Evaluation and comparison of hourly solar radiation models

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  • INTERNATIONAL JOURNAL OF ENERGY RESEARCHInt. J. Energy Res. 2009; 33:538552Published online 10 November 2008 in Wiley InterScience(www.interscience.wiley.com). DOI: 10.1002/er.1474

    SHORT COMMUNICATION

    Evaluation and comparison of hourly solar radiation models

    M. Jamil Ahmad,y and G. N. Tiwari

    Centre for Energy Studies, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India

    SUMMARY

    In this paper, an attempt has been made to develop a new model to evaluate the hourly solar radiation for compositeclimate of New Delhi. The comparison of new model for hourly solar radiation has been carried out by using variousmodel proposed by others. The root mean square error (RMSE) and mean bias error (MBE) have been used to comparethe accuracy of new and others model. The results show that the ASHRAE and new proposed model estimate hourlysolar radiation better for composite climate of New Delhi in comparison to other models. Hourly solar radiationestimated by constants obtained by new model (modied ASHRAE model) for composite climate of India is fairlycomparable with measured data. The percentage mean bias error with new constants for New Delhi was found as low as0.15 and 0% for hourly beam and diffuse radiation, respectively. There is a 1.98.5% RMSE between observed andpredicted values of beam radiation using new constants for clear days. The statistical analysis has been used for thepresent study. Copyright r 2008 John Wiley & Sons, Ltd.

    KEY WORDS: solar radiation; beam radiation; diffuse radiation

    1. INTRODUCTION

    The solar radiation, through atmosphere, reaching

    the earths surface can be classied into two

    components: beam radiation and diffuse radiation.

    Beam radiation is the solar radiation propagating

    along the line joining the receiving surface and the

    sun. It is also referred to as direct radiation.

    Diffuse radiation is the solar radiation scattered by

    aerosols, dust and molecules, it does not have a

    unique direction. The total radiation is the sum of

    the beam and diffuse radiation and is sometimes

    referred to as the global radiation. When the

    amount of diffuse radiation reaching the earthssurface is less than or equal to 25% of globalradiation, the sky is termed as clear sky.

    Solar radiation available on the Earths surfacedepends on local climatic conditions. Knowledge ofmonthly mean daily global and diffuse radiation onhorizontal surface is essential to design solar energydevices. Further, there is a need to have knowledgeof hourly solar radiation on horizontal surfaces forbetter performance of solar energy devices. Hourlyvalues of solar radiation enable us to derive veryprecise information about the performance of solarenergy systems [1]. Such hourly data is useful for

    *Correspondence to: M. Jamil Ahmad, Centre for Energy Studies, Indian Institute of Technology Delhi, Hauz Khas, New Delhi110016, India.

    yE-mail: jamil.amu@gmail.com

    Received 28 May 2008

    Revised 8 September 2008

    Accepted 13 September 2008Copyright r 2008 John Wiley & Sons, Ltd.

  • engineers, architects and designers of solar systemsto make effective use of solar energy.

    Most locations in India receive abundant solarradiation and hence solar energy technology canbe protably applied to these regions. The solarradiation data are either obtained fromexperimental measurements of the global anddiffuse radiation or obtained from developedempirical relation for a given latitude. In India,the Indian Meteorology Department (IMD),Government of India, measures sunshineduration, global radiation and diffuse radiationat selected locations. The measured data availablefrom IMD of 11 years have been compiled forpresent study and is given in Table I. Table I givesthe monthly average values of hourly global anddiffuse radiation.

    The rst attempt to analyse the hourly globalradiation data was made by Whiller [2] and Hotteland Whiller [3]. They have used the data of various

    locations in U.S.A., to obtain the variation ofhourly to daily radiation ratio against sunset hourangle. Liu and Jordan [4] have extended the daylength of these variations. By using the correcteddata of ve U.S. locations, Collares-Pereira andRabl [5] have developed an analytical expressionfor hourly to daily global radiation ratio interms of sunset hour angle. The hourlycorrelation between daily diffuse transmissioncoefcient and daily clearness index obtainedby Orgill and Hollands [6], Bruno [7] and Bugler[8] can be used to estimate the ratio of hourlydiffuse to hourly global radiation. Liu and Jordan[4] have determined the hourly distribution ofdiffuse radiation from daily radiation. Gopinathan[1] has also obtained the same from sunshinehour. No general formula is available yet forprediction of the solar radiation reaching theEarths surface over a given period of time atany location [9].

    Table I. Average hourly global and diffuse radiation (Wm2) in (a) January (b) June for allweather types for New Delhi.

    Weather type

    a b c d

    Time Total Diffuse Total Diffuse Total Diffuse Total Diffuse

    (a) January8 132.99 52.60 119.58 52.75 71.11 64.16 51.20 48.169 355.56 86.28 332.50 102.57 235.55 146.66 140.11 107.6710 554.69 107.29 516.25 123.09 360.00 195.56 237.11 175.6611 680.73 121.53 650.41 149.46 457.78 220.00 301.78 221.0012 726.74 126.39 708.75 155.32 515.55 226.12 379.92 246.5013 733.85 136.63 723.33 161.18 515.55 226.12 379.92 255.0014 656.08 128.30 650.41 155.32 462.22 210.84 328.72 240.8315 500.00 110.94 498.75 128.94 353.34 180.28 261.36 187.0016 311.46 90.28 315.00 96.71 217.78 122.22 161.67 138.8317 106.42 41.84 110.84 46.88 71.11 51.94 45.80 42.50

    (b) June8 436.67 123.89 433.34 198.33 358.33 277.77 235.12 169.569 637.22 149.44 641.34 250.83 555.56 350.70 350.12 251.3110 802.22 157.22 794.45 277.08 727.78 378.47 454.88 360.3111 915.00 158.89 912.89 297.50 816.67 416.66 595.44 405.7212 951.67 167.78 999.55 300.42 833.33 434.03 672.12 454.1713 946.11 185.00 996.66 335.41 861.11 423.61 682.34 481.4214 882.78 180.56 912.89 315.00 763.89 402.78 631.22 448.1115 765.56 176.11 808.89 291.67 688.89 385.41 536.66 393.6116 611.67 142.78 635.55 274.17 538.89 347.22 426.78 330.0317 420.00 116.11 416.00 207.08 333.33 246.53 281.12 260.39

    EVALUATION AND COMPARISON OF HOURLY SOLAR RADIATION MODELS 539

    Copyright r 2008 John Wiley & Sons, Ltd. Int. J. Energy Res. 2009; 33:538552

    DOI: 10.1002/er

  • The hourly solar radiation calculated fordifferent locations in India by ASHRAE modelpredicts higher beam radiation and lower diffuseradiation [10]. This may be due to the fact that theASHRAE model has been developed for clear skycondition. Nijigorodov [11] has modied thevalues of empirical coefcients of ASHRAEmodel valid only for climatic conditions ofBotswana, Namibia and Zimbabwe. This modelgives large error for composite climate of NewDelhi. The modied ASHRAE models by Machlerand Iqbal [12] and Parishwad et al. [13] do notvalidate the measured data of climatic conditionsof New Delhi (latitude: 28.581N; longitude:77.021E; elevation: 216m above msl).

    The objective of the present study is to developa new model based on ASHRAE for different skyconditions to estimate hourly global (I) and diffuse(Id) radiation on a horizontal surface. The analysishas been done for the following four types ofweather conditions.

    (a) Clear day (blue sky): If diffuse radiation is lessthan or equal to 25% of global radiation andsunshine hour is more than or equal to 9 h.

    (b) Hazy day(fully): If diffuse radiation is less than50% or more than 25% of global radiation andsunshine hour is between 7 and 9h.

    (c) Hazy and cloudy (partially): If diffuse radiationis less than 75% or more than 50% of globalradiation and sunshine hour is between 5 and 7h.

    (d) Cloudy day (fully): If diffuse radiation is morethan 75% of global radiation and sunshinehour is less than 5 h.

    The above four conditions constitute thecomposite climate of New Delhi [14].

    Table II gives the average number of daysunder different types of weather conditions in eachmonth.

    2. EXISTING MODELS

    2.1. ASHRAE model

    By using ASHRAE model [10], the hourly globalradiation (I), hourly beam radiation in direction ofrays (IN) and hourly diffuse radiation (Id) on thehorizontal surface on a clear day are calculated byusing the following equations:

    I IN cos yz Id 1

    IN A expB= cos yz 2

    Id CIN 3

    where the values of the constants A, B and C aregiven in Table III(a).

    yz is the zenith angle, which depends upon thelatitude of the location (f), hour angle (o) andsolar declination (d), and is evaluated from thefollowing equation:

    cos yz sinf: sin d cosf: cos d: coso 4

    Further, solar declination (d) is obtained from

    d 23:45 sin360284 n=365 5

    The hour angle (o) is an angular measure of timeand is equivalent to 151 per hour. It is measuredfrom noon-based local apparent time (LAT) fromthe following equation

    o 15:012:0 LAT 6

    LAT value is obtained from the standard time(ST) by using the following relation

    LAT ST ET 4:STL l 7

    where STL is standard meridian for the local timezone (For India, its value is 811540), l is thelongitude of the location and E is the equation oftime correction (in minutes) given as

    E 229:20:000075 0:001868 cosB 0:032077 sinB 0:014615 cos 2B 0:04089 sin 2B 8

    Table II. Average number of days under different weather types in different months during 19912001 for New Delhi.

    Weather Jan Feb March April May June July Aug Sep Oct Nov Dec

    a 3 3 5 4 4 3 2 2 7 5 6 3b 8 4 6 7 9 4 3 3 3 10 10 7c 11 12 12 14 12 14 10 7 10 13 12 13d 9 9 8 5 6 9 17 19 10 3 2 8

    M. J. AHMAD AND G. N. TIWARI540

    Copyright r 2008 John Wiley & Sons, Ltd. Int. J. Energy Res. 2009; 33:538552

    DOI: 10.1002/er

  • TableIII.

    (a)EvaluatedvaluesofA,BandCforvariousmodelsand(b)evaluatedvaluesofA,B,CandDfor(a)weathertypea,(b)weathertype

    b,(c)weather

    typecand(d)weather

    typedatNew

    Delhi.

    Months

    Parameter

    Jan

    Feb

    Mar

    Apr

    May

    Jun

    Jul

    Aug

    Sep

    Oct

    Nov

    Dec

    (a)ASH-RAEmodel

    A1230

    1215

    1186

    1136

    1104

    1088

    1085

    1107

    1152

    1193

    1221

    1234

    B0.142

    0.144

    0.156

    0.180

    0.196

    0.205

    0.207

    0.201

    0.177

    0.160

    0.149

    0.142

    C0.058

    0.060

    0.071

    0.097

    0.121

    0.134

    0.136

    0.122

    0.092

    0.073

    0.063

    0.057

    Nijigorodovmodel

    A1163

    1151

    1142

    1146

    1152

    1157

    1158

    1152

    1150

    1156

    1167

    1169

    B0.177

    0.174

    0.170

    0.165

    0.162

    0.160

    0.159

    0.164

    0.167

    0.172

    0.174

    0.177

    C0.114

    0.112

    0.110

    0.105

    0.101

    0.098

    0.100

    0.103

    0.107

    0.111

    0.113

    0.115

    MachlerandIqbalmodel

    A1202

    1187

    1164

    1130

    1106

    1092

    1093

    1107

    1136

    1166

    1190

    1204

    B0.141

    0.142

    0.149

    0.164

    0.177

    0.185

    0.186

    0.182

    0.165

    0.152

    0.144

    0.141

    C0.103

    0.104

    0.109

    0.120

    0.130

    0.137

    0.138

    0.134

    0.121

    0.111

    0.106

    0.103

    Parishwadet

    al.model

    A610.00

    652.20

    667.86

    613.35

    558.39

    340.71

    232.87

    240.80

    426.21

    584.73

    616.60

    622.52

    B0.000

    0.010

    0.036

    0.121

    0.200

    0.428

    0.171

    0.148

    0.074

    0.020

    0.008

    0.000

    C0.242

    0.249

    0.299

    0.395

    0.495

    1.058

    1.611

    1.624

    0.688

    0.366

    0.253

    0.243

    (b)Weather

    typea

    A1100.6

    1095.8

    1065.1

    1017.4

    1058.3

    953.7

    873.7

    836.8

    949.2

    1148.6

    861.9

    914.9

    B0.1137

    0.1715

    0.205

    0.212

    0.286

    0.202

    0.225

    0.205

    0.178

    0.299

    0.075

    0.082

    C0.176

    0.195

    0.224

    0.251

    0.214

    0.274

    0.721

    0.243

    0.223

    0.315

    0.379

    0.264

    D39.99

    31.37

    35.77

    30.03

    2.80

    43.83

    297.92

    7.54

    19.55

    107.6

    173.82

    103.58

    Weather

    typeb

    A1014.4

    1059.1

    1057.5

    1065.7

    1021.7

    990.9

    942.7

    996.0

    901.3

    846.5

    943.0

    101.2

    B0.115

    0.171

    0.2078

    0.2443

    0.4375

    0.3854

    0.4540

    0.4298

    0.2362

    0.2628

    0.3492

    0.1855

    C0.2585

    0.3068

    0.3033

    0.3235

    0.4006

    0.4667

    0.5529

    0.3444

    0.4166

    0.3701

    0.3116

    0.2722

    D71.490

    74.033

    59.647

    56.09

    36.99

    2.2115

    9.860

    47.40

    67.01

    1.5204

    37.989

    42.196

    Weather

    typec

    A685.4

    698.1

    783.2

    832.7

    1049.4

    1028.9

    770.2

    681.6

    700.9

    829.5

    534.3

    658.9

    B0.3001

    0.3912

    0.4384

    0.6050

    0.7414

    0.8589

    0.5810

    0.6334

    0.4030

    0.4384

    0.3780

    0.2056

    C0.4624

    0.4723

    0.4607

    0.5653

    0.5743

    0.5788

    0.7477

    0.7021

    0.6569

    0.3821

    0.6260

    0.5686

    D17.044

    41.541

    41.899

    73.302

    117.74

    170.93

    31.482

    116.3

    44.39

    46.75

    41.82

    59.32

    Weather

    typed

    A300.6

    320.7

    770.9

    976.2

    959.7

    580.2

    321.9

    375.1

    447.1

    1135.0

    4700.4

    362.9

    B0.3768

    0.5669

    0.7787

    0.8686

    1.1016

    1.0200

    0.6642

    0.6850

    0.6928

    1.2596

    1.6837

    0.4351

    C1.1618

    1.1219

    0.9108

    0.7022

    0.9495

    1.4352

    2.1369

    1.8470

    1.3885

    0.5660

    0.3151

    0.6024

    D28.6590

    75.8745

    79.1801

    125.685

    150.0405

    130.221

    54.70

    46.664

    84.379

    194.02

    152.108

    129.588

    EVALUATION AND COMPARISON OF HOURLY SOLAR RADIATION MODELS 541

    Copyright r 2008 John Wiley & Sons, Ltd. Int. J. Energy Res. 2009; 33:538552

    DOI: 10.1002/er

  • where B n 1360=365 and n5 nth day ofthe year.

    We have also calculated constants A, B ofEquation (2) for composite climate of New Delhi.The results are given in Table III(b).

    2.2. Nijigorodov model

    Nijiorodov [11] has revised the constants A, B andC (of ASHRAE model) for clear days in Botswanafrom analysis of different solar radiation compo-nents recorded at the university of Botswana,Botswana Technology Centre and some synopticstations. The results are given in Table III(a).

    2.3. Machler and Iqbal model

    Machler and Iqbal [12] have modied the con-stants A, B and C (of ASHRAE model), whichtake into account the advancement in the solarradiation research over past decades. The resultsobtained for A, B and C of Equations (1)(3) forCanada are given in Table III(a).

    2.4. Parishwad et al. model

    Parishwad et al. [13] have evaluated the constantsA, B and C (of ASHRAE model) using regressionanalysis of measured solar radiation data of sixcities of India. The results are given in Table III(a).

    2.5. Perez et al. model

    Perez et al. [15] proposed the correlation to predictdirect normal terrestrial solar radiation. Theexpression for direct normal terrestrial radiationis given by

    IN ION: expTR=0:9 9:4 cos yz 9

    where TR is Linke turbidity factor and ION isnormal extraterrestrial solar radiation which isexpressed as

    ION ISC1:0 0:033 cos360n=365 10

    where ISC is solar constant.

    2.6. Kasten and Young model

    Kasten and Young [16] have also developed anempirical relation for direct terrestrial solar radia-tion in terms of air mass m, integrated Rayleigh

    scattering optical thickness of atmosphere E andLinke turbidity factor TR. An expression for IN isgiven as

    IN ION: expm:E:TR 11

    The parameters m and E are expressed as

    m cos yz 0:15 93:885 yz1:2531 12

    and

    E 4:529 104:m2 9:66865 103:m 0:108014 13

    2.7. Hottel model

    Hottel [3] has presented a model to estimate thebeam radiation transmitted through clear atmo-sphere in terms of zenith angle and altitude for astandard atmosphere and for four climate types.The atmospheric transmittance tb is IN=ION and itis given by

    tb a0 a1: expk= cos yz 14

    The constants a0, a1 and k are functions of thealtitude of the location, which are given by

    a0 0:4237 0:008216 A2

    a1 0:5055 0:005956:5 A2

    and

    k 0:2711 0:018582:5 A2

    where A is altitude in km.

    2.8. Present model

    It is based on the ASHRAE model describedabove in Section 2.1. Since the evaluated constantsA, B and C in Equations (2) and (3) are notvalidating the data for composite climate, hence itrequires modications. The expressions for hourlyglobal and radiation are same as Equation (1) and(2). The values of constants A and B have beenrevised by using regression analysis of the solarradiation data

    The expression for hourly diffuse radi...

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