1. Solar Radiation
Solar Radiation
The sun is a gaseous body composed mostly of hydrogen
Gravity causes intense pressure and heat at the core initiating nuclear fusing reactions
This means that atoms of lighter elements are combined into atoms of heavier elements, which releases enormous quantities of energy
Even when planet Earth is 93 million miles away, we still received an amazing quantity of usable energy from the sun.
Considering 25% efficient PV modules, if we used 1% of the surface of the earth we could meet 29 times our current total energy demand –These some rough calculations I did, but I’ll be glad to discuss your numbers if you happen to get something different.

2. Solar Radiation
Solar Radiation
Solar irradiance is the intensity of solar power, usually expressed in Watts per square meter [W/m^2]
PV modules output is rated based on Peak Sun (1000 W/m^2).
Since the proportion of input/output holds pretty much linearly for any given PV efficiency, we can very easily evaluate a system performance check by measuring irradiance and the PV module output.
The amount of radiation received is proportional to the inverse of the square of the distance from the source –that is, twice the distance ¼ of the energy, four times the distance 1/16 and so on
Solar irradiation is simply the solar irradiance multiplied by time. It is measured in Watt-hours per square meter [Wh/m^2]

3. Solar Radiation
Solar Radiation

4. Solar Radiation

5. Solar Radiation
Solar Radiation
Solar Spectrum most the energy received from the sun is electromagnetic radiation in the form of waves.
Electromagnetic Spectrum is the range of all types of electromagnetic radiation, based on wavelength.

6. Solar Radiation
Solar Radiation
Atmospheric Effects: Solar radiation is absorbed, scattered and reflected by components of the atmosphere
The amount of radiation reaching the earth is less than what entered the top of the atmosphere. We classify it in two categories:
Direct Radiation: radiation from the sun that reaches the earth without scattering
Diffuse Radiation: radiation that is scattered by the atmosphere and clouds

7. Solar Radiation

8. Solar Radiation
Solar Radiation
Air Mass represents how much atmosphere the solar radiation has to pass through before reaching the Earth’s surface
Air Mass (AM) equals 1.0 when the sun is directly overhead at sea level. AM = 1/ Cos Өz
We are specifically concerned with terrestrial solar radiation –that is, the solar radiation reaching the surface of the earth.
At high altitudes or in a very clear days, Peak Sun may be more than 1000 W/m^2 but it is a practical value for most locations
Peak Sun Hours is the number of hours required for a day’s total radiation to accumulate at peak sun condition.

9. Solar Radiation
Solar Radiation
Zenith is the point in the sky directly overhead a particular location –as the Zenith angle Өz increases, the sun approaches the horizon AM = 1/ Cos Өz

10. Solar Radiation Example problem of Peak sun hours per day:
If during the day we have 4 hours at 500 Wh/m^2 and 6 hours at 250 Wh/m^2 we should compute the peak sun hours per day as follow:
First, multiply 4hs x 500 W/m^2 and add to it 6hs x 250 W/m^2 – This will equal 3500 Wh/m^2
Second, we know that by definition Peak Sun is 1000 W/m^2, so if we divide the total irradiation for the day by Peak Sun we will obtain Peak Sun hours. – That is,
Peak Sun Hours = Total Irradiation [Wh/m^2] / Peak Sun [W/m^2] = Peak Sun hours
In our specific problem:
Peak Sun Hours = 3500 Wh/m^2 / 1000 W/m^2 = 3.5 Peak Sun hours
Note: most solar irradiation data is presented in Peak Sun Hours units

11. Solar Radiation
Solar Radiation
Insolation; this is an equivalent term for solar irradiation and can be expressed in KWh/m^2/day or peak sun hours

12. Solar Radiation
Solar Radiation
Solar spectral distribution is important to understanding how the PV modules that we’re going to utilize respond to it
Most Silicon based PV devices respond only to visible and the near infrared portions of the spectrum
Thin film modules generally have a narrower response range

13. Solar Radiation

14. Solar Radiation
Solar Radiation
Long-term solar irradiation measurements are the basis for developing databases, which help us to calculate output.
Being able to predict the output of our PV system, and this will allow us to know whether it is working adequately or not
Predicting output will help us to calculate the cost of the energy generated over a given time period
Pyranometers measure irradiance. Typically, you will use a handheld pyranometer that uses a silicon cell or photodiodes and you will set it adjacent to the array, in the same plane as the array –not as precise but appropriate for construction
Pyrheliometers measure direct solar radiation (and ignore diffuse) and I’ve never ran into a situation where I had to use one

15. Solar Radiation
Solar Radiation

16. Solar Radiation
Solar Radiation
Two major motions of Earth affect the apparent path of the sun across the sky:
Its yearly revolution around the sun
Its daily rotation about its axis
These motions are the basis for solar timescale and the reason why we have seasons, days and nights
Ecliptic Plane is the plane of Earth’s orbit around the sun
Equatorial Plane is the plane containing Earth’s equator and extending outward into space

17. Solar Radiation
Solar Radiation

18. Solar Radiation
Solar Declination is the angle between the equatorial plane and the ecliptic plane
The solar declination angle varies with the season of the year, and ranges between –23.5º and +23.5º

19. Solar Radiation
Summer Solstice is at maximum solar declination (+23.5º) and occurs around June 21st –Sun is at Zenith at solar noon at locations 23.5º N latitude
Winter Solstice is at minimum solar declination (-23.5º) and occurs around December 21st
At any location in the Northern Hemisphere, the sun is 47º lower in the sky at noon on winter solstice than on the summer solstice – Days are significantly shorter than nights

20. Solar Radiation
Equinoxes occur when the solar declination is zero. Spring equinox is around March 21st and the fall equinox occurs around September 21st –Sun is at Zenith at solar noon on the equator.
Around the equinoxes the daily [rate of] change is at maximum as oppose to change of declination during the solstices when it is at its minimum

21. Solar Radiation
Solar Radiation
Standard meridian is located at a multiple of 15º east or west of zero longitude –located at Greenwich.
15º represents one hour of change, so we can infer the 1º will be 4 minutes
Both of these facts are interesting to know; however, you will not apply either of these things to design or install PV systems.
You’re concerned with the average peak sun hours for your location and your shading analysis tool will be reading in solar time –but this irrelevant to you.

22. Solar Radiation
Solar Radiation

23. Solar Radiation
Solar Radiation
Solar Altitude Angle is the vertical angle between the sun and the horizon –added to the Zenith angle is equal to 90º
Azimuth Angle is the horizontal angle between a reference direction.
In the solar industry we call south 180º and this angle will range between 90º (east) and 270º (west)

24. Solar Radiation
Solar Window is the area of sky between sun paths at summer solstice and winter solstice for a particular location

25. Solar Radiation
Solar Radiation
Incidence Angle is the angle between the direction of direct radiation and a line exactly perpendicular to the array angle

26. Solar Radiation Array orientation is defined by two angles:
Tilt angle is the vertical angle between the horizontal and the array surface

27. Solar Radiation
2. Array Azimuth Angle is the horizontal angle between a reference direction –typically south- and the direction an array surface faces

28. Solar Radiation
Solar Radiation
Maximum energy gain will be achieved by orienting the array surface at a tilt angle close to the value of the local latitude –In high latitudes arrays should be very steep and vice versa
For optimal performance the tilt angle should be adjusted from the latitude angle by an amount equal to the average declination during that time
During the summer the average declination is +15º, so we should have a tilt of latitude minus 15º to make the array perpendicular to the average solar path –during the summer
Array Azimuth angle will be optimal when that array is due south
Sun trackers allow the PV array to change the tilt angle, the azimuth angle, or both –generally is not considered cannot be made cost effective

29. Solar Radiation
Solar Radiation

30. Solar Radiation
Solar Radiation
Computer models and the average climate conditions are used to calculate an optimal tilt angle factor –aka correction factor we have to subtract from the latitude.
In our area we use an optimal tilt angle factor of 15º
By making our tilt angle equal to the latitude angle minus this angle factor, we will improve the performance of our PV array
Example for our area: If we look at dataset provided by NREL, we can see that for a 0º tilt we would have 4.7 peak sun hours and for a latitude - 15º tilt we would have 5.3 peak sun hours
In other words, we would have an output roughly 13% higher by using this correction factor
You can calculate this percentage as follows:
(5.3 – 4.7) / 4.7 = or 12.7%

31. Solar Radiation
Solar Radiation

32. Solar Radiation
Solar Radiation
With NREL dataset we can find the most convenient tilt for our system and use the average peak sun hours of this tilt to calculate the annual production of our system.
Annual energy production = Avg peak sun hours per year [hr/day] x 365 Days x system size [Kw] = [KWh/year]
Example:
For a 4 KW system, located in San Francisco where we can expect 5.3 peak sun hours per day the annual production of the system will be equal to 7738 KWh/yr –(4KW x 5.3 peak sun hours per day x 365 days)
If we multiply this result by the number of years that we expect the system to be producing energy and we divide the cost of the PV system by this number, we will know how much it cost each KWh produced.
In our example: 7738 KWh/yr x 25 years = KWh . Let’s say that this system cost $26500 after rebate, then $26500/ KWh =13.5 ¢/KWh

33. Solar Radiation
Typical Inclination/Orientation Factors for Parallel Roof Mounted PV Systems in California
WOW! Don’t worry about it and match the roof line!
If the bad news was how traumatic hard shadows were, the good news is how little imperfect orientation and inclination affect output.
Remember that if you have the freedom (without extra costs, hassles or poorer aesthetics), point the modules due south (not magnetic south) at an angle somewhere between latitude minus 15 degrees and latitude.
If the perfect angle costs you in money, hassle or aesthetics, don’t worry about it! Look at how little it matters.
On flat roofs, go more horizontal than the ideal if there is any inter-row shading.
For maximum value on TOU rate structures, point south west since afternoon power will be more valuable than morning power.
Likewise, if given the choice of an east facing roof or west facing roof with neither shaded, go for the western face and get on a time of use rate structure (consider TOU for any PV system). You will lose 4 or 5%, but you will shift almost three hours of near peak day production into the afternoon, and since afternoon power is worth roughly 3 times morning power, the 5% decrease in production is well worth it.

34. Solar Radiation
Solar Radiation
Typical Inclinations

35. Solar Radiation
Solar Radiation