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  • Temperature rise assumptions

    What do people here use as assumptions for module temperature rise for a typical roof mount? (i.e. 10 inches clearance, 4/12 pitch, no wind, full sun.)

  • #2
    For assumptions and estimates of module temp. rise, or to estimate cell temp. as f(POA, wind vector, amb. temp. and array to roof orientation), See Sandia report : Sand2004-3535, Dec. 2004, "Photovoltaic Array Performance Model", Kink, Boyson and Kratochvill, PP 17-19:

    Tc= Tm + (E/1000)*Delta T (Eq. 12, P 19)


    Where :

    Tc = estimated cell temp., deg. C.

    Tm = Back plate temp. == E*{EXP [a+(b*ws)]}+Ta (Eq. 11, P.18)
    E= POA irradiance, W/m^2
    Delta T=3 deg. C.
    a = empirical constant = - 3.56
    b= empirical constant = -0.075
    ws = wind speed, m/sec.
    Ta = ambient temp. , deg. C.

    Or, from NREL, CD-520-33586, another empirical correlation:

    Tc = (0.943*Ta) + (0.028*E) - (1.528* ws) + 4.2 (As published, using the same variable definitions as the Sandia method.)

    I found that the NREL correlation gave a better fit to my data if the last term was changed to 4.2 from 4.3, so that's what I used (the 4.2) for the NREL estimates shown below.

    POA (Plane of Array) irradiance is estimated by conversion of the measured GHI by using the HDKR model as found in Duffie and Beckman.

    Between 10/09/2014 - 02/09/2015 (with n= 34) and 06/14/2015 - 08/15/15 (with n=26) as part of my ongoing efforts to estimate the effects of array fouling on performance, I used an IR thermometer to measure the back plate temps of each of 16 panels in four places, approximately for the period +/- 6-8 min. on either side of the minute of minimum incidence angle for clear days, that is, a total of 128 temp. measurements, 64 on each side of min. incidence angle time on a total of 60 days, ~ 6-8 minutes on either side the time of minimum incidence angle of beam radiation on the array. Also measured was the temp. of the roof deck under the array, in the same fashion as the back of the panel temps., again 128 temps., 64 ea. on either side of minimum incidence angle time. The array to roof clearance is ~ 8"-11", and while it's a tight squeeze, I can get under the entire array, but there's a lot of ass and elbow action for those 16 or so minutes, including a hussle to and from the garage ~ 90 sec. on either side of the mi. incidence angle time. I also recorded array output voltage, current, and power in/out, to/from the inverter off the inverter display as close to min. incidence angle time as possible, usually within 10 sec. or so, as well as all pertinent weather data including ambient air temp. wind vector, Global Horizontal Irradiance (GHI), dew point temp. and barometric pressure as recorded at 1 min. intervals and as measured by a Davis Pro II + weather station located about 4 ft. north of the array at about the same elevation as the north side of the array. The data is logged in 1 minute intervals.

    One of the outputs from all this was an estimate of the average array temperature. Long story short, there seemed to be pretty good agreement between the average of the measured temps. and the two NREL empirical correlations noted above, and a least squares fit of the recorded voltage and estimated temps. from the correlation I conjured up.

    For the 10/09/2015 to 02/09/2016 data: The est. aver. of 16 panel temps. for 34 measuring events:

    Ave amb. air temp. = 23.9 C.
    Ave. GHI = 634 W/m^2
    Ave. POA = 822 W/m^2

    Est. cell temps.:
    Ave.measured temp. = 46.9 C.
    Sandia method = 46.8 C.
    NREL method = 46.8 C.
    Temp. est. from Voltage = 47.0 C.

    For the 06/14/2015 to 08/15/2015 period (with n = 26):

    Ave. ambient temp. = 33.1 C.
    Ave. GHI = 945 W/m^2
    Ave. POA = 967 W/m^2

    Est. cell temps.:
    Ave. measured temp. = 59.0 C.
    Sandia method = 59.7 C.
    NREL method = 59.4 C.
    Est. temp. from Voltage = 59.0 C.

    As usual, take what you want of the above. Scrap the rest.

    Details on request, but they're more boring than what's above.
    Last edited by J.P.M.; 01-11-2017, 01:36 AM.

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