Effects of temperature

**J.P.M.** · 08-29-2023, 12:43 AM

Your included graphs show the resulting instantaneous output of all the energy inputs and outputs to the system time integrated over 24 hours for 3 days.

Ambient temperature is but one system input and most of the time not the biggest one. Irradiance (and the nature of the atmospheric clearness as it may influence the wavelength distribution of that irradiance) and the solar angle of incidence are the two biggest inputs. The ambient air temp. is actually a tertiary input (along with the wind vector imposed on the array) and influences cell temperature which has the largest influence in cell efficiency.

To a pretty good 1st approximation, under full sun at say, 1,000 W/m^2 P.O.A. (Plane Of Array) irradiance and zero wind vector (no wind blowing), my array's average cell temperature will be about 28 - 30 C above the ambient air temperature immediately adjacent to the array (which ambient air temp. is as measured by the Davis weather station located about 1m north of the array on the N-S array centerline and with an anemometer elevation about 15 cm above the highest array elevation.

A rough estimate for cell temp. as f(P.O.A irradiance) is ~ +0.03 C * P.O.A. irradiance + ambient air temp. at the array.

For those interested in a bit of methodology/background, a reader's digest version is below. It may help or frustrate those interested in some information about what an array's temp. behavior is under the various major parameters that have the most influence over an array's average cell temperature.

I have what I believe are pretty close to the average cell temperatures of my array and which I believe are pretty typical for most equator facing rooftop arrays from extensive measurements taken of cell temps. at 4 random spots at each of the 16 Sunpower 327 panels of my array taken from under the array w/an infrared thermometer 8 minutes before and 8 minutes after the time (within probably ~ 10 seconds or so) of the max. daily value of Cos(solar incidence angle). I did that 64 times in 2014-2015, 26 in winter and 34 in summer. All readings were done on very clear days with a VERY clean array rinsed/washed each day with soap and a soft brush/rinsed that A.M.
Voltage was read at the monitor for each string between each 8 minutes of taking temps. under the array.
All that got me a value for array's voltage gradient (and lots of asses/elbows for 16 or so minutes on 64 occasions.
All 60 events were analyzed statistically as was each winter and summer set of data. a lot of other data was also collected but I'll stick to array temps. for now.
Some of the output was average cell temp. with a mean and std. dev. for both summer and winter operations and for all 60 trials combined.
FWIW, I got reasonably close to the published value of the voltage coeff. of temperature (-1.408V/deg. C/string of 8 panels from the data sheet vs. an average of 1.48V/deg.C/string of 8 panels measured with a std. dev. of 0.148 for both winter and summer runs and for the combined N=60 data set. I'd guess part of the difference between data sheet and measured gradients was in wiring and connection loss changes as things heated up.

I also derived an empirical correlation to estimate the average array cell temp. as f(ambient air temp. at the array, P.O.A. irradiance, wind vector magnitude.)
The correlation for my array looks like this:

T,(Array) ~ = (0.94 * T(a) + (0.0311 * P.O.A.) - (1.542 * WIND) + 2.324

Where:

T,(array) = average cell temp. of the array, deg. C.
T(a) = ambient air temp. at the array as measured and described above.
P.O.A. = Plane of array irradiance in W/m^2.
Wind = Magnitude of the wind vector (m/sec.).
The 2.34 C is added to account for the average difference between the cell temp. and the temp. of the back surface of the panels as I measured them.

The practical problem with using the correlation is that most folks don't have access to the instrumentation to rather the data and wouldn't know what to do with it if they did. That's why I included the approximate method in the above text.

Over the following years, I did similar measurement sets on the array twice/year for about 6 years. I did so for all cloudless days and on those days at the exact minute when the cos (max. solar incidence angle was > 0.99). The readings I took were of array (string) voltage, current, string power output and inverter output as well as all the weather data as recorded by the Davis at 1 minute intervals. I also cleaned the array in the A.M. before each set of readings as described above.
I did all this to get some idea of array performance under clean and cloudless conditions and to perhaps estimate how the array performance changes both as f(weather conditions) as well as seasonal changes and also to maybe get some idea/guess as to array performance degradation as f(time).
The readings I took were at the daily time of max. cos of solar incidence angle similar to how I took all the readings as before but not climbing under the array and instead relying on my measured voltage gradients of temp. as described above.

One such set of readings taken on 45 cloudless days between 06/30/2018 and 09/04/2018 with n=45 gave a set of average results for some of the data relative to temperatures as follows:
Average ambient air temp. : 33.15 C.
Ave. P.O.A : 986 W/m^2
Ave. Wind : 1.84 m/sec.
Ave. Calc'd cell temp. from array voltage : 61.52 C.
Ave. Calc'd cell temp. from empirical correlation: 61.45 C.

So, average cell temp. above average ambient air temp. ~ = 28.3 C.

The 11 other data sets seem to correlate well with one another over a range of weather and irradiance conditions.

Effects of temperature

Effects of temperature

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