Solar Irradiance
Simulating horizontal irradiance¶
We can simulate solar irradiance components using PVGIS!
To start with, let us check the interface of the irradiance commands :
Usage: pvgis-prototype irradiance [OPTIONS] COMMAND [ARGS]...
⸾ Calculate the solar irradiance incident on a solar surface
╭─ Options ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ --help Show this message and exit. │
╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
╭─ Introduction ────────────────────────────────╮
│ introduction Primer on solar irradiance │
╰───────────────────────────────────────────────╯
╭─ Solar irradiance time series ──────────────────────────────────────╮
│ global ⤋ Calculate the global irradiance │
│ direct ⇣ Calculate the direct irradiance │
│ diffuse 🗤 Calculate the diffuse sky-reflected irradiance │
│ extraterrestrial ⍖ Estimate the extraterrestrial irradiance │
╰─────────────────────────────────────────────────────────────────────╯
╭─ Toolbox ────────────────────────────────────────────────────────────────────────╮
│ kato-bands [⸾] Kato spectral bands limits and center wavelengths │
│ reflectivity ⭜⋅ Calculate the reflectivity effect factor Yet not complete! │
│ limits [⸾] Calculate physically possible irradiance limits │
╰──────────────────────────────────────────────────────────────────────────────────╯
We can simulate all components of solar radiation : direct, diffuse, reflected and global. Let us begin, however, with the global and direct components. These are, after all, the ones we will compare against the SARAH3 satellite-based observations.
Global horizontal irradiance¶
As a first step, we can simulate the global horizontal irradiance over our location of interest and moment in time :
Consult the help text!
It's always a good idea to consult the help for a command. While effort has been given to keep the same order for the input parameters, not all commands share the exact same required positional parameters!
For the above command, we can get the help via
Usage: pvgis-prototype irradiance global horizontal [OPTIONS] LONGITUDE
LATITUDE ELEVATION
[TIMESTAMPS]
Calculate the broadband global horizontal irradiance over a time series
╭─ Arguments ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ * longitude FLOAT RANGE Longitude in decimal degrees ranging in [-180, 360]. If ranging in [0, 360], consider the `--convert-longitude-360` option. │
│ [required] │
│ * latitude FLOAT RANGE Latitude in decimal degrees ranging in [-90, 90] [required] │
│ * elevation FLOAT RANGE Topographical elevation [required] │
╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
╭─ Timestamps ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ timestamps [TIMESTAMPS] Quoted date-time strings of data to extract from series, example: '2112-12-21, 2112-12-21 12:21:21, 2112-12-21 21:12:12'' │
╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
╭─ Options ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ --resample-large-series --no-resample-large-series [default: no-resample-large-series] │
│ --log -l INTEGER Enable logging [default: 0] │
│ --help Show this message and exit. │
╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
╭─ Timestamps ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ --start-time,--st PARSE_TIMESTAMP Start timestamp of the period. Overrides the `timestamps` parameter! [default: None] │
│ --periods INTEGER Number of timestamps to generate [default: None] │
│ --frequency TEXT A common date/time frequency unit optionally with a multiples number, such as │
│ H(hourly), min(utely), S(econdly), D(aily), W(eekly), M(onth end), Y(early) or 30min. │
│ See Pandas time series offset aliases. │
│ [default: None] │
│ --end-time,--et PARSE_TIMESTAMP End timestamp of the period. Overrides the `timestamps` parameter! [default: None] │
│ --timezone,--tz,--zone PARSE_TIMEZONE Timezone (e.g., 'Europe/Athens'). Use the system's time zone via the `--local` option. │
│ [default: None] │
│ --random-timestamps --no-random-timestamps Generate a random date, time and timezone to demonstrate calculation │
│ [default: no-random-timestamps] │
╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
╭─ Atmospheric properties ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ --linke-turbidity-factor-series PARSE_LINKE_TURBIDITY_FACTOR_SERIES Ratio of total to Rayleigh optical │
│ depth measuring atmospheric turbidity │
│ [default: name=None title='Linke │
│ Turbidity' description='The Linke │
│ Turbidity Factor describes the │
│ attenuation of the extraterrestrial │
│ solar radiation by solid and liquid │
│ particles under cloudless sky │
│ conditions. It indicates the optical │
│ density of hazy and humid atmosphere │
│ in relation to a clean and dry │
│ atmosphere. In other words TLK is the │
│ number of clean dry air masses that │
│ would result in the same extinction │
│ then real hazy and humid air. Due to a │
│ dynamic nature of the turbidity │
│ factor, its calculation and subsequent │
│ averaging leads to a certain degree of │
│ generalisation. There are clear │
│ seasonal changes of the turbidity │
│ (lowest values in winter, highest in │
│ summer), the values of turbidity │
│ factor always differ from place to │
│ place in a similar degree of magnitude │
│ and these differences are also │
│ correlated with the terrain elevation. │
│ It increases with an intensity of │
│ industrialisation and urbanisation. │
│ The values of Linke turbidity for │
│ different landscapes or world regions │
│ can be found in literature [e.g. 16, │
│ 19, 30] or in http://www.soda-is.com/ │
│ [20]).' symbol='⋅' value=2 │
│ unit='unitless' minimum=0 maximum=8] │
│ --adjust-for-atmospheric-refraction --no-adjust-for-atmospheric-refraction Correct solar azimuth and altitude │
│ angles for atmospheric refraction │
│ [default: │
│ adjust-for-atmospheric-refraction] │
│ --refracted-solar-zenith FLOAT Refracted solar zenith angle (in │
│ radians) for sun -rise and -set events │
│ [default: 1.5853349194640094] │
╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
╭─ Advanced ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ --apply-reflectivity-factor --no-apply-reflectivity-factor Apply angular loss function [default: apply-reflectivity-factor] │
╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
╭─ Solar position ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ --solar-position-model,--position-model,--positi… [all|NOAA|Hofierka|Jenco|pvlib|Skyfield|suncalc] Model to calculate solar position [default: NOAA] │
╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
╭─ Solar time ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ --solar-time-model [all|Milne1921|NOAA|PVGIS|pvlib|Skyfield] Model to calculate solar time [default: NOAA] │
╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
╭─ Earth orbit ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ --solar-constant FLOAT RANGE [x>=1360] Top-of-Atmosphere mean solar electromagnetic radiation (W/m-2) 1 au (astronomical unit) away from │
│ the Sun. │
│ [default: 1360.8] │
│ --eccentricity-phase-offset FLOAT Eccentricity phase offset (in radians) aligning the eccentricity correction with Earth's │
│ perihelion position in its orbit, part of calculation of the solar declination angle. │
│ [default: 0.048869] │
│ --eccentricity-amplitude FLOAT Amplitude of the Earth's orbital eccentricity effect on solar irradiance variation throughout the │
│ year, part of the calculation of the solar declination angle. │
│ [default: 0.03344] │
╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
╭─ > Input : < Output ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ --angle-output-units -aou TEXT Angular units for solar geometry calculations (degrees or radians) [default: radians] │
│ --rounding-places -r INTEGER Number of digits to round results to [default: 3] │
│ --csv PATH CSV output filename [default: None] │
│ --verbose -v INTEGER Show details while executing commands [default: 0] │
│ --index,--idx -i Index rows in output table (meaningful with at least 1x -v) │
│ --quiet Do not print out the output │
╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
╭─ Data processing ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ --dtype TEXT Data type [default: float32] │
│ --array-backend TEXT Array backend [default: numpy] │
╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
╭─ Statistics ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ --statistics --no-statistics Calculate and display summary statistics [default: no-statistics] │
│ --groupby TEXT Group statistics, ex. M or 3h. A number and date/time unit : (Y)ear, (S)eason, (M)onth, (D)ay, (W)eek, (h)our. See │
│ Xarray's group-by operations. │
│ [default: None] │
╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
╭─ Plotting ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ --uniplot --no-uniplot Plot the PV power output time series in the terminal [default: no-uniplot] │
│ --terminal-width-fraction FLOAT Fraction of number of columns of the current terminal, ex. 0.9 [default: 0.9] │
╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
╭─ Metadata ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ --fingerprint,--fp Fingerprint the output time series │
│ --metadata --no-metadata Print command metadata [default: no-metadata] │
╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
We can see how this simulated quantity breaks down in its sub-components too by using a few -vs :
Global Horizontal Irradiance in-plane irradiance series W/m²
Global Horizontal ⤋
Time Altitude ⦩ Unrefracted ⦧ Linke Turbidity ⋅ Extra Normal ⦜ Direct Horizontal ⇣ ⭳ Diffuse Horizontal 🗤⭳ ⭳
──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
2010-01-27 12:00:00 0.442 True 2.0 1402.426 406.281 52.892 459.173
⅀ / μ 406.281
╭─────────────────────────────────────────────────────────────────────────────────╮ ╭─────────────────────────────────────────────────────╮
│ Location Longitude ϑ, Latitude ϕ = 0.151, 0.8 Angular units Unitless │ │ ⸾ Irradiance 🗤 Diffuse ⋅ Factor │
│ Algorithms Timing : NOAA, Positioning : NOAA, Adjusted for refraction : True, │ │ ⇣ Direct ⏲ Timing ⅀ N-ary Summation │
│ Radiation model ⸾ : Hofierka 2002, Irradiance units W/m² │ │ ⭳ Horizontal ⦩ Altitude μ Mean │
│ Constants Solar constant : 1367.0 │ │ ⦜ Normal ⯐ Positioning │
╰───────────────────────────────────────────────────────────────────── Reference ─╯ ╰──────────────────────────────────────────── Legend ─╯
Direct horizontal irradiance¶
We will get the same simulated direct horizontal estimation by using the direct horizontal commands :
Diffuse horizontal irradiance¶
The diffuse component is the difference between global and direct. As with the previous command examples, we can derive the diffuse horizontal component via :
Note
The diffuse horizontal irradiance component does not need to know of an elevation value, hence compared to the command for the direct irradiance, the number 214 was removed in this example command.
Satellite observations of solar irradiance¶
Instead of relying on the model, let's read-in observations of solar irradiance from the SARAH3 data collection :
SARAH3 SIS¶
- Read the
SIScomponent from SARAH3 :
pvgis-prototype series select \
sarah2_sis_over_esti_jrc.nc \
8.628 45.812 \
'2010-01-27 12:00:00' \
--neighbor-lookup nearest \
--mask-and-scale \
-v
SARAH3 SID¶
- Read the
SIDcomponent from SARAH3 :
pvgis-prototype series select \
sarah2_sid_over_esti_jrc.nc \
8.628 45.812 \
--neighbor-lookup nearest \
-v \
--mask-and-scale \
'2010-01-27 12:00:00'
Optional and required parameters
The latter command differs from the one before in that the order of the optional and required input parameters is not the same. The message here is that : indeed, we can mix the order of optional parameters in-between as long as we keep strictly the order of the required ones, as indicated in the help section of a command.
Just run pvgis-prototype series select and read the help text !
Indeed, the simulated values differ from the satellite-based observations retrieved from the SARAH3 datasets. Aren't they close enough ? We need to keep in mind that a series of assumptions and simplifications are part of the solar radiation model.
Direct normal irradiance¶
In estimating the photovoltaic power output, the solar radiation component with the greatest impact, is the direct normal irradiance.
From the theory, we know that
\[ Direct Normal Irradiance = Direct Horizontal Irradiance / cos(Solar Zenith Angle) \]
or using acronyms frequently used in solar science
\[ DNI = SID / cos(Solar Zenith Angle) \]
Note
Equation 3-6 from https://www.cmsaf.eu/SharedDocs/Literatur/document/2023/saf_cm_dwd_pum_meteosat_hel_sarah_3_3_pdf.pdf?__blob=publicationFile.
- First, let's get the zenith angle in radians
Solar Zenith Series
Time Zenith ⦭
────────────────────────────────
2010-01-17 12:00:00 1.168
⅀ / μ
╭─────────────────────────────────────────────────╮ ╭────────────────────────────────────────────────────────────────────────╮ ╭─────────────╮
│ Start Every End Zone │ │ Location Longitude ϑ, Latitude ϕ = 0.151, 0.8 Angular units Unitless │ │ ⦭ Zenith │
│ 2010-01-17 12:00 - 2010-01-17 12:00 UTC │ │ Definitions Unrefracted zenith: True │ │ │
│ │ ╰──────────────────────────────────────────────────────────── Reference ─╯ ╰──── Legend ─╯
│ │
╰─────────────────────────────────────────────────╯
Bug
There is likely a bug in the position zenithcommand currently!
-
Next, open a Python interpreter
-
Set the direct horizontal irradiance reported in SARAH3 and the zenith angle calculated previously
-
Calculate the
DNIusing simple PyhonDNI = 1062.5725738840667
Let's compare with PVGIS' model :
We can assume the model in the new software is close and not wildly out of range !
Horizontal irradiance¶
If we simulate also the Direct Horizontal Component, it should be close to the SARAH3 observation.
Is it ? Let's find out ...
Note
Isn't this close enough to 431 ?
Inclined irradiance¶
Next, the simulated direct inclined component :
And the simulated global inclined component is :
Analytically, the above figure is broken down to its inclined components as :
Global Inclined Irradiance in-plane irradiance series W/m²
Ref… Lin… Dir… Sky… Gro… Sky… Dir… Extra Ext… Sha…
Dir… Sky… Gro… Glo… alt. Tur… Inc… ⇣ ∡ 🗤 ∡ ⭞ ∡ Hor… Hor… Hori… Nor… Alti… Inc… Sun-… sta… In-s…
Time ⇣ ∡ 🗤 ∡ ⭞ ∡ ⤋ ∡ ⦧ ⦩ ⋅ Irr… ☉ ☉ ☉ 🗤⭳ ⇣ ⭳ ⍖ ⭳ ⍖ ⦜ ⦩ ⭸ ⛰ 🮞 🮞
──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
2010-01-27 12:00:00 887… 96.… 12.… 996… 25.… 2.0 100… 890… 97.… 13.… 52.… 406… 600.… 140… 0.442 1.22 Above Sun… False
⅀ / μ 887… 96.… 12.… 996… 890… 97.… 13.… 52.… 406… 600.… 140…
╭──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ Location Longitude ϑ, Latitude ϕ = 0.151, 0.8, Elevation: 210.0 m │
│ Position Surface Orientation ↻: 3.142, Surface Tilt ⦥: 0.785 Angular units None │
│ Definitions Incidence angle: Sun-Vector-to-Surface-Plane, Sun-to-Horizon: ['Below', 'Low angle', 'Above'] │
│ Algorithms Timing : NOAA, Positioning : NOAA, Incidence : Iqbal, Shading : PVGIS, Shading states : ['Sunlit', 'In-shade', 'Potentially-sunlit'] │
│ Radiation model ⸾ : Hofierka 2002, Irradiance units W/m² │
│ Equation : Direct ⇣∡ + Sky-Diffuse 🗤∡ + Ground-Diffuse ⭞∡ │
│ Constants Solar constant : 1367.0 │
╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── Reference ─╯
╭───────────────────────────────────────────────────────╮
│ ⸾ Irradiance 🗤 Diffuse ↻ Orientation │
│ - Loss ⭞ Reflected ⦥ Tilt │
│ ∡ Inclined ⏲ Timing ⭸ Incidence │
│ ⇣ Direct ⦩ Altitude 🮞 Shading │
│ ⭳ Horizontal Azimuth ⋅ Factor │
│ ⍖ Extra Normal ⯐ Positioning ⅀ N-ary Summation │
│ ⦜ Normal ⛰ Horizon μ Mean │
╰────────────────────────────────────────────── Legend ─╯
Default orientation and tilt angles
The default values for the orientation and tilt angles of a solar surface are (currently) set to 180 and 45 degrees respectively. Hence, we'd get the same result if we
EXTRA
If we read the SIS and SID SARAH3 components to get the Global Inclined Irradiance :
- The diffuse inclined component here uses, of course, SARAH3 SIS and SID and goes through the math to derive to
69.08706.
From normal to horizontal irradiance¶
\[ Direct Horizontal Irradiance = Direct Normal Irradiance * sin(Solar Altitude) \]