Equations for = Day Angle, Hour Angle, Declination etc.

[QuasiPhoto]

I found a significant error in my Perez model. Once corrected I am
finding my model in close agreement with the SAM output excel file.
There are many ways to calculate Day Angle, Hour Angle, Declination
etc.

I am using the following formulas as inputs into Zenith, Azimuth etc.

Day Angle (Dang) = 2 * Pi / 365.25 * Day

Declination = 0.006918 - 0.399912 * Cos(Dang) + 0.070257 * Sin(Dang) -
0.006758 * Cos(2 * Dang) + 0.000907 * _
Sin(2 * Dang) - 0.002697 * Cos(3 * Dang) + 0.00148 * Sin(3
* Dang) 'Spencer 1971

Hour angle = 0.2617993875 * (Hour - 12.5)

There are many many ways to skin this cat.... these cats? I have tried
dozens and dozens of combinations. Averaging, refraction correction,
etc. I can't seem to match things up. Any advice?

[Chris_Gueymard]

Indeed there are many algorithms you can use. All depends on the
accuracy in the end result (through zenith angle and air mass) you
want to achieve. The Spencer equation is OK for your purpose and
hourly calculations in general, but would be too coarse for more
specialized applications, such as 1-min calculations or tracker
positioning. I have personally implemented the far more accurate
algorithms of Blanco-Muriel (PSA) and Michalsky in the SMARTS and
REST2 codes.

Chris


On Jan 12, 9:24 am, QuasiPhoto

[QuasiPhoto]

Thanks Chris

I can put my head down and chew into these higher accuracy algorithms
but my thinking is there's no point in trying for accuracy past a
certain point. I am only interested in modeling non-tracking PV so the
payoff of these more sophisticated algorithms is limited. If SAM uses
these higher accuracy algorithms I'd prefer to stop where I am, choose
a position averaging technique and move onto a different problem.

I suppose I could rephrase my questions. Does SAM use position
algoritms (for non-tracking systems) that are comparable in accuracy
to the ones I listed off? Can you tell me if SAM incorporates a
refraction correction? Can you tell me how many time steps SAM
averages together to arrive at a position estimation?




On Jan 12, 9:32 am, Chris_Gueymard <ch...@solarconsultingservices.com>
wrote:

> > etc. I can't seem to match things up. Any advice?- Hide quoted text -
>
> - Show quoted text -

[Paul Gilman]

SAM allows you to choose the algorithm it uses to calculate the total
incident radiation. The choices are under "Tilt Radiation Type" on the
Array page: Isotropic sky model, Hay and Davies model, Reindl model,
Perez model 1988, and Perez model 1990.

You can see the source code for each algorithm in the file \exelib
\trnsys\source\sam_GetIncidentRadiation.for, which is in the SAM
installation folder, c:\SAM\2010.11.9 by default.

Best regards,
Paul.


On Jan 12, 6:01 pm, QuasiPhoto

[QuasiPhoto]

Paul,

I built my own version of SAM's non-tracking PV model. I know the
source code is available but if I use it, I lose the freedom to share
the work I've done. It's a licensing thing that I already ran into
with a version of PVFORM that I translated. The King paper and this
board have provided plenty of guidance. At this point my translation
is only a few percent off of SAM on an annual basis. The bulk of my
errors are coming in the first and last hours of the day. I know a
small part of this is due to my sun position calculations (which
aren't specified in the King paper) but the main issue is that there's
some sort of special condition at low POA values. Given the low power
output during these time periods I'm happy with the results I have.
Sure I'd like them to be spot on but if you guys and the TRNSYS folks
are restricted from sharing this info that's fine by me. I'm not going
to push it. I've moved onto working on a synthetic weather generator.
If you can lead me to a Synthetic Weather Generation Users Group that
would be awesome. Just kidding.

I am sincerely grateful for the assistance I have received on this
board. Thank you all very very much.

[Paul Gilman]

For the first and last hours of the day, SAM uses the sun angle that
at the midpoint between sunrise and the end of the sunrise hour, and
between sunset and the beginning of the sunset hour rather than at the
midpoint of those hours.

Best regards,
Paul.

On Jan 17, 9:38 pm, QuasiPhoto

[QuasiPhoto]

Thank you Paul

It made sense to average the sunrise/sunset time and the adjacent hour
so that's what I did. I'm still off in the first/last hour of the day
unfortunately. As I said, I think there's a special case algorithm for
POAs below a certain value. I could look at the results and see the
cutoff by comparing my errors to the POA values. The cutoff would be a
round number no doubt. At the end of the day I'm not too worried. I'm
working out the 5-parameter model now. Maybe its results will have the
same problem. Maybe they won't. Maybe my Perez model is still off.
We'll see.

Thanks again for the info.