# Solar array arrangement calculation method (not due south)

• Foxyquik
In summary, this person is looking for a way to optimise the spacing between solar panels on a roof so that the entire roof is shaded and illuminated by the sun all day on the winter solstice.
Foxyquik
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,

Charlie

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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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.

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.

Baluncore said:
Winter solstice optimisation is used for isolated PV systems.
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.

Foxyquik said:
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:
russ_watters said:
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.
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.

The following online calculator may be useful for a broad stroke approach to considering differing mounting methodologies:
http://rredc.nrel.gov/solar/calculators/pvwatts/version1/version1_index.html
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 anyone 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 ...

## 1. How do you calculate the optimal arrangement for solar arrays that are not facing due south?

The optimal arrangement for solar arrays that are not facing due south can be calculated by using a mathematical formula that takes into account the tilt angle and azimuth angle of the panels, as well as the latitude and longitude of the location. This formula is based on the amount of sunlight that falls on the panels throughout the day, and can be found in many solar energy textbooks or online resources.

## 2. What factors should be considered when determining the arrangement of solar arrays that are not facing due south?

The factors that should be considered when determining the arrangement of solar arrays that are not facing due south include the angle of the sun's rays at different times of day, the amount of shading from nearby objects or buildings, and the desired energy output. It is also important to consider the local climate and weather patterns, as well as any local regulations or restrictions.

## 3. Can the same calculation method be used for all locations?

No, the calculation method for determining the optimal arrangement for solar arrays that are not facing due south may vary depending on the location. Factors such as latitude, longitude, and climate can affect the amount of sunlight and the angle of the sun's rays, which in turn can impact the optimal arrangement of solar arrays.

## 4. How accurate is the calculation method for determining the optimal arrangement of solar arrays?

The calculation method for determining the optimal arrangement of solar arrays is based on mathematical formulas and can be quite accurate. However, it is important to keep in mind that there are many variables that can affect the actual performance of solar arrays, such as weather conditions, shading, and maintenance. It is always recommended to consult with a professional and conduct site-specific studies for the most accurate results.

## 5. Can the arrangement of solar arrays be changed after installation?

Yes, the arrangement of solar arrays can be changed after installation, but it may require additional equipment and resources. It is important to carefully plan and calculate the best arrangement before installation to avoid any additional costs or complications. However, if needed, adjustments can be made to optimize the performance of the solar arrays.

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