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Solar array arrangement calculation method (not due south)

  1. Jun 13, 2015 #1
    Hi all, First time post, long time lurker, sorry if this is in the wrong section.

    I am currently looking at a project that requires a large solar panel array onto a very tight roof area; maximising space is therefore important. Thus, keeping the panels as close together is important.
    I have a found a calculation methodology that requires the solar altitude angle and solar azimuth angle during the earliest time on the winter solstice (worst case scenario) and then requires the following:

    Dm = h/tan(a) Where Dm = Maximum Shadow length, h=height of panel, a = angle of orientation.

    D= Dm * cos (180 - u). Where D = Min Spacing between panels, u = worst case azimuth on winter solstice.

    However, this method is for due south azimuths only. Therefore, has anyone got any suggestions as to how to accurately calculate the minimum distance between panels. I assume, that I would take away the difference between the actual orientation of the panels and south azimuth away from (180-u), but my trig skills are not up to scratch and would like some help on this one.

    Thanks so much in advance,

  2. jcsd
  3. Jun 14, 2015 #2
    Interesting problem, thought about it, wheels spinning, made a model of an array out of folded paper, now less confusing. Fold a piece of paper as below and lay it on a table. Let it represent your array. Pretend you are the sun. Move about as if you, the sun, were moving about the array. Now Imagine rotating the array so it does not face due south and continue to imagine you are the sun illuminating the array. With this done maybe the math will be more obvious?

    If the array aligns due south, then with the proper spacing on the shortest day of the year the entire roof will be shaded by the array and every inch of the array will be illuminated by the sun all day. If the array does not align due south then it will be a compromise between panels being shaded and roof not being shaded?

    This seems to be a complicated optimization problem for alignments not due south. Panels are relatively expensive, you don't want them to shade each other except for a small amount near the end of the day when not using a due south alignment?

    Good luck!



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  4. Jun 16, 2015 #3


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    Winter solstice optimisation is used for isolated PV systems. Is this a stand alone system providing essential power? or a grid connected system?

    Depending on panel internal connections, any partial shadow on a panel may result in a significant loss of current from the entire array.
    The directional characteristics of panels is often sufficiently broad that a planar array will outperform a stepped array.

    Useful information would be the local latitude, roof slope and roof aspect.
  5. Jun 18, 2015 #4
    I have to agree. I did "solar array farm" into google image search. Virtually all the panels are flat. All the panels on rooftops in the UK are flat, even when not pointing south. Unless you have a very weird geometry to your roof, you might consider the project with a planar array.
  6. Jun 19, 2015 #5


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    Not an expert, but it would seem to me that the choice of optimization method would depend on several unique assumptions, such as local utility rate structure, other alternative energy sources, and load profile.

    For example, if the building arleady has natural gas heat, it may make more economic sense to maximize summer output instead of winter output. But then that could also depend on the rate structure: is net metering month-to-month or annual? If annual, then total kwh regarless of peaks is the goal.
  7. Jun 19, 2015 #6


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    The " winter solstice (worst case scenario)" is only applicable for stand alone systems with battery storage. Before dawn on the morning of the winter solstice the batteries are cold, there is least sunlight and it has been a long night. That is usually when a stand alone system will first fail to satisfy a continuous load.

    We need more data.
    Are there alternative sources of energy? What is the local latitude, roof slope, roof aspect and the make and model of the panels to be used.
  8. Jul 6, 2015 #7
    The following online calculator may be useful for a broad stroke approach to considering differing mounting methodologies:
    It is quite surprising how well 'flat' panels do compared with the ideal attitude. It's less of course, but really not too terribly so compared with other alternatives - such as 'not doing it at all', or 'having the whole lot facing the wrong direction all day'. Does depend on your latitude of course. This becomes less so as you gain higher latitudes.

    With reference to the shading concern voiced above - yes absolutely. Depending on the panel internal architecture a hand sized shadow on a 18 sqft panel can drop the output to 50% and bring down the entire string (often up to about 12 or 18 panels) down to 50% as well.

    There are two primary solutions to this:
    1 - String combiners/optimizers that manage to isolate the shading effect through circuitry applied at each panel.
    2 - if you are a grid tied installation you have the option of using micro-inverters that in effect turn each panel into its own stand alone generating plant and any one panel shaded does not affect the others in the string. Even better - micro-inverters have technology to store energy internally and release it as a burst of energy when it reaches a useful threshold. Traditional string inverters typically require something like 300vDC to fire up and all the early morning and late afternoon energy is simply ignored. Micro inverters will continue to produce literally until dark - albeit not much as ultimate darkness approaches but overall and annually aggregated a significant improvement on ROI can be had with micro-inverters.

    Good luck on your project ....
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