Q:
Thanks Sean. Do you know which formula they would expect us to use? I've run across several in previous studies of varying accuracy levels:
Basic inter-row shading distance
(d) = 3H
H = height of module from back edge to surface
Better inter-row shading distance
(d) = H/tan AltA
H = height of module from back edge to surface
AltA = Altitude Angle on December 21st at 9:00 AM
Best inter-row shading distance:
(d) = [ (Sin TiltA) x M ] / tan AltA ] x cos AzAD
M = Module Length
TiltA = Desired Tilt Angle
AltA = Altitude Angle on December 21st at 9:00 AM
AzA = Azimuth Angle on December 21st at 9:00 AM
AzAD = Difference between AzA and due south
A:
I don't think that the NABCEP Exam is going to make you do the inter-row shading 3-part calculation.
I use the calculation when teaching trig often, because it covers sine, cosine and tangent all on one calculation. Very cool.
Usually nabcep will have a single stage trigonometry calculation on their exams. Often it will have something to do with shading from a tree.
It will probably be easier than any of the equations that you are promoting. Usually the trick that will get people on an inter-row shading calculation is the azimuth correction angle.
For your first example:
Basic inter-row shading distance
(d) = 3H
H = height of module from back edge to surface
This is very common in the industry, however for most places a 3:1 ratio is overkill. The California Solar Initiative used to require a 2:1 ratio. If you are closer to the equator, the 2:1 ratio is overkill and if you are closer to the arctic circle, 3:1 is good and moving south is better:) Not really, I loved living in Alaska.
For your second example:
Better inter-row shading distance
(d) = H/tan AltA
H = height of module from back edge to surface
AltA = Altitude Angle on December 21st at 9:00 AM
With this calculation, you are not taking into consideration the fact that at 9am, your sun is not yet facing the PV and you would be able to reduce your inter-row space with an azimuth correction. At 9am in the winter, your sun can be low and at an angle around 40 degrees from south in many places. 3 hours later at solar noon when your sun is south (and hopefully your array facing south), then the north to south distance between your rows will be less than that longer shadow that the 9am sunbeam will have to take at a 40 degree angle from south.
Here is something that I put together years back on my 1970s era website that has an inter-row spacing example with an image of the azimuth correction half way down the page:
http://www.pvstudent.com/Advanced-PV-Course-Notes-2.html
For your 3rd example:
Best inter-row shading distance:
(d) = [ (Sin TiltA) x M ] / tan AltA ] x cos AzAD
M = Module Length
TiltA = Desired Tilt Angle
AltA = Altitude Angle on December 21st at 9:00 AM
AzA = Azimuth Angle on December 21st at 9:00 AM
AzAD = Difference between AzA and due south
This is the correct industry way to do the calculation, however it is not an exact science for the following reasons:
1-Closer to the arctic circle the sun dies not rise until after 9am, so you would have to improvise.
2-At place with different air densities morning sun has different potentials (Arizona morning sun is a lot brighter than a humid or smoggy place).
3-If your array is not facing directly south, west facing for example, then 9am would be less important than 4pm.
4-If you have thin film PV where the solar cells are uniform stripes from the bottom to the top of the module, then the cells will all be shaded to the same proportion, so inter-row shading effects are not quite as severe as with typical crystalline PV modules.
5-Some places might work better to do the calculation for sun angles at 8:45am and others might be best at 9:15am, also it depends on the price of the system, 9am weather, inverter prices, etc, etc, etc...
Many racking manufacturers have pre determined inter-row spaces, such as ballasted rooftop mounting systems.
Horizontal axis trackers have the best option, they will back-track and go flat at sunrise and sunset to prevent any-inter-row shading.
For large solar farms, they will spend a lot of time using software simulations with software, such as PVSYST or HelioScope to determine the best inter-row shading distance.
2.5:1 is also a good distance used by many.
Remember, solar is related to weather and is not an exact science, unless you are in space.
Thanks,
Sean White