# How to calculate

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**2,511**admin
Ok so Im trying to raise my understanding of PV math...

I have known about the PV Watts Site for some time but my question is how that math works. how does one take a given radiation level (lets say 4.43 kWh/m^2/Day) and a given derate lest say 80% and lets not forget the angle (for my location 40 degs)

how does the program take all that and turn it in to a power out put turn that in to a power out put. (111 kWh for jan)

does any one have the formula?

I have known about the PV Watts Site for some time but my question is how that math works. how does one take a given radiation level (lets say 4.43 kWh/m^2/Day) and a given derate lest say 80% and lets not forget the angle (for my location 40 degs)

how does the program take all that and turn it in to a power out put turn that in to a power out put. (111 kWh for jan)

does any one have the formula?

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## Comments

30,738adminOK,

First the Solar Calculator site uses measured data for sun intensity that has been collected over some 20 years. So that part is just a look up table of "average sun for an average day"... If you look on the results page, you can output the entire 1 year of estimated solar power output with hour by hour data points... It will also give you the year and date for the "average day" is uses for each calculation.

You can also go to the PDF Summaries where you can see the min/max values by month (such as weather variations).

Next, it needs to calculate the angle between the sun and your solar panel. If you know the angle, then the formula should be:

Solar Intensity * Sine (sun angle) * 1 hour * solar panel conversion * derate Fac = Watts for 1 hour at that angle.

If you need to track both angles (such as fixed panel), then I believe I read from somebody else here that you take the two angles and multiply them:

Sine (A) * Sine (B) = Sine (sun angle)

The value, such as 4.43 kWh/m^2/Day, is the sum of the above equation over the entire day (based on measured average solar radiation).

When we say you get 4.43 "hours of sun per day"--that is based on the fact that "full noon sun" is around 1.0 kWh/m^2... So, even though the sun shines on your panels for 6-10 hours per day--the "integrated" intensity (based on sun angles to your fixed/tracking panel, measured solar radiation through the atmosphere, including weather and smoke and such) give the starting numbers...

The Derating Factor is really the product of a bunch of factors:

The major ones are solar panel derating (based on the fact the standard panel test conditions give much better Watt Rating than average), dust/dirt on panels, and the Inverter Efficiency.

So, the program runs the default to 77% of solar panel name plate rating to AC output to the grid.

You can estimate the effects of solar cell temperature on solar panel output--virtually every solar panel gives the temperature constant for Vmp (which is what is most affected by temperature).

I use the same program to estimate off-grid solar systems too... I just change the derating factor to include 85% for DC to AC inverter efficiency, and 80% for a flooded cell lead acid battery efficiency:

77% * 85% * 80% = 52% for off-grid calcutions.

In the end, the program seems to give pretty good results (matches my average data for my Grid Tied system). And if you are within +/- 10% of your estimates--you cannot really get any closer (because of weather variability).

-Bill

PS: The program help file describes much of what I typed in more detail.

6,290adminDoes any one know the algorithm that PVWATTS uses to find the radiation vs the angle? or better yet the CGI file that they use?

30,738adminFor their code, have you tried contacting the National Renewable Engery Lab directly? They also have some tools and data available for download...

Otherwise, just looking around found a couple pages on how to calculate solar path and software (source) for a 3D irradiation modeler...

Square One Solar Position

Solar Radiation Calculator 3D, Visual Basic

-Bill

30,738adminGoing through the NREL site, found they have lots of open source functions and data there too...

Entry page

-Bill

6,290adminLOL right after i got your reply i found that same site. looks like i got some code looking to do! trying to build a set of solar tools for the mac and for the iPhone & iPod Touch