As solar
energy we understand the energy that falls on the earth in the form
of sunlight. The sun is the source of solar energy and it is
renewable and virtually inexhaustible source of energy. The sun
produces 1,1*1020 kWh per second [1].
On the border of the earth's atmosphere
the average solar energy varies from 1340 to 1390 W.m-2.
The average value of the energy is called the solar constant. Solar
constant is the maximum quantity that can fall into the stratosphere,
and this is the maximum value that can be obtained per square meter.
[2]
Spreadsheet in available for download in LibreOffice Calc and MS Office Excel format for easy and fast calculations.
1. Parameters determining the position of the sun in the sky
An important particularity
regarding the use of solar energy is the movement of the sun the sky.
Movement is caused by the Earth's rotation about its axis and
changing the path of the sun the sky during the year.
An important parameter for
determining the position of the sun in the sky are:
- Height of the sun above the horizon (h),
- Azimuth angle of the sun (α),
- Angle of incidence sunbeam (γ),
1.1 Height of the sun above the horizon
Height if the sun above the horizon is angle between horizon and sun and you can calculate it with the following formula:
Where:
δ solar
declination [°]
Φ laditude
[°]
τ time
angle [°]
Spreadsheet calculator:
Spreadsheet calculates height if the sun above the horizon from 8:00 hours to 16:00 hours for every month of the year.
1.1.1 Solar declination
Values of solar declination are for every day
differed in spreadsheet values of solar
declination are only for specific dates of the month:
- 22.XII
- 22.XI and 21.I
- 23.X and 20.II
- 23.IX and 21.III
- 23.VIII and 21 IV
- 23.VII and 22.V
- 22.VI
Spreadsheet
calculator:
In
spreadsheet values of solar declination can be changed in “Sun
azimuth and height” sheet.
1.1.2 Latitude
Spreadsheet
calculator:
Latitude in spreadsheet is in WGS84 format and can be changed in
“Home” sheet.1.1.3 Time angle
Time angle is measured from 12:00 hours, one hour corresponds to an angle of 15 °.
Spreadsheet
calculator:
In
spreadsheet values of time angle
can be changed in “Sun azimuth and height” sheet.
1.2 Azimuth angle of the sun
Azimuth angle of the sun can be calculated with the following formula:
Where:
δ solar
declination [°]
h height
if the sun above the horizon [°]
τ time
angle [°]
Spreadsheet
calculator:
Azimuth
angle from -180 to 180. East=-90, South=0
Spreadsheet
calculates azimuth angle of
the sun from
8:00 hours to 16:00 hours for every month of the year.
 |
| Calculated parameters determining the position of the sun in the sky in spreadsheet |
1.3 Angle of incidence sunbeam
Angle of incidence sunbeam can be calculated with
following formula:
Where:
h height
if the sun above the horizon [°]
α azimuth
angle of the sun [°]
a slope
angle of surface (panel) [°]
as azimuth
of the surface (panel) [°]
Spreadsheet
calculator:
Spreadsheet calculate angle of incidence sunbeam from
8:00 hours to 16:00 hours for every month of the year. For
six slope angles (default 0°,
15°,
30°,
45°,
60°,
75°
and 90°)
and given azimuth of surface (default 0°).
 |
| Calculated angle of incidence sunbeam in spreadsheet |
2 Solar irradiance
We distinguish:
- Intensity of the diffuse irradiation (ID),
- Intensity of direct irradiation (IP),
- Total irradiation (I).
2.1 Intensity of direct irradiation
As intensity of direct irradiation we understand solar radiation in clear sky that falls directly onto the surface. We can calculate intensity of direct irradiation with following formula:
IPn direct solar radiation on the surface perpendicular to the direction of sun ray [W.m-2]
γ Angle of incidence sunbeam [°]
Spreadsheet
calculator:
Values
of intensity of direct irradiation are available in “Intensity of
direct irradiation” sheet. From
8:00 hours to 16:00 hours for every month of the year. For
six slope angles (default 0°,
15°,
30°,
45°,
60°,
75°
and 90°)
and given azimuth of surface (default 0°).
 |
| Calculated intensity of direct irradiation in spreadsheet |
2.1.1 Direct solar radiation on the surface perpendicular to the direction of sun ray
Direct solar
radiation on the surface perpendicular to the direction of sun ray
can be calculated with following formula:
Where:
Io solar constant [W.m-2]
Z coefficient
of atmospheric pollution [-]ε coefficient [-]
Spreadsheet
calculator:
Values
of direct solar radiation on the surface perpendicular to the
direction of sun ray are available in “Irradiance + coefficient”
spreadsheet.
2.1.2 Coefficient ε
Coefficient ε depends on the height of the sun above the horizon and the altitude and can be calculated with following formula:
Where: H altitude [m]
Spreadsheet
calculator:
alues
of coefficient ε are available in “Irradiance + coefficient”
spreadsheet.
2.1.3 Coefficient of atmospheric pollution
Coefficient of atmospheric pollution represents value of air pollution in different areas for a period of 12 months. You can get value of coefficient of atmospheric pollution from table bellow. |
| Table 1. Coefficient of atmospheric pollution |
Spreadsheet
calculator:
Coefficient
of atmospheric pollution can be specified in “Home” sheet.
2.2 Intensity of the diffuse irradiation
Diffuse sky radiation is solar radiation reaching the Earth's surface after having been scattered from the direct solar beam by molecules or suspension in the atmosphere.Diffuse irradiation can be calculated with following formula:
r reflective ability [-]
IPh direct solar irradiation on a horizontal surface [W.m-2]
IDh diffuse irradiation on horizontal surface [W.m-2]
Spreadsheet
calculator:
Values
of intensity of diffuse irradiation are available in “Intensity of
diffuse irradiation” sheet. From
8:00 hours to 16:00 hours for every month of the year. For
six slope angles (default 0°,
15°,
30°,
45°,
60°,
75°
and 90°)
and given azimuth of surface (default 0°).
 |
| Calculated intensity of the diffuse irradiation in spreadsheet |
2.2.1 Direct solar irradiation on a horizontal surface
Direct solar irradiation on a horizontal surface can be calculated with following formula:
Spreadsheet
calculator:
Values
of
2.2.2 Diffuse irradiation on horizontal surface
Diffuse
irradiation on horizontal surface can be calculated with following
formula:
Spreadsheet
calculator:
Values
of
2.3 Total irradiation
Total solar irradiation represents summation of direct and diffuse solar irradiation and it can be calculated with following formula:
Where:
IP
intensity of direct irradiation [W.m-2]
ID intensity of the diffuse irradiation [W.m-2]
Spreadsheet
calculator:
Values
of total irradiation are available in “Total irradiation” sheet.
From
8:00 hours to 16:00 hours for every month of the year. For
six slope angles (default 0°,
15°,
30°,
45°,
60°,
75°
and 90°)
and given azimuth of surface (default 0°).
In
sheet “Average irradiation” are average daily values for direct,
diffuse and total solar irradiance for six
slope angles (default 0°,
15°,
30°,
45°,
60°,
75°
and 90°)
and given azimuth of surface (default 0°).
 |
| Calculated average total, direct and diffuse irradiation in spreadsheet |
Charts
for direct, diffuse and total solar irradiance are available in
“Charts (irradiation)” sheet.
 |
| Chart created in spreadsheet |
How to get started with spreadsheet.
Spreadsheet is available in both LibreOffice Cals and MS Office Excel format. To get started just navigate to "Home" sheet and fill the following fields:
Azimuth - azimuth angle of surface (solar panel).
Altitude - altitude of location.
Solar constant - default value in 1360, but you can specify your own value of solar constant.
Coefficient of atmospheric pollution - value of atmospheric pollution.
Reflective ability
You can also specify seven slope angles for solar panel, default and most common values are 0°, 15°, 30°, 45°, 60°, 75° and 90°.
Download Solar Power Calculator [Spreadsheet] in LibreOffice Calc format.
Download Solar Power Calculator [Spreadsheet] in MS Office Excel format.
Reflective ability
You can also specify seven slope angles for solar panel, default and most common values are 0°, 15°, 30°, 45°, 60°, 75° and 90°.
 |
| Input fields in spreadsheet |
Download Solar Power Calculator [Spreadsheet] in MS Office Excel format.
References:
[1] - Boleman, T., Fiala, J.: Obnoviteľné zdroje energie, Tlačové štǔdio Váry, Trnava 2009. ISBN 987-80-89422-07-4
[2] - Cihelka, J.: Solární tepelná technika, T. Malina, Praha, 1994
[3] - Rybar R., Tauš P., Cehlár M.: Solárna energia a jej využitie I. Košice. TU-BERG. 2009. ISBN: 978 – 80 – 533 – 0318 – 5
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