Tuesday, February 25, 2014

Quantification Of Solar Energy, Solar Power Calculator [Spreadsheet]

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]

This article will explain how to calculate direct, diffuse and total solar energy emitted from sun to earth surface and also parameters that determine position of the sun in the sky.

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


Is a key parameter in determining the theoretical solar energy. It represents the energy flux of solar radiation reaching the surface of the earth.
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:





Where:
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:





Where:
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:

Latitude - latitude of location.
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°.

Input fields in spreadsheet


Download Solar Power Calculator [Spreadsheet] in LibreOffice Calc format.
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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