Off-ideal Array Tilt Output [RE-wrenches]
Antony Tersol
tony at appliedsolarenergy.com
Sat Apr 3 10:04:14 PST 2004
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Allan wrote:
Fellow Wrenches,
I will generally include Kwhr-year performance projections for all of our
Sunny Boy systems as part of my proposal package. The actual output has
exceeded prediction in all but one case, I recall, which makes customers
happy. But most arrays have faced very close to true solar south.
I have a specific roof now that is less than ideal: fixed 26 degree angle
and 50 degrees west of true south. Can anyone assist me to predict annual
output as a percentage of [true south and latitude tilt] for my Santa Fe NM
site (latitude 37 degrees)?
Thanks in advance,
Allan at Positive Energy
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Allan,
What are your projections for production? What is your package? The following calculations are assuming 18 Sharp 165 panels, 1 SB2500. I would be interested in comparing my projections with your results to validate (or invalidate) my model.
According to my calculations: (using the weather data for Albuquerque)
the annual total for tilt at 30 degrees, south is
5420 kwh (for a specific combination of panels and inverter)
and at tilt 26 degrees, azimuth 50 degrees west of south the annual total is
5002 kwh
so the relative performance is 92.3%.
I don't know if 30 degrees is actually optimum (or 0 azimuth for that matter), but could find out - just requires doing the simulation (based on every 5 degrees in azimuth, every 5 degrees of tilt) 1368 times. My software will do that, but it takes a little time, since each of the simulations is calculating every hour for a year (8760 discrete data points).
Optimum azimuth, when you account for weather, is very often not directly south, since typically cloud cover is not symmetric in time around solar noon. In albuquerque, you get more skycover in the afternoon (roughly 55%/45%), whereas in our area there is more in the morning. Thus our optimum azimuth is more towards the west, whereas yours would be more towards the east.
For example trying 5 degrees east of south yields a total of 5422 kwh / year.
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with
Site Latitude 35.6 degrees
Array Tilt 29.0 degrees
Array Azimuth 0.0 degrees
Tracking fixed tilt
Array Area 23.418 sq meters
Average Array Height 2.0 meters
Mismatch and Line Losses 3.5 %
Ground Albedo 0.300
Installed NOCT 40.0 degrees C
Reference temperature 25.0 degrees C
Reference Efficiency 11.1 %
Efficiency Reduction Coeff. 0.430 % change / degree C
PCU Input Rating 2.5 kilowatts
PCU Efficiency 94.0 %
Yearly totals of ac power by the hour without shading (the model allows inputting Pathfinder data to account for approximate shading).
0 0.000
1 0.000
2 0.000
3 0.000
4 0.000
5 0.056
6 41.500
7 204.995
8 420.880
9 591.099
10 705.034
11 754.846
12 755.613
13 689.315
14 579.647
15 412.174
16 211.714
17 52.000
18 1.021
19 0.000
20 0.000
21 0.000
22 0.000
23 0.000
Total 5419.894
Monthly totals of ac power by the hour without shading
Summer Month 5 6 7 8 9 10
0 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1 0.000 0.000 0.000 0.000 0.000 0.000 0.000
2 0.000 0.000 0.000 0.000 0.000 0.000 0.000
3 0.000 0.000 0.000 0.000 0.000 0.000 0.000
4 0.000 0.000 0.000 0.000 0.000 0.000 0.000
5 0.014 0.007 0.008 0.002 0.000 0.000 0.031
6 9.944 9.498 8.496 4.309 1.825 3.327 37.401
7 28.214 25.358 24.663 22.465 19.327 20.190 140.216
8 45.420 40.639 41.102 39.336 35.063 39.147 240.707
9 58.340 53.016 52.462 52.977 47.336 51.598 315.729
10 66.122 60.239 61.697 61.594 56.903 61.771 368.327
11 67.732 64.976 66.064 66.471 62.544 64.685 392.471
12 68.263 65.277 66.783 64.621 64.217 63.451 392.612
13 64.611 53.968 61.279 57.111 58.304 58.975 354.248
14 52.812 47.581 52.931 48.342 47.374 48.590 297.630
15 39.853 36.998 34.439 39.100 32.860 31.852 215.102
16 24.312 23.544 21.441 22.828 16.692 13.498 122.315
17 9.603 10.814 8.979 8.548 1.811 0.597 40.352
18 0.028 0.149 0.133 0.051 0.000 0.000 0.361
19 0.000 0.000 0.000 0.000 0.000 0.000 0.000
20 0.000 0.000 0.000 0.000 0.000 0.000 0.000
21 0.000 0.000 0.000 0.000 0.000 0.000 0.000
22 0.000 0.000 0.000 0.000 0.000 0.000 0.000
23 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Winter Month 11 12 1 2 3 4
0 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1 0.000 0.000 0.000 0.000 0.000 0.000 0.000
2 0.000 0.000 0.000 0.000 0.000 0.000 0.000
3 0.000 0.000 0.000 0.000 0.000 0.000 0.000
4 0.000 0.000 0.000 0.000 0.000 0.000 0.000
5 0.000 0.000 0.000 0.000 0.000 0.024 0.024
6 0.016 0.000 0.000 0.000 0.335 4.595 4.946
7 11.024 6.525 4.537 5.361 14.847 22.534 64.829
8 31.860 27.575 22.246 21.746 35.540 40.386 179.353
9 45.336 43.849 41.217 38.553 48.459 56.657 274.072
10 55.150 54.895 52.095 49.106 58.536 65.327 335.108
11 59.204 55.989 55.669 57.519 63.585 68.855 360.822
12 57.741 54.020 56.988 59.654 66.538 66.489 361.429
13 53.318 49.735 54.340 55.440 61.586 59.145 333.564
14 42.547 42.220 45.015 46.833 51.423 52.634 280.673
15 26.497 24.434 32.999 34.145 39.012 39.035 196.121
16 5.669 6.506 13.124 18.154 23.936 21.762 89.152
17 0.000 0.000 0.117 2.065 3.297 6.723 12.201
18 0.000 0.000 0.000 0.000 0.002 0.627 0.629
19 0.000 0.000 0.000 0.000 0.000 0.000 0.000
20 0.000 0.000 0.000 0.000 0.000 0.000 0.000
21 0.000 0.000 0.000 0.000 0.000 0.000 0.000
22 0.000 0.000 0.000 0.000 0.000 0.000 0.000
23 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Total power / value 5410.428 kwh 938.69 938.69
Value is based on PG&E tariff so not applicable to your area.
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Array Tilt (tilt) 26.0 degrees
Array Azimuth (azim) -50.0 degrees
Yearly totals of ac power by the hour without shading
0 0.000
1 0.000
2 0.000
3 0.000
4 0.000
5 0.092
6 3.461
7 56.284
8 228.428
9 415.404
10 567.417
11 668.710
12 722.863
13 706.138
14 645.524
15 513.460
16 326.279
17 130.190
18 17.991
19 0.007
20 0.000
21 0.000
22 0.000
23 0.000
Total 5002.249
Monthly totals of ac power by the hour without shading
Summer Month 5 6 7 8 9 10
0 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1 0.000 0.000 0.000 0.000 0.000 0.000 0.000
2 0.000 0.000 0.000 0.000 0.000 0.000 0.000
3 0.000 0.000 0.000 0.000 0.000 0.000 0.000
4 0.000 0.000 0.000 0.000 0.000 0.000 0.000
5 0.010 0.004 0.005 0.001 0.000 0.000 0.019
6 0.521 0.547 0.541 0.222 0.085 1.384 3.300
7 12.271 11.330 11.302 8.126 3.613 1.016 47.657
8 29.464 27.070 26.852 24.211 19.895 18.986 146.478
9 45.476 42.182 41.191 40.098 34.068 34.433 237.449
10 57.022 52.906 53.688 52.247 46.601 47.918 310.382
11 63.257 61.511 62.114 61.096 55.785 55.425 359.189
12 68.384 66.191 67.382 63.870 61.689 58.927 386.443
13 69.499 58.568 66.300 60.557 60.354 59.205 374.484
14 61.257 55.601 61.809 55.258 53.157 53.235 340.317
15 51.351 47.721 43.678 49.788 41.277 39.575 273.389
16 37.641 36.001 31.729 34.400 25.979 21.890 187.640
17 22.520 22.825 17.782 17.781 8.526 2.912 92.345
18 3.439 6.334 3.927 1.893 0.001 0.000 15.594
19 0.000 0.007 0.000 0.000 0.000 0.000 0.007
20 0.000 0.000 0.000 0.000 0.000 0.000 0.000
21 0.000 0.000 0.000 0.000 0.000 0.000 0.000
22 0.000 0.000 0.000 0.000 0.000 0.000 0.000
23 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Winter Month 11 12 1 2 3 4
0 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1 0.000 0.000 0.000 0.000 0.000 0.000 0.000
2 0.000 0.000 0.000 0.000 0.000 0.000 0.000
3 0.000 0.000 0.000 0.000 0.000 0.000 0.000
4 0.000 0.000 0.000 0.000 0.000 0.000 0.000
5 0.000 0.000 0.000 0.000 0.000 0.072 0.072
6 0.001 0.000 0.000 0.000 0.005 0.155 0.161
7 0.179 0.012 0.007 0.108 1.468 6.853 8.627
8 13.120 9.235 7.527 9.252 18.511 24.303 81.949
9 28.043 25.266 23.995 24.321 34.096 42.235 177.955
10 40.809 39.492 37.624 37.245 47.291 54.573 257.035
11 49.016 45.497 45.670 48.588 57.191 63.558 309.521
12 52.117 48.039 51.061 54.913 64.567 65.723 336.420
13 52.129 47.968 52.761 55.118 62.235 61.442 331.654
14 45.526 44.468 47.748 50.710 56.872 59.882 305.207
15 32.322 29.312 39.592 41.449 48.113 49.284 240.071
16 10.004 10.526 20.493 27.868 36.272 33.476 138.639
17 0.000 0.000 0.998 5.781 13.357 17.710 37.846
18 0.000 0.000 0.000 0.000 0.082 2.315 2.397
19 0.000 0.000 0.000 0.000 0.000 0.000 0.000
20 0.000 0.000 0.000 0.000 0.000 0.000 0.000
21 0.000 0.000 0.000 0.000 0.000 0.000 0.000
22 0.000 0.000 0.000 0.000 0.000 0.000 0.000
23 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Total power / value 5002.249 900.07 900.07
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