How does one calculate the output of a solar system? Its an incredibly long formula that at first glance looks incredibly complicated. But if we use average terms for some of the minor and less important factors we can quickly obtain a very accurate figure without the brain drain.
Firstly the formula itself using real English rather than an engineers abbreviations is;
Annual Production in Wh = (System Size (W) x AVG Sun Hrs/Day x 365) x temp Losses (%) x panel tolerance losses (%) x dirt/dust losses (%) x invertor losses (%) x cable losses (%) x tilt/azimuth losses (%)
Wow – pretty long huh?
So how to simplify all THAT? Firstly let’s explain what this all means.
System Size – The size of your solar system in W.
AVG Sun Hrs/Day – A number provided by the BOM giving the average amount of sun per day per area.
Temperature Losses – Average losses due to temperature. Usually around 0.45% per degree of difference.
Panel Tolerance Losses – The losses in the panel. Most panels are positive tolerance these days so it’s often nil.
Dirt Dust Losses – The effect of dirt or dust on systems output over time. It can be as high as 20% if heavily exposed to ongoing dust but is usually around 5%.
Invertor Losses – Usually around 3%
Cable Losses – Losses caused by voltage drop over the cable run. Usually around 1-2%
Tilt Azimuth Losses – Losses caused by the pitch and orientation of the solar system. This is the most important factor in the calculation and can vary output by up to 50%.
So now that we know what we’re talking about let’s rewrite the formula using some numbers in place of some of the smaller and less variable factors.
Annual Production in Wh = (System Size (W) x AVG Sun Hrs/Day x 365) x temp Losses (%) x panel tolerance losses (1) x dirt/dust losses (0.95) x invertor losses (0.97) x cable losses (0.98) x tilt/azimuth losses (%)
So that leaves us with AVG Sun Hrs/Day, Temp Losses and Tilt/Azimuth Losses plus entering the size of the solar system which for all intents and purposes we shall say is 5kW.
AVG Sun Hrs/Day
The magic number for Brisbane is 5.39 sun hours per day. What this is is science saying ok how many hours of sunlight at 1000w/m2 do we have in a given area per day. This allows us to calculate the output for any given system in any given area.
OK, this one is a bit of a pain – take the average daily temperature for Brisbane which is 25 degrees, and add 25-35 degrees depending on the mounting system. Use common sense here – a tilt system has better airflow so it is at the 25-degree end of the range. Roof racking set high is around 30 degrees and those ridiculous systems screwed straight to the roof are at the 35-degree end. Rule of thumb? Allow 30 degrees.
That gives us 25 + 30 = 55 degrees panel temperature on average. . Pretty hot! After that its a simple matter of deducting the standard test condition temp (25 degrees) and multiplying that by the temp coefficient. . To really simplify it since were in Brisbane;
30 degrees x temp coefficient/100 = derating factor. With a panel average de-rating of around 0.5% per degree that gives us 0.825 derating factor. You could make this a lot more accurate by using the temp coefficient for the specific panel type. A lot will be around 0.43 these days.
Finally tilt and azimuth. Tilt is obvious Azimuth is a very old name for the number of degrees away from true north. The easiest way to tell this is to look at a satellite image and estimate how many degrees left or right of north the panels are. Check the roof pitch. Now using the clever tables provided by the Clean Energy Council one can obtain the derating value for the orientation.
A Working Example
5kW system at 18 degrees pitch 30 degrees off north.
Annual Production in Wh = (System Size (5000) x 5.39 x 365) x temp Losses (0.97) x panel tolerance losses (1) x dirt/dust losses (0.95) x invertor losses (0.97) x cable losses (0.98) x tilt/azimuth losses (0.98)
Annual Production in Wh = (5000 x 5.39 x 365) x 0.97 x 1 x 0.95 x 0.97 x 0.98 x 0.98
= 8444440Wh or 8444kWhr per year or 23kWhr per day
Noting that the maximum possible with no losses would be 9836750 or 9836kWhr!