Stochastic prediction of hourly global solar radiation profiles S. Kaplanis, E. Kaplani

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Stochastic prediction of hourly global solar radiation profiles S. Kaplanis, E. Kaplani Mech. Engineering department, T.E.I. of Patra , Meg. Alexandrou 1, Patra kaplanis@teipat.gr. Abstract. - PowerPoint PPT Presentation

Text of Stochastic prediction of hourly global solar radiation profiles S. Kaplanis, E. Kaplani

  • Stochastic prediction of hourly global solar radiation profiles S. Kaplanis, E. KaplaniMech. Engineering department, T.E.I. of Patra, Meg. Alexandrou 1, Patra kaplanis@teipat.gr

  • Abstract A stochastic prediction model of the hourly profile of the I(h;nj) for any day nj at a site is outlined. It requires 1,2,or 3 measurements of the global solar radiation in a day nj, uses a D.B. and gives I(h;nj) for the rest hours. The model is validated against solar measurements. Conclusions are deducted for the predictive power of the model developed in MATLAB It provides I(h;nj) profile predictions very close to the measured values and offers itself as a promising tool for a predictive on-line daily load management.

  • IntroductionThe prediction of the global solar radiation I(h;nj) on an hourly, h, basis, for any day, nj, was the target of many attempts internationally. Review papers outline and compare the mean expected, Im,exp(h;nj), values which are the results of several such significant approaches. A reliable methodology to predict the I(h;nj) profile, based on few data, taking into account morning measurement(s) and simulating the statistics of I(h;nj), is a challenge.

  • A model to predict close to reality I(h;nj) values would be useful in problems such as:1. Meteo purposes2. Sizing effectively and reliably the solar power systems i.e. PV generators 3. Management of solar energy sources, i.e. the output of the PV systems, as affected by the meteo conditions in relation to the power loads to be met .

    The above issues drive the research activities towards the development of an improved effective methodology to predict the I(h;nj) for any day, nj, of the year at any site with latitude .

  • One of those methodologies to predict the mean expected hourly global solar radiation, as proposed by the authors, provided a simple approach model based on the function: (1)where, and b are constants, which depend on the day nj and the site ,

  • This model, overestimates I(h;nj) at the early morning and late afternoon hours, while it underestimates I(h;nj) around the solar noon hours. Although, the Ipr(h;nj) values fall, in general, within the range of the measured Imes(h;nj) fluctuations, a more accurate and dynamic model had to be developed. That model should have inbuilt statistical fluctuations, like the METEONORM package, but with a more effective prediction power.

    A comparison of the Ipr(h;nj) values between METEONORM and the generalised model versions, outlined, in contrast to measured Imes(h;nj) values, during the years (1995-2000), will be highlighted.

  • Basic Theoretical AnalysisDue to the mentioned drawback of the simple model , a correction factor is introduced, normalized at solar noon

  • Zone123456A16.60715.86215.14014.89214.28313.742B9.7319.30510.3269.6509.2908.950C9.3679.3989.4059.39428.26578.535

  • x(z) is the distance the solar beam travels within the atmosphere and x(z;=0) is the distance at solar noon, for which =0. Notice that,

    where, Rg is the earths radius = 6.35103 km, and Hatm the height of the atmosphere =2.5 km. Also, cos(Z) is given by formula below, where is the solar declination and is the hour angle.

  • For =0 or h=12, at solar noon, we get: Notice that, at sunset z =900, and therefore, for sunsegett we :

  • xm(z) is the mean daily distance the solar beam travels in the atmosphere. It is determined by the formula: More accurately, xm(z) should be weighted over the solar intensity.Finally, the model to predict the mean expected hourly global solar radiation now takes the form:

  • and b, are determined , using the boundary conditions to be highlighted below :I(h; nj ) = 0 at h = hss , where hss = 12h + ss /150/h

    Integration of I(h,nj) over a day, from sr to ss, provides H(nj) and via these 2 boundary conditions we may determine a and b

  • A comparison of the predicted mean Im,pr(h; 17.1 ) and the measured Imes(h; 17.1 ) values, during winter for Patra, Greece, for the years 1995-2000.

    Chart1

    0000000

    34170575823108.9

    21319719316320780255.9

    352354331363330157362.9

    461463447482454243425.7

    521835499350498256441.9

    516586498295474230410.8

    428452428308383277333.6

    292310289170247227213.4

    9912912248834657.2

    1212916040

    1995

    1996

    1997

    1998

    1999

    2000

    Predicted

    hour

    Solar Radiation (Wh/m^2)

    Hnj

    17jan

    time9101112131415161718

    1995342133524615215164282929912

    19961719735446383558645231012912

    199701933314474994984282891229

    1998571633634823502953081704816

    199958207330454498474383247830

    20002380157243256230277227464

    average31.5175.5314.5425493.1666666667433.1666666667379.3333333333255.833333333387.83333333338.8333333333

    sum=2604.6666666667Wh=2.605KWh*3.6=9.378MJ

    17jul

    time67891011121314151617181920

    1994168626546865881793797481373363852738718553

    1995121032704536557959049669218266384533238933

    199687522139458676987893893683469051632514643

    1997178824442060576990197694785368452533414029

    19981699276471663823955101698387871655937819544

    19991210622646664379590396588547853546924116233

    20001610816233767981492497394984268453034715141

    average=13.857142857195237.7142857143429.8571428571641.2857142857797.4285714286914.5714285714972.5714285714919.1428571429777.7142857143655511.2857142857333.5714285714152.571428571439.4285714286

    sum=7491Wh=7.491KWh*3.6=26.968MJ

    17jan

    17janMeasured values

    hour7891011121314151617

    19950342133524615215164282929912

    199601719735446383558645231012912

    1997001933314474994984282891229

    19980571633634823502953081704816

    1999058207330454498474383247830

    200002380157243256230277227464

    Theoritikes times me Hnj=9.378 gia Patra (fi:38) 17Jan

    hourI(h;nj)

    I(7.16)=0.00070.0

    I(8.16)=108.9488108.9

    I(9.16)=255.9439255.9

    I(10.16)=362.86310362.9

    I(11.16)=425.70111425.7

    I(12.16)=441.91212441.9

    I(13.16)=410.76013410.8

    I(14.16)=333.63214333.6

    I(15.16)=213.44615213.4

    I(16.16)=57.2181657.2

    170.0

    Previous paper

    THEORETICAL (Hnj:9.4)

    HourIrun317.01

    70

    8109.5

    9256.7

    10363.6

    11426.4

    12442.6

    13411.5

    14334.4

    15214.1

    1657.7

    170

    17jan

    1995

    1996

    1997

    1998

    1999

    2000

    Predicted

    hour

    Solar Radiation (Wh/m^2)

    Sheet3

  • The means of Imes(h;nj ), the Im,pr(h;nj ) values, as predicted by this model, and the IMET(h;nj) values, with the inbuilt stochastic generator for fluctuations, provided by the METEONORM package for the days 17.1 and 17.7, are shown below. The results show the presence of expected strong fluctuations in I(h;nj) especially, for winter months. Values of the mean Imes(h;17.1), Im,pr(h;17.1) and IMET(h;17.1) for Patra,Greece.

    Chart4

    000

    108.931.547

    255.9175.5113

    362.9314.581

    425.742527

    441.9493.240

    410.8433.2287

    333.6379.3351

    213.4255.8232

    57.287.849

    08.83

    Predicted

    Avg Measured

    METEONORM

    hour

    Solar Radiation (Wh/m^2)

    Hnj

    17jan

    time9101112131415161718

    1995342133524615215164282929912

    19961719735446383558645231012912

    199701933314474994984282891229

    1998571633634823502953081704816

    199958207330454498474383247830

    20002380157243256230277227464

    average31.5175.5314.5425493.1666666667433.1666666667379.3333333333255.833333333387.83333333338.8333333333

    sum=2604.6666666667Wh=2.605KWh*3.6=9.378MJ

    17jul

    time67891011121314151617181920

    1994168626546865881793797481373363852738718553

    1995121032704536557959049669218266384533238933

    199687522139458676987893893683469051632514643

    1997178824442060576990197694785368452533414029

    19981699276471663823955101698387871655937819544

    19991210622646664379590396588547853546924116233

    20001610816233767981492497394984268453034715141

    average=13.857142857195237.7142857143429.8571428571641.2857142857797.4285714286914.5714285714972.5714285714919.1428571429777.7142857143655511.2857142857333.5714285714152.571428571439.4285714286

    sum=7491Wh=7.491KWh*3.6=26.968MJ

    17jan

    Patra17janMeasured values

    hour7891011121314151617

    19950342133524615215164282929912

    199601719735446383558645231012912

    1997001933314474994984282891229

    19980571633634823502953081704816

    1999058207330454498474383247830

    200002380157243256230277227464

    average031.5175.5314.5425493.2433.2379.3255.887.88.8

    Theoritikes times me Hnj=9.378 gia Patra (fi:38) 17Jan

    hourI(h;nj)

    I(7.16)=0.00070.0

    I(8.16)=108.9488108.9

    I(9.16)=255.9439255.9

    I(10.16)=362.86310362.9

    I(11.16)=425.70111425.7

    I(12.16)=441.91212441.9

    I(13.16)=410.76013410.8

    I(14.16)=333.63214333.6

    I(15.16)=213.44615213.4

    I(16.16)=57.2181657.2

    170.0

    Previous paperolder values

    THEORETICAL (Hnj:9.4)

    HourIrun317.01

    70

    8109.5

    9256.7

    10363.6

    11426.4

    12442.6

    13411.5

    14334.4

    15214.1

    1657.7

    170

    meteonormexperimental

    Hour\Date17-Jan

    70

    847

    9113

    1081

    1127

    1240

    13287

    14351

    15232

    1649

    173

    17jan

    1995

    1996

    1997

    1998

    1999

    2000

    Predicted

    hour

    Solar Radiation (Wh/m^2)

    17jul

    Predicted

    Avg Measured

    METEONORM

    hour

    Solar Radiati