22.09536 | 24.465775 | 42.776474 | 31.682003 | 64.774162 | 54.570091 | 85.145699 | 62.486748 |
| Paco | 250.0 | 250.0 | 300.0 | 300.0 | 300.0 | 300.0 | 10000.0 | 10000.0 | 12000.0 | 3000.0 | ... | 3180.0 | 230.0 | 1100.0 | 2000.0 | 2500.0 | 3000.0 | 3500.0 | 4600.0 | 4800.0 | 5200.0 |
| Pdco | 259.588593 | 259.492065 | 311.66925 | 311.580872 | 312.421082 | 312.004578 | 10488.306641 | 10295.979492 | 12358.804688 | 3142.30127 | ... | 3315.654297 | 245.630447 | 1194.094849 | 2161.879639 | 2632.835693 | 3205.932617 | 3641.840332 | 4797.806641 | 4968.027832 | 5382.856934 |
| Vdco | 40.0 | 40.0 | 40.0 | 40.0 | 45.0 | 45.0 | 320.0 | 362.0 | 370.0 | 310.0 | ... | 375.0 | 40.0 | 182.0 | 199.0 | 218.0 | 222.5 | 263.0 | 254.0 | 263.0 | 280.0 |
| C0 | -0.000041 | -0.000039 | -0.000033 | -0.000034 | -0.000045 | -0.000035 | -0.000003 | -0.000001 | -0.000001 | -0.000008 | ... | -0.000008 | 0.000062 | -0.000021 | -0.000013 | -0.000014 | -0.000008 | -0.000009 | -0.000006 | -0.000006 | -0.000005 |
| C1 | -0.000091 | -0.000132 | -0.000192 | -0.000256 | -0.000196 | -0.000227 | -0.000036 | -0.000049 | -0.000056 | -0.000011 | ... | -0.000075 | -0.000098 | 0.000057 | 0.000055 | 0.000061 | 0.000036 | 0.000035 | 0.000028 | 0.000034 | 0.000044 |
| C2 | 0.000494 | 0.002418 | 0.000907 | 0.002453 | 0.001959 | -0.000526 | 0.000305 | -0.00052 | -0.001437 | 0.000999 | ... | 0.000544 | 0.000231 | 0.002001 | 0.001703 | 0.002053 | 0.001708 | 0.001417 | 0.001381 | 0.000586 | 0.00126 |
| C3 | -0.013171 | -0.014926 | -0.031742 | -0.028223 | -0.023725 | -0.041214 | -0.002351 | -0.003855 | -0.007112 | -0.000287 | ... | -0.000338 | 0.121032 | 0.000623 | 0.000315 | 0.00153 | 0.00086 | 0.001218 | 0.000889 | 0.000195 | 0.000367 |
| Pnt | 0.075 | 0.075 | 0.09 | 0.09 | 0.09 | 0.09 | 0.1 | 0.4 | 0.4 | 0.1 | ... | 0.954 | 0.069 | 0.33 | 0.6 | 0.75 | 0.9 | 1.05 | 1.38 | 1.44 | 1.56 |
| Vdcmax | 50.0 | 50.0 | 50.0 | 50.0 | 60.0 | 60.0 | 416.0 | 416.0 | 416.0 | 480.0 | ... | 400.0 | 49.0 | 380.0 | 380.0 | 400.0 | 380.0 | 400.0 | 400.0 | 400.0 | 400.0 |
| Idcmax | 6.489715 | 6.487302 | 7.791731 | 7.789522 | 6.942691 | 6.933435 | 32.775958 | 28.441932 | 33.402175 | 10.136456 | ... | 8.841745 | 6.140761 | 6.560961 | 10.863717 | 12.077228 | 14.408686 | 13.847302 | 18.889003 | 18.88984 | 19.224489 |
| Mppt_low | 30.0 | 30.0 | 30.0 | 30.0 | 30.0 | 30.0 | 220.0 | 220.0 | 250.0 | 100.0 | ... | 100.0 | 30.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 240.0 |
| Mppt_high | 50.0 | 50.0 | 50.0 | 50.0 | 60.0 | 60.0 | 416.0 | 416.0 | 416.0 | 480.0 | ... | 400.0 | 49.0 | 380.0 | 380.0 | 400.0 | 380.0 | 400.0 | 400.0 | 400.0 | 400.0 |
| CEC_Date | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | ... | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| CEC_Type | Utility Interactive | Utility Interactive | Utility Interactive | Utility Interactive | Utility Interactive | Utility Interactive | Utility Interactive | Utility Interactive | Utility Interactive | Utility Interactive | ... | Utility Interactive | Utility Interactive | Utility Interactive | Utility Interactive | Utility Interactive | Utility Interactive | Utility Interactive | Utility Interactive | Utility Interactive | Utility Interactive |
16 rows × 3264 columns
For the temperature parameters, we assume an open rack glass-glass configuration.
temperature_model_parameters = pvlib.temperature.TEMPERATURE_MODEL_PARAMETERS['sapm']['open_rack_glass_glass']
We calculate the Sun’s coordinates and the irradiance on the plane of array (POA).
# calculate Sun's coordinates
solar_position = location.get_solarposition(times=tmy.index)
# calculate irradiante at the plane of the array (poa)
poa_irradiance = pvlib.irradiance.get_total_irradiance(surface_tilt=tilt,
surface_azimuth=orientation,
dni=tmy['dni'],
ghi=tmy['ghi'],
dhi=tmy['dhi'],
solar_zenith=solar_position['apparent_zenith'],
solar_azimuth=solar_position['azimuth'])
The reference yield can be estimated as the sum of the irradiance on the plane of the array.
Y_R=0.001*poa_irradiance['poa_global'].sum() # Wh->kWh
print('Reference Yield = '+str(Y_R.round(1)) + ' kWh')
Reference Yield = 2245.3 kWh
We calculate now the effective irradiance, for which we need to estimate the air mass and the angle of incidence (AOI).
#calculate airmass
airmass = pvlib.atmosphere.get_relative_airmass(solar_position['apparent_zenith'])
pressure = pvlib.atmosphere.alt2pres(altitude)
am_abs = pvlib.atmosphere.get_absolute_airmass(airmass, pressure)
#calculate the angle of incidence (aoi)
aoi = pvlib.irradiance.aoi(surface_tilt=tilt,
surface_azimuth=orientation,
solar_zenith=solar_position['apparent_zenith'],
solar_azimuth=solar_position['azimuth'])
effective_irradiance = pvlib.pvsystem.sapm_effective_irradiance(poa_irradiance['poa_direct'],
poa_irradiance['poa_diffuse'],
am_abs,
aoi,
module)
We calculate the DC power generation of the system, the array yield \(Y_A\), and the capture losses.
# calculate the solar cell temperature
cell_temperature = pvlib.temperature.sapm_cell(poa_irradiance['poa_global'],
tmy["temp_air"],
tmy["wind_speed"],
**temperature_model_parameters,)
#calculate the DC generation in every hour
dc_power = pvlib.pvsystem.sapm(effective_irradiance, cell_temperature, module)
P_STC=module['Impo']*module['Vmpo']
Y_A = dc_power['p_mp'].sum()/P_STC
L_C = 1-Y_A/Y_R
print('Array Yield, Y_A = '+str(Y_A.round(1)) + ' kWh')
print('Capture Losses, L_C = '+str(100*L_C.round(2))+ ' %')
Array Yield, Y_A = 2021.0 kWh
Capture Losses, L_C = 10.0 %
We calculate the AC power generation of the system, the final yield, the system losses, and the performance ratio.
ac_power = pvlib.inverter.sandia(dc_power['v_mp'], dc_power['p_mp'], inverter)
Y_F = ac_power.sum()/P_STC
L_S=1-Y_F/Y_A
PR=Y_F/Y_R
print('Final Yield, Y_F = '+str(Y_F.round(1))+ ' kWh')
print('System Losses, L_S = '+str(100*L_S.round(2))+ ' %')
print('Performance Ratio, PR = '+str(100*PR.round(2))+ ' %')
Final Yield, Y_F = 1938.2 kWh
System Losses, L_S = 4.0 %
Performance Ratio, PR = 86.0 %
We can also plot the ac power vs the irradiance and use the color plot to represent the cell temperature.
plt.figure()
pc = plt.scatter(poa_irradiance['poa_global'], ac_power, c=cell_temperature, cmap='jet')
plt.colorbar(label='Cell temperature [C]', ax=plt.gca())
pc.set_alpha(0.3)
plt.grid(alpha=0.5)
plt.xlabel('Irradiance [W/m²]')
plt.ylabel('AC power [W]')
plt.show()
plt.figure()
pc = plt.scatter(poa_irradiance['poa_global'], dc_power['p_mp'], c=cell_temperature, cmap='jet')
plt.colorbar(label='Cell temperature [C]', ax=plt.gca())
pc.set_alpha(0.3)
plt.grid(alpha=0.5)
plt.xlabel('Irradiance [W/m²]')
plt.ylabel('Power PV generator [W]')
plt.show()
