Photovoltaic Performance
You might have followed the sections for solar position and solar irradiance or maybe not. Regardless, this tutorial is both a stand-alone document and a building block in the chain of calculations to estimate photovoltaic power output.
Analysis of Performance¶
We start right away with an analysis of the photovoltaic performance for our sample location behind the ESTI facilities in the JRC, Ispra.
pvgis-prototype performance broadband \
8.628 45.812 214 180 0.001 \
--start-time '2013-01-01' \
--end-time '2013-12-31' \
--global-horizontal-irradiance sarah2_sis_over_esti_jrc.nc \
--direct-horizontal-irradiance sarah2_sid_over_esti_jrc.nc \
--spectral-factor-series spectral_effect_cSi_over_esti_jrc.nc \
--temperature-series era5_t2m_over_esti_jrc.nc \
--wind-speed-series era5_ws2m_over_esti_jrc.nc \
--neighbor-lookup nearest \
-aou degrees \
--quiet
/builds/NikosAlexandris/pvgis-prototype/.venv/lib/python3.11/site-packages/sparklines/sparklines.py:33: UserWarning: Found negative value(s): -787.1695556640625, -1062.1922607421875, -1555.4775390625, -2422.764892578125, -3658.6083984375, -3766.09423828125, -2714.02734375, -1595.6473388671875, -675.1864624023438, -597.9326171875, -571.8305053710938. While not forbidden, the output will look unexpected.
warnings.warn(msg)
╭──────────────────────────────────────────────────────────────╮ ╭───────────────────────────────────────────────────╮
│ Latitude Longitude Elevation Orientation Tilt Unit │ │ Start Every End Zone │
│ 45.812 8.628 214.0 3.142 0.0 radians │ │ 2013-01-01 00:00 - 2013-12-31 00:00 UTC │
╰────────────────────────────────────────────── Solar Surface ─╯ ╰───────────────────────────────────────────────────╯
╭──────────────────────────────────────────────────────────────╮
│ Tech Peak-Power Mount Type │
│ cSi 1.0 Peak Power Unit Free standing │
╰────────────────────────────────────────────────── PV Module ─╯
╭─────────────────────────────────────────────────────────── Analysis of Performance ────────────────────────────────────────────────────────────╮
│ │
│ Quantity Total Unit % of Monthly Sums Mean Unit Variability Source │
│ ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── │
│ In-Plane Irradiance 1693.5 ㎾/m² ▃▃▃▄▅▇██▆▁▂▃ 193.7 W/m² │
│ │
│ Reflectivity -20.0 ㎾/m² -1.2 In-Plane Irradiance ██▇▆▄▁▁▃▆███ -2.3 W/m² 3.4 │
│ Irradiance After Reflectivity 1673.5 ㎾/m² 139.5 ㎾/m² │
│ │
│ Spectral effect +17.3 ㎾/m² +1.0 In-Plane Irradiance █▇▆▄▄▃▁▃▅▆▇▇ 2.0 3.2 │
│ Effective Irradiance 1690.9 ㎾/m² 139.5 ㎾/m² │
│ │
│ Temperature & Low Irradiance Effect -135.4 ㎾/m² -8.0 Effective Irradiance -139.3 ㎾/m² │
│ Power ⌁ without Loss 1555.5 ㎾ ▃▄▄▄▅███▆▁▃▄ 178.0 W 244.2 │
│ │
│ System Loss -217.8 ㎾ -14.0 Power ⌁ without Loss -18.1 ㎾ │
│ Power ⌁ 1337.7 ㎾ ▃▄▄▄▅███▆▁▃▄ 153.1 W 210.0 │
│ │
│ Energy 🔌 1337.7 ㎾h 153.1 Wh │
│ Net Effect -355.8 ㎾/m² -21.0 In-Plane Irradiance -40.7 W/m² │
│ │
╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
PVGIS provides a compact overview of the calculations that generate the final power output.
Nonetheless, in order to make better sense of the reported figures, we can go through the algorithmic structure of the power-rating model implemented in PVGIS.
The flow of calculations is :
Efficiency¶
To do
Add content!
Photovoltaic power¶
PVGIS uses a modified version of the power-rating model by King.
Huld, 2011
Thomas Huld, Gabi Friesen, Artur Skoczek, Robert P. Kenny, Tony Sample, Michael Field, Ewan D. Dunlop, A power-rating model for crystalline silicon PV modules, Solar Energy Materials and Solar Cells, Volume 95, Issue 12, 2011, Pages 3359-3369, ISSN 0927-0248, doi.org/10.1016/j.solmat.2011.07.026 (https://www.sciencedirect.com/science/article/pii/S0927024811004442)
Abstract
A model for the performance of generic crystalline silicon photovoltaic (PV) modules is proposed. The model represents the output power of the module as a function of module temperature and in-plane irradiance, with a number of coefficients to be determined by fitting to measured performance data from indoor or outdoor measurements. The model has been validated using data from 3 different modules characterized through extensive measurements in outdoor conditions over several seasons. The model was then applied to indoor measurement data for 18 different PV modules to investigate the variability in modeled output from different module types. It was found that for a Central European climate the modeled output of the 18 modules varies with a standard deviation (SD) of 1.22%, but that the between-module variation is higher at low irradiance (SD of 3.8%). The variability between modules of different types is thus smaller than the uncertainty normally found in the total solar irradiation per year for a given site. We conclude that the model can therefore be used for generalized estimates of PV performance with only a relatively small impact on the overall uncertainty of such estimates resulting from different module types.
Keywords Crystalline silicon; PV energy rating; PV performance; Performance rating
We can simulate the photovoltaic power output via
or estimate it by reading external irradiance time series via
pvgis-prototype power broadband \
8.628 45.812 214 180 45 \
'2010-01-27 12:00:00' \
--global-horizontal-irradiance sarah2_sis_over_esti_jrc.nc \
--direct-horizontal-irradiance sarah2_sid_over_esti_jrc.nc \
--neighbor-lookup nearest
Panel tilt¶
The default tilt angle for a solar surface is 45 degrees. In order to get the calculations done for a horizontally flat panel, we need to request this via the fifth positional parameter with a value close to 0 like 0.0001.
Let's add it to the power commands :
- simulating the photovoltaic power output
- using SARAH2 data
pvgis-prototype power broadband \
8.628 45.812 214 180 0.0001 \
'2010-01-27 12:00:00' \
--global-horizontal-irradiance sarah2_sis_over_esti_jrc.nc \
--direct-horizontal-irradiance sarah2_sid_over_esti_jrc.nc \
--neighbor-lookup nearest
We can request more details on the calculations
pvgis-prototype power broadband \
8.628 45.812 214 180 0.0001 \
'2010-01-27 12:00:00' \
--global-horizontal-irradiance sarah2_sis_over_esti_jrc.nc \
--direct-horizontal-irradiance sarah2_sid_over_esti_jrc.nc \
--neighbor-lookup nearest \
-vvv
Power series [W]
Power ⌁ Linke
without Efficien… Turbidity Altitude Incidence Sun-Hori… Shading In-shade
Time Power ⌁ Loss ⋅ ⋅ ⦩ ⭸ ⛰ state 🮞 🮞 Horizon ⛰ Visible 👁
──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
2010-01-27 12:00:00 520.878 605.672 0.928 unset 2.0 0.442 1.128 Above Unset False 0.0 True
⅀ / μ 520.878 605.672 0.928286…
╭──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ Location Longitude ϑ, Latitude ϕ = 0.151, 0.8, Elevation: 214.0 m Angular units radians │
│ Module Type: Mono-Facial, Technology: cSi, Mount: Free standing, Peak Power: 1.0 kWp │
│ Definitions Azimuth origin : Not Required!, UTC, Incidence angle: Sun-Vector-to-Surface-Normal, Sun-to-Horizon: ['Above', 'Below', 'Low angle'] │
│ Algorithms Power model ⌁: Huld 2011, Shading : PVGIS, Shading states : ['all'] │
│ Radiation model ⸾ : Hofierka 2002, Irradiance units W │
│ Equation : P(G₀, T₀) = G₀(P₀ₛₜ₃, m + k₁G₀) + k₂G₀)² + k₃T₀ + k₄T₀G₀ + k₅T₀G₀² + k₆T₀² │
│ Constants Solar constant : 1367.0 │
╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── Reference ─╯
╭───────────────────────────────────────────────────────╮
│ ⌁ Power Azimuth 🮞 Shading │
│ ⸾ Irradiance ⯐ Positioning ⋅ Factor │
│ - Loss ⛰ Horizon ⅀ N-ary Summation │
│ ⍖ Extra Normal ↻ Orientation μ Mean │
│ ⦜ Normal ⦥ Tilt │
│ ⏲ Timing ⭸ Incidence │
│ ⦩ Altitude 👁 Visible │
╰────────────────────────────────────────────── Legend ─╯