Panel angle

[zƬesla]

More of a PV than PW question – I have pole-mounted PV arrays with 1 axis that I can crank to change the angle, and have been using the website suncalc.org monthly to determine what that angle should be for optimal production. However, there is also a formula commonly shown on other sites (latitude * 0.92 - 24.3 [for summer]) that gives a very different angle. Anyone have a reliable resource for determining the best angle throughout the year for a non-major city?

 

[Alonzo]

At high noon, set a cylindrical container on the panel and rotate until the shadow doesn't show.

 

[zƬesla]

At high noon, set a cylindrical container on the panel and rotate until the shadow doesn't show.

Pole-mounted. Panels too high to set anything on it. I use an angle-finder app; just need a reliable way to know the angle to set.

 

[jrweiss98020]

Get a cheap sextant.

 

[zƬesla]

Get a cheap sextant.

Haven't used one but don't you sight the "star" in which case I'll burn my retina:-?

 

[jrweiss98020]

They usually come with a sun filter for noon sunlines.

 

[zƬesla]

Good to know. Would still like a good online reference though

 

[holeydonut]

Maybe you can try this approach if you have a stick that you can get perpendicular to the ground.

https://www.chegg.com/homework-help...r-17.1b-problem-1a-solution-9780321957962-exc

The Astronomical Noon or Solar Noon time you take your measurement can be found here (I don't know where you live...):

https://sunrise-sunset.org/search?location=san+francisco

 

[zƬesla]

For anyone else looking, after a bit more digging, I came across the following:
NOAA Solar Position Calculator

It seems to match suncalc pretty closely, so I’ll keep using it. Not sure why so many sites list the equation when, at least where I’m at, it doesn’t seem to be accurate.

 

[wwhitney]

For a given month, how are you picking the angle to set your array to?

Cheers, Wayne

 

[jrweiss98020]

Good to know. Would still like a good online reference though

LMDDGTFY (Let Me DuckDuckGo That For You)...

https://www.amazon.com/Davis-Artifi...hild=1&keywords=sextant&qid=1597361005&sr=8-6

 

[zƬesla]

New For a given month, how are you picking the angle to set your array to?

For suncalc and the NOAA site linked above, you enter a date and time; both auto-populate the current date/time.

Something I'm curious about is whether it is more efficient to set the angle based on exactly high-noon, or slightly lower as the sun will be lower on either side of it.

 

[zƬesla]

LMDDGTFY (Let Me DuckDuckGo That For You)...

https://www.amazon.com/Davis-Artifi...hild=1&keywords=sextant&qid=1597361005&sr=8-6

Not sure if you're just having fun or attempting to provide a serious reply, however that's not what I meant. I don't want to have to purchase devices or learn how to use something new just to figure out the angle. I was simply looking for an online web resource that can spit out the angle based on lat/long and date/time. The NOAA site that was buried down several pages of DDG search results (yeah, I know how to use it) ended up confirming what suncalc spits out, which is good enough for me. It's unclear why so many places have the equation when it doesn't match up, but I won't worry about it.

 

[Flick75]

Maybe to generic for you, but link below. You have to scroll down a ways to see the calculator.

Solar Angle Calculator

 

[wwhitney]

Something I'm curious about is whether it is more efficient to set the angle based on exactly high-noon, or slightly lower as the sun will be lower on either side of it.

Right, that was what I was driving at, suncalc gives you the sun elevation at high noon for a given date and time, but that doesn't tell you the optimal angle for that day, let alone the whole month.

Cheers, Wayne

 

[shs1]

The optimum angle depends on many thing, most importantly your latitude. And that optimum angle changes with time of year – a lower angle in the summer and a greater tilt angle in the winter when the sun does not rise much above the horizon. It also depends on your site and shading. I locating and aimed my solar array(s) using an app that used my iPhone's camera to scan the horizon and note where the view of the sky near the horizon was blocked by trees, mountain tops and ridges, etc. The app then produced graphs of how the azimuth (e.g. due south) and angle would effect the output of solar panels in that location. In the more complex of the attached graphs (below) shows the results for that app for the various months of the year for four different angles, 0, 10, 20, and 30 degrees. Since 20 and 30 degrees were the ones most easily achieved by my ground mount, I then compared the 20 and 30 degree tilt output in a much simpler graph (above) that indicated that it was worth lowering the tilt angle in the spring and raising it in the fall. It is not a huge difference in productivity, but I do it most years just to get the best out of our system.

 

[wwhitney]

Sure, but how is the app determining the optimum angle for a given day? You often read that it should be the sun's elevation at solar noon that day, but that angle is definitely too high:

For the given day's sun path, consider the total production P as a function of the panel elevation angle E. For angles near the optimum P will be a smooth function of E. Therefore at the optimal angle E, P'(E) = 0. But when E = the sun's noon elevation, it's clear that increasing E will decrease P (since at all times of the day, increasing E will increase the angle between the panel and the sun). So at that elevation, P' is non-zero, and that is not the optimum elevation angle.

I've yet to find a discussion that tells you how to calculate the optimum angle for a given day, let alone the optimum angle for a month, if you want to change your panel elevation monthly.

Cheers, Wayne

 

[power.saver]

That's correct @wwhitney. You have to average the elevation angles over the entire period of daylight, and consider the lowest angle where there is sunlight on the panels (I used 5 degrees, but it's adjustable). I wrote a program to do this, and a sample output is shown below for my lat/lon. You can see the optimal angle is less than the highest elevation at solar noon. From this a table can be generated showing the angle each month (I did it on the 15th of each month, but any date is possible).

Here is the hourly data by month:

Here is just the monthly summary:

 

[wwhitney]

That's correct @wwhitney. You have to average the elevation angles over the entire period of daylight, and consider the lowest angle where there is sunlight on the panels (I used 5 degrees, but it's adjustable).

But to maximize production on a given day, it's not enough to just use the time average of the sun elevation angles as your panel elevation angle. You want to choose the panel elevation angle which maximizes the time average (or integral) of the dot product between the panel normal and the sun's vector in the sky. So you need to know the sun's azimuth and elevation as a function of time.

Cheers, Wayne

 

[power.saver]

But to maximize production on a given day, it's not enough to just use the time average of the sun elevation angles as your panel elevation angle. You want to choose the panel elevation angle which maximizes the time average (or integral) of the dot product between the panel normal and the sun's vector in the sky. So you need to know the sun's azimuth and elevation as a function of time.

Cheers, Wayne

The azimuth is accounted for in the formula. I did not show that in the results as the OP was asking about only the angle. There are two cases to consider though: one is a tracking array where the panel azimuth tracks the sun, and the other where the panel azimuth is fixed. But of note, there is little change during the summer months (at least at my latitude) where 42 degrees would be adequate from March to August. In the other months, an adjustment of ±5 degrees per month would be close to optimal.