This
is Affordable Solar’s blog series on best practices, tips, and tricks to being
a successful solar designer or installer. My inspiration for these
entries is pulled from my years of experience working in solar photovoltaics,
from shipping to sales to design and drafting, and from my work with installers
around the country. I am not the ultimate authority, but we have had a
track record of success and I want to share that with you.
For
my second installment, I am sharing the equations and resources I use to
calculate tilted array spacing and solar panel spacing from obstructions.
Without further ado...
Calculating Tilted Array Spacing
When
you’re designing a solar array, shading is the enemy. Most locations for solar projects tend to get
around 5 to 6 net sunhours per day, so anything that obstructs that sunlight
needs to be avoided at all costs. Shading
just one corner of a module can cut production in half, so avoiding shade on the
array is important. This is mainly an
issue on ground mounts and some flat roof mounts, where rows of solar panels
need to be optimally spaced to best use the available space. With limited solar resource and steep
penalties for failure, properly determining correct shade spacing is a critical
calculation in solar system design.
The
procedure for calculating shadow spacing starts with the sun’s position in the
sky on the winter solstice, December 21^{st}. You need to obtain the minimum solar altitude
angle α, which is the minimum angle the sun makes with the ground in
your shadefree solar window (figure 1).
For a 4 hour solar window, you want to obtain the sun’s altitude angle
at 10 AM or 2 PM on December 21^{st}, because that is when the sun will
be lowest in the sky. For a 5 hour
window, you will need the sun’s altitude at 9:30 AM or 2:30 PM instead. When you find this angle, you will most
likely also be able to get the suns azimuth angle, ψ. This is how far off true south the sun’s
position is (figure 2), and will be needed to obtain the minimum allowable row
spacing.
Finding values
for local Solar Azimuth and Altitude angles on the winter solstice can be a
challenge. Luckily for the modern solar
designer, there are tools available that greatly simplify the process. The tool I have selected is the NOAA Solar
Calculator, available for free online at http://www.esrl.noaa.gov/gmd/grad/solcalc/. By clicking a location on the map, you are
given coordinate and time zone information, and by entering the date for the
winter solstice, December 21, the “worst case” position of the sun is easily
obtainable. The procedure for using NOAA’s Solar
Calculator has been visually outlined on the webpage below.
Figure 3: NOAA Solar Calculator showing workflow and relevant
data

Step 1:
Red – Enter your initial project inputs.
This is your location in coordinates, the time zone, and December 21^{st}. Select a city in your time zone that has a
marker on the map to find your time zone value.
As easy way to find coordinates is to go to itouchmap.com/latlong.html and put
the pointer on your location.
Step 2:
Blue – Find Solar Noon based on your location, time zone, and the date. If you are located in the western half of
your time zone, this value is typically later than local time. For the eastern half of a time zone, it will
be earlier than local time.
Step 3:
Green – Enter in the earliest time in the day on December 21^{st} that
the solar array should be without shading.
If you are designing for a shadefree solar window in the middle of the
day, take the overall length of the solar window in hours and divide by two. Subtract this value in hours from Solar Noon
and enter it for Local Time.
Step 4: Orange
 Obtain your worstcase Solar Azimuth and Altitude angles at Local Time, which
will be used in the shading calculations to determine the minimum spacing. The top value is the Solar Azimuth angle,
while the bottom is the Solar Altitude angle.
Using the morning sun position, the Solar Azimuth angle should always be
less than 180 degrees, and the Solar Altitude angle should be between 15 and 35
degrees for most locations in the United States.
After
finding the Solar Altitude and Azimuth angles, the calculations to determine
row spacing can begin. For most ground
and roof mounted systems where row spacing is a concern, the height (h) of the
obstruction can be directly obtained from the dimensions of the solar panel and
the array tilt. Alternately, it can be
measured as the difference in height between the bottom/leading edge of one row
and the maximum height of the next row south of it, or a direct measurement of
whatever obstruction you want the array to avoid (figure 1). Using this height, the maximum shadow
distance can be obtained. The shadow
distance is found through using simple trigonometry. The equation:
D’ = h / tan (α)
From here, just one more calculation gives the minimum interrow spacing
needed to avoid shade within your solar window.
This is called the “Solar Azimuth Correction” (figure 2). Using the morning sun position, the equation
is:
D = D’ * cos (180 – ψ)
Using
NOAA’s solar position calculator, the only information you need to quickly and
painlessly determine shadow spacing is the height of the row or obstruction, your
desired shadefree solar window, and the location in decimaldegree coordinate
form. With this method, you can
accurately determine your solar panel spacing from obstructions with only a few
simple steps.
Appendix:
Variables/Equations for Calculating Tilted Array Spacing
 α = solar altitude angle
 ψ = solar azimuth angle
 h = height of obstruction x = tilted module length θ=tilt angle
 h = x * sin(θ)
 D = Minimum array row spacing
 D’ = Maximum shadow length (morning/afternoon)
 D’ = h / tan (α) D = D’ * cos (180 – ψ)(morning) D = D’ * cos (ψ  180)(afternoon)
I never realized all of the mathematical equations that go into making sure you have the best angles to save energy with your solar shades. So is this what the specialists have to look at and calculate when finding the best places for solar shades? It's helpful that you also include the different colors that correspond with the diagram above with what the benefits of each time of day will have on the locations of the sun rays.
ReplyDeletehttp://www.blindsanddesignsofflorida.com/SolarShades