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 irradiance [OPTIONS] COMMAND [ARGS]...
🌞 Calculate the solar irradiance incident on a solar surface
╭─ Options ────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ --help Show this message and exit. │
╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
╭─ Introduction ───────────────────────────────────────╮
│ introduction A short primer on solar irradiance │
╰──────────────────────────────────────────────────────╯
╭─ External solar irradiance time series ─────────────────────────────────╮
│ global ⸾ Calculate the global irradiance │
│ direct ⇣ Calculate the direct irradiance │
│ diffuse 🗤 Calculate the diffuse irradiance │
│ ground-reflected ⭞ Calculate the clear-sky ground reflected irradiance │
│ extraterrestrial 🌣 Calculate the extraterrestrial normal 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 SARAH-3 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 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 <parse_timestamp_series> 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 <int> 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! │
│ --periods <int> Number of timestamps to generate │
│ --frequency <str> 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. │
│ --end-time,--et <parse_timestamp> End timestamp of the period. Overrides the │
│ `timestamps` parameter! │
│ --timezone,--tz,--zone <parse_timezone> Timezone (e.g., 'Europe/Athens'). Use the │
│ system's time zone via the `--local` option. │
│ --random-timestamps --no-random-timestamps Generate a random date, time and timezone to │
│ demonstrate calculation │
│ [default: no-random-timestamps] │
╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
╭─ Atmospheric properties ─────────────────────────────────────────────────────────────────────────────────────────────╮
│ --linke-turbidity-factor-s… <parse_linke_turbidity_fac Ratio of total to Rayleigh │
│ tor_series> optical depth measuring │
│ atmospheric turbidity │
│ [default: 2] │
│ --apply-atmospheric-refrac… --no-apply-atmospheric-re… Correct solar azimuth and │
│ altitude angles for │
│ atmospheric refraction │
│ [default: │
│ apply-atmospheric-refracti… │
│ --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-m… <all|noaa|hofierka|jenco|pvlib|pys Model to calculate solar position │
│ olar|skyfield|suncalc> [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] │
│ --perigee-offset <float> Perigee offset [default: 0.048869] │
│ --eccentricity-correction-factor <float> Eccentricity correction factor [default: 0.03344] │
╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
╭─ > Input : < Output ─────────────────────────────────────────────────────────────────────────────────────────────────╮
│ --angle-output-units -aou <str> Angular units for solar geometry calculations (degrees or radians). ⚠ Under │
│ development │
│ [default: radians] │
│ --rounding-places -r <int> Number of digits to round results to [default: 3] │
│ --csv <path> CSV output filename │
│ --verbose -v <int> 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 <str> Data type [default: float32] │
│ --array-backend <str> Array backend [default: numpy] │
╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
╭─ Statistics ─────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ --statistics --no-statistics Calculate and display summary statistics [default: no-statistics] │
│ --groupby <str> 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. │
╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
╭─ 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:
Global Irradiance & relevant components in-plane irradiance series W/m² (1/3)
Time ⭳ Global Horizontal Irradiance ⭳ Direct Horizontal Irradiance
───────────────────────────────────────────────────────────────────────────────────────
2024-01-27 12:00:00 458.814 405.941
⅀ / μ 405.941
Global Irradiance & relevant components in-plane irradiance series W/m² (2/3)
Time ⭳ Diffuse Horizontal Irradiance ⦜ Extraterrestrial Normal Irradiance ⦩ Altitude
───────────────────────────────────────────────────────────────────────────────────────────────────────────
2024-01-27 12:00:00 52.874 1402.449 0.442
⅀ / μ 52.874
Global Irradiance & relevant components
in-plane irradiance series W/m² (3/3)
Time Linke Turbidity
───────────────────────────────────────
2024-01-27 12:00:00 2.0
⅀ / μ
╭────────────────────────────────────────────────────────╮ ╭─────────────────────────────────────╮
│ Angular units ㎭ radians │ │ ⭳ Horizontal ⅀ N-ary Summation │
│ Location Longitude, Latitude = 0.151, 0.8Zone : UTC, │ │ ⦜ Normal μ Mean │
│ Algorithms Radiation model: Hofierka 2002 │ │ ⦩ Altitude │
╰──────────────────────────────────────────── 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:
Satellite observations of solar irradiance¶
Instead of relying on the model, let's read-in observations of solar irradiance from the SARAH-3 data collection:
SARAH-3 SIS¶
- Read the
SIScomponent from SARAH-3:
pvgis series select \
data/sample_sarah3_sis_over_esti.nc \
8.628 45.812 \
'2024-01-27 12:00:00' \
--neighbor-lookup nearest \
--mask-and-scale \
-v
SARAH-3 SID¶
- Read the
SIDcomponent from SARAH-3:
pvgis series select \
data/sample_sarah3_sid_over_esti.nc \
8.628 45.812 \
--neighbor-lookup nearest \
-v \
--mask-and-scale \
'2024-01-27 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 series select and read the help text.
Indeed, the simulated values differ from the satellite-based observations retrieved from the SARAH-3 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:
$$
\operatorname{DNI} = \frac{\operatorname{SID}}{\cos\!\left(\theta_{z}\right)}
$$
See also
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
────────────────────────────────
2024-01-17 12:00:00 1.168
╭────────────────────────────────────────────────────────────────╮
│ ⏳ Start Time ⏱ Frequency ⌛ End Time Timezone │
│ 2024-01-17 12:00 Single timestamp 2024-01-17 12:00 UTC │
╰────────────────────────────────────────────────────────────────╯
╭─────────────────────────────────────────────────────────╮
│ Position longitude, latitude = 0.151, 0.8, Unitless │
│ Algorithms Timing : NOAA, Zone : UTC, Positioning : NA │
╰───────────────────────────────────────────── Reference ─╯
╭─────────────╮
│ ⦭ Zenith │
│ │
╰──── Legend ─╯
-
Next, open a Python interpreter
-
Set the direct horizontal irradiance reported in SARAH-3 and the zenith angle calculated previously
-
Calculate the
DNIusing simple PythonDNI = 946.4469113172491
Let's compare with PVGIS' model:
I guess 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 SARAH-3 observation.
Is it? Let's find out...
Note
Isn't this close enough to 371?
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 & relevant components in-plane irradiance series W/m²
(1/3)
Time ∡ Global Inclined Irradiance ∡ Direct Inclined Irradiance
───────────────────────────────────────────────────────────────────────────────────
2024-01-27 12:00:00 995.905 887.152
⅀ / μ 995.905 887.152
Global Inclined Irradiance & relevant components in-plane irradiance series W/m² (2/3)
Time ∡ Diffuse Inclined Irradiance ∡ Ground Reflected Inclined Irradiance ☂ In shade
────────────────────────────────────────────────────────────────────────────────────────────────────────────
2024-01-27 12:00:00 96.26 12.493 False
⅀ / μ 96.26 12.493
Global Inclined Irradiance & relevant components
in-plane irradiance series W/m² (3/3)
Time ☉ ⛰ Sun-Horizon Position
────────────────────────────────────────────────
2024-01-27 12:00:00 Above
⅀ / μ
╭──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ Angular units ㎭ radians │
│ Location Longitude, Latitude = 0.151, 0.8, Elevation: 210.0 m │
│ Position Surface Orientation: 3.142, Surface Tilt: 0.785 │
│ Definitions Zone : UTC, Incidence angle: Sun-Vector-to-Surface-Plane, Sun-Horizon Positions: Above, Low angle, │
│ Below, Shading states: Sunlit, Potentially-sunlit, In-shade, │
│ Algorithms Radiation model: Hofierka 2002, Timing : NOAA, Positioning : NOAA, Incidence : Iqbal, │
│ Constants Solar constant : 1360.8, Perigee : 0.048869, Eccentricity : 0.03344 │
╰────────────────────────────────────────────────────────────────────────────────────────────────────────── Reference ─╯
╭───────────────────────────────╮
│ ∡ Tilt μ Mean │
│ ☂ In shade │
│ ☉ Sun │
│ ⛰ Horizon │
│ - Loss │
│ ⅀ N-ary Summation │
╰────────────────────── 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 information
If we read the SIS and SID SARAH-3 components to get the Global Inclined Irradiance:
- The diffuse inclined component here uses, of course, SARAH-3 SIS and SID and it is calculated using the command:
pvgis irradiance diffuse inclined \
8.628 45.812 210 180 45 \
'2024-01-27 12:00:00' \
--global-horizontal-irradiance data/sample_sarah3_sis_over_esti.nc \
--direct-horizontal-irradiance data/sample_sarah3_sid_over_esti.nc \
--neighbor-lookup nearest
From normal to horizontal irradiance¶
\[
\mathrm{DHI} = \mathrm{DNI} \cdot \sin(\alpha_{\mathrm{solar}})
\]
Solar Altitude Series
Time ⦩ Altitude
──────────────────────────────────
2024-01-17 12:00:00 0.403
╭────────────────────────────────────────────────────────────────╮
│ ⏳ Start Time ⏱ Frequency ⌛ End Time Timezone │
│ 2024-01-17 12:00 Single timestamp 2024-01-17 12:00 UTC │
╰────────────────────────────────────────────────────────────────╯
╭─────────────────────────────────────────────────────────╮
│ Position longitude, latitude = 0.151, 0.8, Unitless │
│ Algorithms Timing : NOAA, Zone : UTC, Positioning : NA │
╰───────────────────────────────────────────── Reference ─╯
╭───────────────╮
│ ⦩ Altitude │
│ │
╰────── Legend ─╯