Direct irradiance in tilted plane not as expected

[spelland74]

Hello,

I am modeling a one-axis East-West tracker. I have been doing some verifications on the irradiance data in the plane of the array. For certain times of day, PVsyst gives direct normal irradiance non-zero, and incidence angle less than 90 degrees, but direct irradiance in the plane of the array is 0. I am wondering why that is. Is direct in the plane of the array always calculated using DNI*cos(incidence_angle), or are there cases where there are added complications?

I am attaching the file I used which includes data from PVsyst. I am including only the 29 hours for which DNI*cos(incidence_angle) does not give the same value as the BeamInc reported by PVsyst. For all other hours, the results were the same.

Best regards,

Sophie

Note: I was unable to attach the file. I am copying a csv version of it below. The two last columns are the direct irradiance in the array plane calculated by PVsyst (BeamInc) and the value calculated using the direct normal from PVsyst and the angle of incidence from PVsyst.

kT,date,GlobHor,DiffHor,BeamHor,T Amb,GlobInc,WindVel,HSol,AzSol,AngInc,AngProf,PlTilt,PlAzim,PhiAng,DifSInc,Alb Inc,BeamNor,BeamInc,BeamNor*cos(AngInc)

1.416,19/11/97 06:00,6.007,1.0027,5.0043,22.7,1.0028,1.8,1.0426,-68.597,87.872,1.1199,1.166,-90,-1.166,1.0027,0.0001,275.8,0,10.24102444

1.22,20/11/97 06:00,5.0033,1.9986,3.0046,21.4,1.9987,2.5,1.1185,-68.319,87.717,1.2036,1.2533,-90,-1.2533,1.9986,0.0001,154.3,0,6.146590466

0.831,18/11/97 06:00,3.9995,1.9986,2.0009,22.6,1.9987,2.3999,1.1827,-68.789,87.586,1.2686,1.3211,-90,-1.3211,1.9986,0.0001,97.2,0,4.094043028

1.17,21/01/97 18:00,6.9953,3.9973,2.998,19.9,3.9974,0,1.2118,68.361,87.526,1.3036,1.3576,90,1.3576,3.9973,0.0002,141.4,0,6.103676527

1.755,07/10/97 18:00,10.995,1.9986,8.9962,25.1,1.9989,1.4,1.3064,83.445,87.333,1.315,1.3694,90,1.3694,1.9986,0.0003,393.7,0,18.31930339

1.486,16/11/97 06:00,9.0028,1.9986,7.0041,23.3,1.9989,2.3,1.2437,-69.284,87.461,1.3297,1.3847,-90,-1.3847,1.9986,0.0003,323.4,0,14.32642847

2.392,08/10/97 18:00,14.006,1.0027,13.003,25.3,1.0031,0.3,1.3287,83.024,87.288,1.3386,1.394,90,1.394,1.0027,0.0004,559.5,0,26.47310991

0.867,20/01/97 18:00,5.0033,3.0013,2.0019,21.3,3.0015,1.1,1.2754,68.092,87.397,1.3746,1.4316,90,1.4316,3.0013,0.0002,89.7,0,4.073751876

1.352,17/11/97 06:00,7.999,3.0013,4.9977,23.4,3.0016,2.8,1.3223,-68.987,87.301,1.4164,1.4752,-90,-1.4752,3.0013,0.0003,217,0,10.21831664

1.916,11/03/97 06:00,11.999,1.9986,9.9999,16.3,1.999,0.3,1.4166,-85.554,87.108,1.4209,1.4799,-90,-1.4799,1.9986,0.0004,405.4,0,20.45384568

1.788,22/01/97 18:00,11.999,1.9986,9.9999,21,1.9991,0.6,1.3641,68.543,87.215,1.4656,1.5265,90,1.5265,1.9986,0.0004,419.2,0,20.36820752

1.931,15/11/97 06:00,13.002,1.9986,11.004,23.2,1.9991,2.5,1.3818,-69.495,87.179,1.4753,1.5365,-90,-1.5365,1.9986,0.0005,457.3,0,22.50640733

2.667,06/10/97 18:00,21.001,1.9986,19.003,25.2,1.9994,0,1.5174,83.774,86.902,1.5264,1.5898,90,1.5898,1.9986,0.0008,716.2,0,38.70628232

0.98,13/11/97 06:00,7.999,1.0027,6.9963,23,1.003,1.7,1.4372,-70.028,87.066,1.5291,1.5927,-90,-1.5927,1.0027,0.0003,279.5,0,14.30637049

0.838,24/01/97 18:00,6.9953,1.0027,5.9926,23.7,1.003,2.2,1.4509,69.018,87.038,1.5539,1.6186,90,1.6186,1.0027,0.0003,236.2,0,12.20531107

1.496,14/11/97 06:00,11.999,3.0013,8.9972,22.4,3.0018,2.5,1.5192,-69.712,86.898,1.6197,1.6872,-90,-1.6872,3.0013,0.0005,340,0,18.39864728

1.975,23/01/97 18:00,15.998,1.9986,13.999,23.7,1.9993,2.0999,1.5162,68.73,86.905,1.627,1.6948,90,1.6948,1.9986,0.0007,528.1,0,28.51300305

0.335,12/11/97 06:00,2.9958,1.9986,0.9971,21.8,1.9988,1.5,1.5726,-70.257,86.789,1.6708,1.7405,-90,-1.7405,1.9986,0.0001,36.4,0,2.038880146

1.337,05/10/97 18:00,11.999,1.9986,9.9999,24.4,1.9992,0.3999,1.7305,84.103,86.467,1.7397,1.8125,90,1.8125,1.9986,0.0006,330.5,0,20.36653824

0.323,28/06/97 19:00,2.9958,1.9986,0.9971,25.2,1.9988,2.6,1.6039,114.5,86.725,1.7625,1.8363,90,1.8363,1.9986,0.0002,35.6,0,2.033771492

0.674,11/11/97 06:00,6.9953,3.0013,3.994,18.5,3.0017,1.0001,1.7071,-70.493,86.515,1.811,1.8868,-90,-1.8868,3.0013,0.0004,134.3,0,8.163724501

2.199,30/06/97 19:00,21.001,1.0027,19.999,25.1,1.0038,4.5,1.6514,114.39,86.628,1.8131,1.889,90,1.889,1.0027,0.0011,692.8,0,40.74948071

0.352,09/11/97 06:00,3.9995,3.0013,0.9982,19.4,3.0016,1.5,1.7528,-71.074,86.421,1.8529,1.9307,-90,-1.9307,3.0013,0.0002,32.7,0,2.041288325

0.305,08/07/97 19:00,2.9958,1.0027,1.9931,24.5,1.0029,1.7,1.7003,113.68,86.528,1.8565,1.9344,90,1.9344,1.0027,0.0002,67.1,0,4.063626431

0.537,10/11/97 06:00,6.007,6.0027,0.0043,18.6,6.003,1.3001,1.8405,-70.734,86.242,1.9496,2.0316,-90,-2.0316,6.0027,0.0004,0.1,0,0.006554246

0.429,06/11/97 06:00,6.007,6.0027,0.0043,19.4,6.0031,0.9,1.9206,-71.943,86.078,2.02,2.1052,-90,-2.1052,6.0027,0.0004,0.1,0,0.006839837

0.78,30/01/97 18:00,10.995,6.0027,4.9921,22.4,6.0034,2,1.9119,70.497,86.096,2.0282,2.1137,90,2.1137,6.0027,0.0007,149.4,0,10.17189034

0.724,29/01/97 18:00,10.007,5,5.0065,22.7,5.0007,3.8,1.9832,70.173,85.95,2.1081,2.1972,90,2.1972,5,0.0007,144.5,0,10.20559947

[André Mermoud]

The times when this arises are very close to sunrise or sunset.

For these hours including the sunrise (or sunset), PVsyst considers the time between sunrise and the end of the hour, and computes the solar geometry at the middle of this interval.

The Direct normal is computed on the basis of the GlobHor, DiffHor and divided by the sin(sun height). The cut on Sun height is rather low (I dont remember the value).

But there is a cut of 10 W/m2 on the GlobInc value for the rest of the simulation.

Now for your tracking situation (probably with backtracking), the plane is almost horizontal (1-2 degrees) so that the GlobInc value is very low at sunrise. On the other hand, there is a cut on the incidence angle (>88° doesn't make much sense due to the IAM loss). This explains the null values of BeamInc.

[spelland74]

Thanks Andre!