A reality based independent journal of observation & analysis, serving the Flathead Valley & Montana since 2006. © James Conner.
Flathead Electric’s Stillwater solar garden will be used as a benchmark for other photovoltaic arrays in the Flathead. So far, FEC has focused on the economics of the project, but has not yet provided a lot of information on the solar science involved. Rather than wait for something that might never happen, Flathead Memo will present an occasional, and rudimentary, post on the sunshine part of the project.
Today, FM provides a spreadsheet of five daily values for the sun for 2016: (1) beginning of morning civil twilight, (2) time and azimuth of sunrise, (3) time and altitude of meridian transit (solar noon, also called high noon), (4) time and azimuth of sunset, and (5) end of evening civil twilight. At meridian transit, the sun’s azimuth is 180°, but as displayed in the analemma below, the time of day by the clock varies. The spreadsheet provides data for both standard and daylight saving time.
The spreadsheet has two values not familiar to all. One is the angle of incidence for the sunbeam at meridian transit for the south facing Stillwater array, which is tilted up 30° from the horizontal. The calculation is 90° minus the sum of the sun’s altitude and the tilt. When the sunbeam is square to the panel, a condition that occurs just before and after the summer solstice, the angle incidence is zero. But at the winter solstice, the sun’s altitude is just 18°, the AOI is 42°, and the intensity of the sunbeam on the photovoltaic is diminished as a function of the cosine of the absolute value of the AOI. The cosine of 42° is 0.74, so the 285-watt panels at Stillwater function as 210-watt panels at that AOI.
And there’s a further reduction: the effect of the atmosphere on the sun’s intensity. When the sun’s altitude is 60°, it delivers to the panels a kilowatt per square meter. But at 18°, it delivers approximately 680 watts per square meter. The manufacturer’s rated DC output of a PV panel usually assumes the sun is delivering a kilowatt per square meter. Assuming the panel’s output is a linear function of the sun’s intensity, the panel’s actual DC output is approximately 140 watts (210 watts times 0.68).
My quick and dirty calculations put the Stillwater solar garden’s mean annual high noon DC rating at 235 watts per panel, or 82 percent of the nameplate rating. The AC output probably is around 200 watts per panel, or 71 kilowatts for the array. FEC’s calculations may yield a different result, but FEC should disclose its numbers.
Although the mean annual high noon output is a better measure of output than the manufacturer’s kilowatt per square meter rating, it’s still not good enough. Cosine loss plus atmospheric extinction loss should be calculated for every hour of sunshine to arrive at the true capacity of the array. That capacity will seem shockingly low to begin with, while solar consumers and news media are being educated, but there will be an honest capacity rating at last.
Now, that analemma:
Photographs of analemmas usually are a series of exposures taken at the same clock time of day. The result is the figure-8 with unequal loops, but canted at an angle.
