Converting insolation from flat plate to heliostat, etc

[Rei]

I'm currently working on a spreadsheet to crunch the numbers to determine the economic viability of solar power in various conditions (I already did such a spreadsheet for windpower).  My partner, who's studying to be an actuary, set up the calculations for determining whether it is a valid investment after inflation and cost amortization (with interest) is taken into account.

Obviously, when choosing a system, it's not only peak production or year-round average production that matters.  You need to know when you'll be getting less power as well, too.  So, I found a set of insolation values from a city near mine that were taken on a day to day basis across an entire year; I then broke things down into months, and for each month gave it a daily average, daily minimum, and daily maximum.

Now, here's the issue: this data was taken with a pyranometer:

http://www.apogeeinstruments.com/pyr_spec.htm

My interpretation of this is that it is calibrated to function as an ideal plate collector, laying flat and pointing straight up at the sky.  So, using these insolation values, I get roughly the equivalent of what I would get using such a flat plate pointing straight up.  However, that's obviously not the only situation that matters, when it comes to solar*.  I also need:

  A fixed plate pointing at various angles altitude (no need for different angles azimuth)

 * A plate mounted to an ideal heliostat

Now, this data should, in theory be derivable from the flat plate data.  After all, one could determine the "cloudiness" values by comparing the insolation data with the maximum theoretical insolation for the flat plate at different points in the year, and then apply this cloudiness to how it would affect a heliostat or angled plate.  And I do, after all, have the equations for where the sun will be in the sky at any latitude at any given point in time.

However, the concept of doing this looks pretty ugly.  There will be integration involved, and so on.  And the point of the matter is that it should, in the end, condense down to a relatively simple conversion function from the flat plate insolation values.  So, what I'm wondering here is if anyone knows such a conversion function, from a plate pointing straight up to a plate pointing at an arbirary angle and to a plate mounted on a heliostat.

I already have the numbers punched in, and using a flat plate pointing straight up, prices would have to come down about threefold for it to ever be a realistic investment (ignoring the obvious gains for the environment) where I live.  However, it's obvious that tilting it southward will be a big improvement with little to no extra cost, and a heliostat would probably be an even bigger improvement.  I need to figure out how much.  

 ** There's also concentrators and thin, two-sided cells mounted sparsely over a reflective plate, but I'm not going to worry about them for now.  The former would add extra modelling challenges (reduced lifespan, reduced power at higher temperatures so the response to increased solar output isn't roughly linear, etc), and the latter isn't common yet.

[GaryGary]

Hi,

Here are two possibilities:

1) I did software that figures out the radiation on a flat plate collector set at any bearing and tilt.  It takes the direct component of the sun, and factors it by the cosine of the incidence angle, and then it adds a part of the diffuse component based on how much sky the collector sees (e.g. 100% for horizontal collector, 50% for vertical collector, ...).  You could look through this software and find the part that does these calcs and use it.  The software source code is here:

http://www.builditsolar.com/References/Source/sourcecode.htm

If I am remembering correctly, the part that does this is in the Collector Class.

2) I got the logic to do this from this book:

Solar Thermal Engineering, Peter J. Lunde

The book is out of print, but should be available as used on amazon.com or the like.

I think the used price was pretty reasonable.

You might be able to work the equations it gives around to what you want.

---

Another thought -- The Radiation On Collector program will give sunny day radiation (direct + diffuse) for any collector tilt.  For sunny days, you could just run ROC for your latitude at various tilt angles (facing south), and do a little table of correction factors that could then go in the spread sheet.  The correction for cloudy days would, of course, be different, and would depend on the ratio of direct to diffuse radiation.  I would be tempted to just use the sunny day correction on the idea that you are not going to collect a whole lot of useful radiation on days that are cloudy anyway, so the correction factor being off a bit may not mater that much.

You could do a couple trial calcs to see how big the error would be.

The Radiation On Collector program is here:

http://www.builditsolar.com/Tools/RadOnCol/radoncol.htm

and the source for it is at the link above.

You may be aware of this already, but there are TMY files available for several hundred cities that give hourly readings for temperatures, direct solar, diffuse solar, ...

The data for any given day is the day that most nearly matches the average of the last 30 years of days on that date (if that makes sense )  -- anyway, its a real day, but one that is as close a possible to average for that date of the year.

The link to the source code above has a class that reads these TMY files, and extracts whatever you want from them.  This might be another way to go.

I think if you Google something like "NREL TMY" this will get you to the place that has these files.

Gary

[Rei]

Thanks!  I'll check into all of that.  It looks like those links will be a big help.  

[jimovonz]

NASA makes available quite detailed solar insolation data collected over the last 10 years. Depending on your latitude the sample areas are around 100 miles square over the whole globe. The information includes both horizontal, ideal angle, and many other angle collection areas. I have described how to get the data here in this post: http://www.fieldlines.com/story/2004/10/6/164945/703

[jimovonz]

What I forgot to mention was that this information takes into account indirect insolation as well as direct. While you could calculate the insolation on a panel of arbitary inclination given horizontal data, the NASA data has an advantage in that it takes into account local atmospheric conditions that affect the distribution of energy for different orientations.