Array Spacing To Avoid Shadowing

djohnyvonnedjohnyvonne Registered Users Posts: 17 ✭✭
I've been using a formula to try and figure out distance I should have between ground mount arrays to avoid shadowing, but my results do not seem correct. Here is a shot of that formula:

Here is a snapshot of the ersi page this article led me to with my values put in:

So solar altitude angle is 23.5. Solar azimuth angle is 145.97. X=13'3". Tilt angle=25°.
By my calculations, h=-1.7536606888. D'= -.10876949735. D= .0939832138.
Obviously, I need help.
Thank you.

Comments

  • djohnyvonnedjohnyvonne Registered Users Posts: 17 ✭✭
    Just refigured it using actual height=7'. Came up with -4.06680640889. I'm confused.
  • EstragonEstragon Registered Users Posts: 4,478 ✭✭✭✭✭
    At solar noon at ~35°N lat on Dec 21, shadow will be roughly twice height. If you aren't facing south, which 145° isn't, you'll get max production somewhat off solar noon, so it gets to be a bit of a trade off between spacing panels far enough apart so they get max production in the period when the array is nearer 90°to the sun, and getting as many panels as possible in available space.

    There could be lots of variables. Could hills or trees render the exercise moot? Does typical Dec weather get gloomy, so shadows don't matter? What is the cost of alternative power, grid or generator.

    It may or may not be worth trying to get this figured out to 2 decimal points. It would help to know more about the application.
    Off-grid.  
    Main daytime system ~4kw panels into 2xMNClassic150 370ah 48v bank 2xOutback 3548 inverter 120v + 240v autotransformer
    Night system ~1kw panels into 1xMNClassic150 700ah 12v bank morningstar 300w inverter
  • djohnyvonnedjohnyvonne Registered Users Posts: 17 ✭✭
    Estragon:
    Thank you for your response.
    1.arrays will be due south
    2.high desert of Los Angeles county, no external shade obstructions
    3.not gloomy 95% of winter months(we are in a severe drought)
    4.off-grid application with 48v/2220Ah battery bank & 8500w generator
    5. 7' from top corner to bottom corner of next array
  • djohnyvonnedjohnyvonne Registered Users Posts: 17 ✭✭
    Sorry, 2 Outback Radian GS8048A inverters & 48- Silfab SLA280M modules=13,440 watts.
  • djohnyvonnedjohnyvonne Registered Users Posts: 17 ✭✭
    145.97 is the solar azimuth angle
  • EstragonEstragon Registered Users Posts: 4,478 ✭✭✭✭✭
    Ok. I thought 146° was the orientatation of the array.

    For LA latitutude I get ~11' as the length of shadow for a 7' object. If you search for paragon solar and length of a shadow you can see where I got that.

    At that spacing though, all but the front group would be partially shaded except around solar noon, so it's a trade-off between spacing and charging time.

    Generally speaking, winter sun is weaker, so we want as long a charge time as possible. If constrained for space, you may be able to arrange and wire panels so some series strings at the top of each array stay lit and still produce while in parallel with shaded strings.
    Off-grid.  
    Main daytime system ~4kw panels into 2xMNClassic150 370ah 48v bank 2xOutback 3548 inverter 120v + 240v autotransformer
    Night system ~1kw panels into 1xMNClassic150 700ah 12v bank morningstar 300w inverter
  • djohnyvonnedjohnyvonne Registered Users Posts: 17 ✭✭
    Okay, I "think" this may do it. This is from Iron Ridge Mounting Company.
    • How do I calculate row spacing to avoid shading? 

      This question depends on what is considered an acceptable amount of annual “shade loss” (system output lost to inter-row shading). If your goal is zero shade loss, visit the first the NOAA Solar Calculator (http://www.esrl.noaa.gov/gmd/grad/solcalc/) to find the minimum solar altitude angle (El) on December 21st at 10 A.M., by inputting the coordinates of the project area. Use the following formula to find distance (D) between arrays to avoid shading: D’=h/tan(El). Height (h), is the difference between the rear edge of the first array and leading edge of the second array.

      So with lat=34.749 long=-118.268/Dec. 21st/10:00AM The solar altitude angle is 26.13°. 7' divided by the tangent of 26.13= 3.875. So I'm looking at a 4' row spacing to avoid shading.(I think)

      If someone could confirm or dispute, I would really appreciate it. Thank you Estragon for your comments!

  • djohnyvonnedjohnyvonne Registered Users Posts: 17 ✭✭
    Alright, I just spoke with Mike at Iron Ridge, he is a mathematical engineer. He said simply multiply height by 2.5 if you are below 35 latitude. Multiply by 3 if above 35 latitude. My problem was my iPad calculator, tangent of 26.13°=1.548 on it. He said tangent of 26.13°=.49054437. Which 7' divided by .49054437=14.26'.  7' multiplied by 2.5=17.5'.   Sooooo, his calculation suggestion of 2.5 times the height is considerably further than the formula of spacing=height divided by tangent of solar angle on Dec.21 @ 10:00AM. So I will be going with the "real" formula. Thank you again Estragon!
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