Normalizing Solar Array Efficiency

[whitsett2010]

Hello Everyone,
I am an Electrical Engineering student at the University of Cincinnati and I am currently on co-op. I have been tasked with normalizing the efficiency of several different PV arrays which are all at different constant angles.
In other words, if array A is at an angle of 35 degrees and has an efficiency of 35%. What is the efficiency of the array at 0 degrees? (these are just random numbers of course)
I have done a LOT of looking around for a simple solution online and it seems that it does not exist, so I have attempted to create one myself.

What I did:
I wrote a program (in C++ because that is the only language I know) and a table in excel which could calculate the Solar Radiation incident on a surface at any angle given : Day of the year, hour of the day, tilt angle, and latitude. (assuming 1000W/m^2)

I used my program, and excel to simulate data for approximately a month from the end of December to the middle of January.

I now took the ratio of (Horizontal Solar Radiation)/(Tilted Solar Radiation)
and averaged this value over the 20ish days.
and recorded the value at times of: 8:00AM to 4:00 PM (the sun sets around 5 in southern Ohio in the winter so the data becomes negative as does the solar declination)
Soooo... Averaging the ratios of the individual hours gives me the average hour during the day and the average ratio at that hour. (using best line fit the data shows the pattern of an upside down parabola for Hour v. Tilt Angle)

Recap, I now have an average ratio from the time period of Dec. 25th to Jan. 18 of the Solar radiation between a tilted 25 degree angle, and a horizontal zero degree angle surface. This will serve as the correction factor for the 25 degree surface.

The company I work for has provided me with some measurements, including instantaneous kW output of each array every hour over the given time period above. I also have the rated output for each array. SO......
After calculating the average kWh of each array,
I take----> (Average kWh)/(Rated kW)*(Correction Factor)
The average kWh data excludes 0 data or data less than 10Wh.

This is my approach, any comments or constructive criticisms are welcome.
Thanks in Advance.

Correction FactorsBased on Latitude 39 degrees)
Tilt Correction Factor
35 0.3977
40 0.3748
10 0.673
25 0.465
7.4 0.7359

Example Calculation: (Array is at 25 degrees)

Roof Ground
Average kWh: 0.8708 2.7381 (From the measured and recorded data)
Corrrected for tilt: 1.26 (correction factor of .465)
Ratio corrected: 69.31% (what percentage of the kWh the roof
array is producing compared to the ground array)
Ratio not corrected: 31.80%

[Mike90250]

Both the cover glass, any anti-Reflection coatings on the cells or glass, and the type of cells, all affect the "off perpendicular" performance of panels. Mix in a couple of panels from different mfg's and you have a nightmare.

I've seen on a hazy day, higher generation, than a pure blue sky - because the panels harvest energy off the bright fuzzy clouds all day, blue sky with a white dot yields less of a harvest (but a higher peak for 20 minutes).

The PV watts caculator is worth a look at, too.

[whitsett2010]

Thanks for the reply!

I know that there are a daunting number of variables to take into account here, but I have kWh data for two different arrays over the given time period.
The first array is at a 25 degree tilt and is rated 12.76kW.
The second array is at a 0 degree tilt and is rated 5.82kW.
Now....
[Sum(0 degree kWh)/5.82kW]/[Sum(25 degree kWh) produces 90.80% (.9080)/12.76kW],
both arrays are using the same exact modules, there are just a different number of them, and at different tilts.
So the only real problem is as you said, will it work for different brand/types of modules.

[crlare]

Seattle Declination?

Optimum angle I understand to be latitude 47.67 - 15 = 32 degrees for Seattle?

Whereas what is the declineation between Solar North and Magnetic North? -22.96, from

http://www.esrl.noaa.gov/gmd/grad/solcalc