Simulation of Solar Radiation System

Transcription

1 American Journal of Applied cience 2 (4): , 2005 IN cience Publication, 2005 imulation of olar Radiation ytem M.. Alam, uhanta Kumar aha, M.A.K. Chowdhury, Md. aifuzzaman and M. Rahman Intitute of Energy Technology, Chittagong Univerity of Engineering and Technology Chittagong-4349, Bangladeh Abtract: In thi reearch work, a mathematical model for imulation of the olar radiation ytem ha been developed by uing a ytem dynamic methodology. Bangladeh i ued here for model validation. The imulated reult obtained from thi model have compared with the experimental reult and found reaonably a good agreement. Therefore the performance of the model i to be expected a atifactory. Key word: olar radiation, ytem dynamic methodology, beam radiation, diffue radiation INTRODUCTION The un i an effective black body whoe outer urface ha a temperature of K [1] and i emitting an incredible amount of olar radiation. The earth intercept only two-billionth of thi radiation and ave all life on the planet from freezing to death [2]. Beide, the emitting radiation can be ued a an alternative ource of energy for mankind by uing modern technology. ince in thi century, we have virtually identified the whole ucceful functioning economic ytem with a teady increaing conumption of energy. When olar radiation/energy i ued to generate electrical/mechanical energy for any pecific place, it mut be needed to forecat olar energy which will convert to electrical energy to recover the demand. ence, the amount of olar energy for that place mut be known. Technology for meaurement of olar radiation i cotly and ha intrumental hazard. o an alternative method for etimation of olar radiation i required. The ytem dynamic methodology i ued here to imulate the olar radiation ytem, which i comparatively a new innovation, in comparion with the known method of operation reearch. Thi method ha been extenively ued by Forreter [3,4] for indutrial dynamic, Meadow [5] for commodity production cycle, Wadhawa [6] for regional planning, yeed [7] for rural development and Alam [8,9] for rural energy ytem planning. In thi paper a mathematical model i developed to imulate the availability of olar radiation in Bangladeh uing ytem dynamic methodology. appropriate ubcript for the beam and diffue radiation. Beam Radiation (I b ): The olar radiation received from the un without being cattered by the atmophere i called beam radiation. It i direct olar radiation. Diffue Radiation (I d ): olar radiation whoe direction ha been changed through cattering by the atmophere i known diffue radiation. Global Radiation or Terretrial/Total olar Radiation (I h ): The um of beam and diffue radiation in hourly on a urface i called global or total olar radiation, i.e. I h = I b + I d. olar Time: olar time i the time baed on the apparent angular motion of the un acro the ky. olar noon i the time where the un croe the meridian of the oberver. There i a difference between clock time and olar time becaue the olar time varie at any intant depending on the eat-wet diplacement. olar time i related to tandard time by Duffie and Beckman [10] : olar time (t) = tandard time -4(L t -L loc ) + E (1) Where: L t = tandard meridian for the local time zone, L loc = Longitude of the location in equation in degree wet, E = 229.2x( B inB CoB in28 Definition of olar Radiation Ued in Mathematical B = (n-1)360/365, Model: For undertanding the mathematical model, it i n = Day of the year numbered from 1 t January. 1 n required to define ome parameter of the olar ytem. 365 Thee are a follow. olar Geometry/Earth Angle: Earth angle and it Irradiance: The rate at which radiant energy i incident component (Fig. 1) are decribed in the following on a unit urface area. The ymbol I i ued with way. 751

2 Fig. 1: Baic un Earth Angle Fig. 3: Angle of Incident on a Plane olar Contant (I c ): The olar beingntant denoted by I c i the energy from the un per unit time received on a unit urface area perpendicular to the direction of propagation of radiation at the earth mean ditance from the un outide the atmophere. The I c value according to NAA/ATM i 1353 Watt per quare meter [10]. Fig. 2: Angle to Decribe the Poition of the un the ky (i) Latitude (φ): The latitude i the angular ditance of the point on the earth meaured north or outh of the equator i latitude -90 φ 90. Extraterretrial olar Radiation (E 0 ): The radiation that would be received in the abence of the atmophere in addition to the olar contant i called extraterretrial olar radiation. Angle to Decribe the Poition of the un in the ky: Figure 2 repreent the angle to decribe the poition of the un in the ky. Angle are decribed in the following way: (ii) Longitude: Angular ditance meaured eat and wet of the prime meridian i longitude. (iii) Declination Angle (δ): Angle made by the line joining the center of the un and the earth with it projection on the equatorial plane, north poitive i declination angle. It i zero at the autumnal and vernal equinoxe, i at the ummer oltice on June 21 and at the winter oltice on December 21 in the northern hemiphere. The range of declination angle i given by δ According to Cooper [11], at the intervening period of the year δ can be approximated by a inuoidal variation (i) olar Altitude Angle (α ): It i the angle between the projection of the un' ray on the horizontal plane the un' reurrection of the un' ray. (ii) Zenith Angle (θ Z ): It i the angle between the ky' ray and a line perpendicular to the plane through the point. ere, θ Z + α = π/2. (iii) olar Azimuth Angle (γ ): It i the angular diplacement from the outh of the projection of beam radiation on the horizontal plane. Angle Incidence on a Plane: Angle decribing the poition of a urface in relation to the un' ray and the earth are defined in thi ection and decribed by the δ = 23.45in 360( n ) / 365 Fig. 3. a. lope of the urface β i the angle between the (iv) our Angle (ω): Angular diplacement of the un plane of the urface and the horizontal. eat or wet of the local meridian due to rotation of the b. urface azimuth angle γ i the angle made in the earth on it axi at 15 0 per hour i hour angle. It horizontal plane between the line due outh and expree the time of the day with repect to the olar formalojection of the formal to the urface of the noon. It can be expreed by ω = 15(t-12). horizontal plane. 752

3 c. Angle of incidence of radiation on a urface θ i the angle between the beam radiation on a urface and the normal to that urface. Attenuation of olar Radiation by Atmophere: olar radiation at normal incidence received at the urface of the earth i ubject to vary due to change in the extraterretrial radiation and to two additional more ignificant phenomena. Thee are a follow: * Atmopheric cattering by air molecule, water vapor and dut and * Atmopheric aborption by O 3, 2 O and CO 2. Atmopheric cattering by Air Molecule, Watervapor and Dut: Air molecule are very mall compared to the wavelength of radiation in a olar energy pectrum. Water vapor cattering depend on the amount of perceptible water and a cattering coefficient which alo be developed for water vapor that varie with λ 2, where λ i the wavelength of the radiation. Dut catter from particle thoe are much larger than air molecule and which vary in ize and concentration, location, height and time, thoe are more difficult to ae. The total effective cattering on the beam radiation i the product of the three exponential term, each i a function of wavelength (for air ma λ 4 and dut λ 0.75 ) and of the amount of molecule, dut and perceptible moiture through which the radiation i tranmitted. Atmopheric Aborption by O 3, 2 O and CO 2 : Aborption of radiation in the atmophere in the olar energy pectrum i due largely to ozone in ultraviolet and water vapor in band of the infrared. When the wavelength i below 0.29 micrometer, the radiation i almot completely aborbed by the atmophere. When wavelength varie from 0.29 to 0.35 micrometer, ozone aborption i decreaed provided that there i no aborption. There i alo a weak ozone aborption band near λ = micrometer. uggeted that there i a mall variation with different periodicitie and variation related to unpot activitie. Other conider the meaurement to be included or not indicative of regular variability. Uing Nimbu and Mariner atellite over the period of everal month, it i hown that the variation i within limit of 0.2% over a time when unpot activity i very low. Variation of Earth-un Ditance: Extraterretrial radiation depend on earth-un ditance and varie 3% throughout the year. The dependence of extraterretrial radiation on time of the year, developed by Duffie and Beckman [10], i indicated by the following Eq. 3: 360n E0 = Ic Co 365 (3) Where: E 0 = Extraterretrial radiation meaured on in the plane of the nth day of the year I c = olar contant Fig. 4: Flow Diagram of olar Radiation ytem Formulation of Mathematical Model: Figure 4 how the flow chart of the olar radiation ytem. Uing thi flow diagram, mathematical formulation have been preented here a a model for the olar radiation ytem. Variation of Extraterretrial Radiation: The variation of extraterretrial olar radiation with repect to time of the year i hown in Fig. 5. Two ource of variation are a follow. Variation in Radiation Emitted by the un: There are conflicting report in the literature on periodic Fig. 5: Variation of Extraterretrial Radiation with variation of intrinic olar radiation. It ha been Time (Month) 753

4 Extraterretrial Radiation on orizontal urface: The olar radiation outide the atmophere, that i, the hourly extraterretrial radiation incident on horizontal plane can be written by the following way [10] : 360n I = I Co Coθ c z where, θ z = Zenith angle of the un. (4) For a horizontal urface at any time between unrie and unet, according to Ref [17], the coine of zenith angle can be expreed by: Coθ = inδinφcoβ inδcoφinβcoγ z + CoγCoφCoβCoω + CoγinϕinβCoγCoω + Coinβinγinω (5) Conidering β = 0 and γ = 0, Eq. (5) can be rewritten a: Coθ Z = CoϕCoδCoω + inδinϕ (6) Combining Eq. (4) and (6), we have 360n I0 = Ic Co CoϕCoδCoω + inδinϕ 365 ( ) (7) The extraterretrial daily olar radiation on a horizontal urface can be obtained by integrating Eq. (7) over the period from unrie to unet. Uing ω = ω, we have: The original angtrom-type regreion Equation related monthly average daily radiation to clear day radiation at any location i a follow: g = a + b (10) c 0 Where: ω 0 = 2 15 g = Monthly average daily global radiation, c = Average clean ky daily radiation on a horizontal urface, = Mean monthly average daily unhine hour, 0 = Maximum poible unhine hour and a, b = Empirical contant. The monthly average of maximum poible daily hour of bright unhine can be computed from the above relation. In Eq. (10), there i intrumental problem and uncertaintie in the definition of a clear day. For thi reaon, Page [12] and other modified the method baed on extraterretrial radiation on a horizontal urface (obtained from Eq. (7), monthly daily average extraterretrial radiation), rather than on clear day radiation: g = a + b (11) n = + π o Ic Co 365 ( CoϕCoδCoω + inδinϕ) (8) uain [14] ha correlated thi Eq. (11) for weather data in Bangladeh a well a aider [13] and uain [14] reported the following angtrom-type regreion Equation for Bangladeh: Where: 0 = ω = Daily extraterretrial olar radiation on a horizontal urface, unet hour angle in degree. Let u conider, Coθ z = 0 and ω = ω. Uing Eq. (6), we have: CoϕCoδCoω + inδinϕ = 0 1 Therefore, ( ) ω = Co tan δ tan ϕ (9) g = (12) 0 0 Prediction of ourly Radiation from Daily Radiation Data: When hour-by-hour performance calculation are to be done, it may be neceary to tart with daily data and etimated hourly value of the daily number (hourly value and daily number). In an invetigation by Collre- Pereira and Rabl [15] developed an analytical expreion for the ratio of hourly to daily global radiation: Etimation of Average olar Radiation: Radiation data are the bet ource of information for etimation average incident radiation. Lacking of thee data from a nearby location of imilar climate like Bangladeh, it i poible to ue the empirical relationhip to etimate radiation from hour of unhine or cloudine. 754 Ih 24 g = π ( a + bco ω)(coω Coω ) ( 2πω Coω ) inω 360 The Coefficient a and b are defined by: (13)

5 a = in( ω 60), b = in( ω 60), Where, ω = hour angle in degree and ω = unet hour angle. Terretrial olar Radiation for Beam and Diffue Radiation: The correlation between hourly diffue and global radiation developed by Muneer et al. [16] can be expreed by the following way: Error! Bookmark not defined. when K T < Id 2 3 = KT K T KT Ih When 0.175<K T < Id = 0.26 When < K T I h Totalolar radiation on a horizontalurface where KT = Extraterretrialolar radiation on a that urface I = h I0 = Clearne index. We have, Beam radiation = ourly radiation Diffue radiation ρ= Diffue ground reflectance, ρ= 0.2 [16], ρ= 0. 7 of freh now covered countrie [16]. Liu and Jordan [17] ued the relation for ρ=0. 2 (1-c) +0.7c, Where, the c=fractional time of a month when the ground in covered in more than one inch of now. REULT AND DICUION In thi ection, the model wa imulated during 7 A.M. to 5 P.M. uing ytem dynamic methodology. The diffued olar radiation of the typical day 19 th Augut, hourly radiation on 4 th May, diffued radiation on 19 th January from horizontal urface are preented and compared with the meaurement reult [19]. The imulated and meaurement reult are hown in Fig Validation of imulated Reult: The model reult of hourly and diffued radiation on a horizontal urface for the ame above mentioned typical day are compared with the repective experimental data [19] and are hown in Fig Terretrial olar Radiation for Tilted urface: The hourly olar radiation on a tilted urface i given by conidering the radiation to be made up of three / component i.e. beam radiation I b, diffue olar / radiation I d and olar radiation diffuely reflected from the ground I [18] dg : / / i. e. I = I + I + I ere: T b d dg / / 1+ Coβ Ib = Ib + R b, Id = Id 2 And: Fig. 6: imulated and uain [18] Diffued olar Radiation on Aug. 19 for orizontal urface where a =0. 18 and b =0. 39 I (I + I ) ρ(1 Co β) 2 I = I R + I (1 + Co β) (1 Co β) + (I + I ) ρ 2 2 b d dg = i.e., T b b d b d Beam radiation on tilted urface where R b = Beam radiation on a horizontalurface inδin( ϕ β ) + CoδCoωCo( ϕ β) = inδinϕ + CoδCoωCoϕ =Geometric ratio or geometric factor Fig. 7: imulated and uain [18] ourly olar β= Angle between horizontal urface and collector Radiation on May 4 for orizontal urface urface, where a = and b =

6 Table 1: enitivity Analyi for Empirical Contant a =0. 14 b =0. 34 imulated uain [18] imulated uain [18] imulated uain [18] Table 2: enitivity Analyi for Empirical Contant a =0. 18 b =0. 39 imulated uain [18] imulated uain [18] imulated uain [18] Table 3: enitivity Analyi for Empirical Contant a =0. 15 b =0. 32 imulated uain [18] imulated uain [18] imulated uain [18] Table 4: enitivity Analyi for Empirical Contant a = b = imulated uain [18] imulated uain [18] imulated uain [18]

7 Table 5: enitivity Analyi for Empirical Contant a =0.175 b =0.375 imulated uain [18] imulated uain [18] imulated uain [18] Table 6: enitivity Analyi for Empirical Contant a =0. 14 b = imulated uain [18] imulated uain [18] imulated uain [18] Fig. 8: imulated and uain [18] Diffued olar Radiation on Jan. 19 for orizontal urface a =0. 15 and b =0. 32 reported value of [19] for the month of January, May and Augut hown in Fig. 6-8 for different et of parameter [a=0. 18 and b=0. 39, a= and b=0. 395, a= and b=0. 375, a=0. 15 and b=0. 32, a=0. 14 and b=0. 34 and a=0. 14, b=0. 345]. The enitivity analyi of the parameter i hown in Table 1-6. The bet agreement wa found between the imulated reult and experimental reult in the month of January, when a=0. 15 and b=0. 32, May, when a= and b= and Augut, when a=0. 18 and b= Therefore it i concluded that the radiation uually vary with the weather variation and the contant a and b will be varied accordingly. It i alo hown that the radiation depend on the other contant uch a diffue ground reflectance (ρ), ground to a collector angle (β) and range of latitude (φ). In cae of Bangladeh, ρ = 0.2, β = 24.5 and φ= / are ued here along with the above et value of a and b for model validation. Thi model i alo applicable to any other country with repect to availability of the aid parameter for the concerned country. The imulated radiation i higher than that of experimental meaured data due to intrumental error, the ambient air temperature, the thermal characteritic of the olar ytem and including the availability of olar energy. The agreement between imulated reult and Ref [19] found atifaction in the et 'a' = 0.18 and CONCLUION 'b' = 0.39 for Augut; 'a' = and 'b' = for May and 'a' =0. 15 and 'b' =0. 32 for January. The model for imulation of the olar radiation The value of empirical contant a and b in ytem i jutified for different et of parameter. The g model ha the bet relation with hourly and diffue Angtrom-type regreion equation = a + b are 0 radiation for clear unny day. The performance of the and 0.39 repectively reported by uain and model i found atifactory a well a ytem dynamic aider [13]. The imulated value are compared with the methodology i applicable to imulate the olar 757

8 radiation ytem. Bangladeh ha got ample olar inulation and ha the ame level of olar inulation throughout the country [17]. It can be tarted from above dicuion that the olar radiation in Bangladeh i maximum in April-May and minimum in December- January. Nomenclature: E 0 = Extraterretrial olar radiation I c = olar contant n = Day of the year δ = Declination angle (degree) I 0 = ourly extraterretrial olar radiation on a horizontal urface 0 = Daily extraterretrial olar radiation on a horizontal urface g = Monthly average daily global radiation on a horizontal urface c = Average clean ky daily radiation on a horizontal urface a, b = Contant in the drying rate equation φ = Latitude ω = our angle = Mean monthly average daily unhine hour 0 = Maximum poible unhine hour I b = Beam radiation on the horizontal urface I h = ourly olar radiation on a horizontal urface I d = ourly diffue radiation on a horizontal urface I T = ourly olar radiation on a tilted urface = Geometric factor or Geometric ratio. R b REFERENCE 1. adrul Ilam, A.K. M and D.G. Infield, Photovoltaic Technology in Bangladeh. Progreive Printer, Bangladeh. 2. Center for Renewable Energy ytem Technology, Loughborough Univerity, UK. 3. Forreter, J. W., World Dynamic. Boton, MA; Wright Allen Pre. 4. Forreter, J. W., Principle of ytem, MA; Wright Allen Pre. 5. Meadow, D.L., Dynamic of commodity cycle, MIT Cambridge, Ma. 6. Wadhawa, LC., A ytem dynamic laboratory for regional analyi. The Bicol River Bain Development, Ph. D. Thei. AIT, Thailand. 7. yeed, K., Rural development and ditribution: The cae of Pakitan. Ph.D. Thei MIT. 8. Alam, M.., Integrated modeling of a rural energy ytem: a ytem dynamic approach, Ph. D. Thei. Dhaka, Electrical and Electronic Engineering Department, BUET. 9. Alam, M.., A. Roy Chowdhury and K.K. Ilam, imulation of rural e1ectrification impact on ocioeconomic ytem of bang1adeh: A cae tudy, Chittagong, Bang1adeh. Paper Preented in 39 th Convention. 10. Duffie, J.A. and W.A. Beckman, olar Engineering on Thermal Proce. New York; Willey Intercience. 11. Cooper, P.I., The aborption of olar radiation in olar till. olar Energy, 12: Page, J.K., The etimation of monthly mean value of daily total hort radiation on vertical and inclined urface from unhine record for latitude 40 0 N-40 0 N. Proceeding of the U.N. Conference on New ource of Energy, 4: uain, M.A. and M.E. aider, Etimation of olar radiation from unhine hour in Dhaka, Bangladeh. Renewable Energy Rev. J., 3: uain, A., olar Radiation in Dhaka. Proceeding of eventh Miami International Conference on A1temative Energy ource, 9-12 Dec. 15. Collare-Pereira, M. and A. Rabl, The average ditribution of olar radiation correlation between diffue and hemipherical and between daily and hourly inulation value. olar Energy, 22: Muneer, T., M.M. awa K. ahili, Correlation between hourly, diffue and global radiation for New Delhi. Energy Conervation and Management, 24: Liu, B.Y.. and Jordan, R.C., Daily inulation on urface tilted toward the equator. ARAE Journal, 3 (10), 53, uain, A., olar radiation meaurement. Mechanical and Chemical Engineering Department, Dhaka, Ilamic Univerity of Bangladeh, (IUB) (Formerly IIT). 19. Bala, B.K., imulation of available olar energy in Bangladeh and computer imulation and optimal deign of indirect natural convention drying ytem, Reearch Report of EC potdoctoral fe11owhip, Department of Agricultural and Environmental cience, Univerity of Newcatle upon Tyne, UK,