When designing a PV system that is tilted or ground mounted, determining the appropriate spacing between each row can be troublesome or a down right migraine in the making. However, it is important to do it right the first time to avoid accidental shading from the modules that are ahead of each row. This can lead to under-performing systems and angry customers. No one wants to have that. The same can be said about over compensation too. Think of how many more kW’s you could have had. This article will get you started off on the right foot with a simple and fast process to get you out in the field faster with great results.
The first step in calculating the inter-row spacing for your modules is to calculate the height difference from the back of the module to the surface. To do that, follow this calculation below.
(Remember your high school maths? I still recall “Tom’s Old Aunt Sat On Her Coat and Hat” which stood for Tan = Opp/Adj Sine = Opp/Hyp Cosine = Adj/Hyp!)
Height Difference = Sine (Tilt Angle) x Module Width
***Make sure you’re calculating in degrees not radians***
In this case I am using a SolarWorld module that has a width of 39.41 inches at a tilt angle of 15º.
Height Difference = Sine (15) x 39.41
Height Difference = 10” rounded to the nearest inch.
To calculate the Module Row Spacing we need to hop over to http://solardat.uoregon.edu/SunChartProgram.php to determine what our Sun Elevation Angle is going to be. You will enter in your site's zip code or to be more precise you should enter the latitude and longitude of the location for more accurate results.
When you get your results it will look something like this:
In this example I picked a 9 AM to 3 PM window during the winter solstice for the worst case scenario. You may opt for a less stringent case to suite your needs. I chose this example because some utilities require the 9am-3pm window when offering rebates for customer owned PV systems.
From the chart you see that I have highlighted this window and drawn a horizontal line out to the left of the chart to narrow in on the Solar Elevation Angle at those times. I estimate a 17º angle which I will use next to determine the Module Row Spacing using the formula below.
Module Row Spacing = Height Difference / Tan (17)
Module Row Spacing = 10 / Tan (17)
Module Row Spacing = 33” rounded to nearest inch.
The inter-row spacing between the trailing edge of the first row of modules and the leading edge of the next row needs to be 33”
However, we’re not done just yet and you’ll be glad you kept reading along…
The next thing we must do is account for the Azimuth angle and use that figure to apply that to another formula. Take a look again at the example below; you’ll see that I have drawn two vertical reference lines down from each time reference. The difference between South going in either direction turns out to be 44º and we will use this in the following formula to determine the Minimum Module Row Spacing!
Minimum Module Row Spacing = Module Row Spacing x Cos (44º)
Minimum Module Row Spacing = 33” x Cos (44º)
Minimum Module Row Spacing = 24” rounded to the nearest inch.
Hey, you just gained an extra 9 ” for every row you have in your system! On cramped roofs or large commercial systems that can make all the difference. Put another way, in this scenario we could potentially increase the system size by 27%! What do you think about that?
And one last thing….
This last calculation is just a bonus and can help you layout your array in CAD a bit easier. The following formula gives you the distance from the trailing edge of one row to the trailing edge of the subsequent row or your Row Width.
Row Width = Minimum Module Row Spacing + Cos (Tilt Angle) x Module Width
Row Width = 24 + Cos (15) x 39.41
Row Width = 62.07”
Taken from an article found at: https://www.civicsolar.com/resource/determining-module-inter-row-spacing