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Mathematical Modeling of Solar Radiation incident on Tilted Surface for Photovoltaic Application at Bhopal, M.P, India a
b
K N Shukla , Saroj Rangnekar & K. Sudhakar a
b
Electrical &Electronics, Lakshmi Narain College of Technology, Bhopal-462021, India
b
Department of Energy, Maulana Azad National Institute of Technology, Bhopal-462051, India Accepted author version posted online: 27 Feb 2015.
Click for updates To cite this article: K N Shukla, Saroj Rangnekar & K. Sudhakar (2015): Mathematical Modeling of Solar Radiation incident on Tilted Surface for Photovoltaic Application at Bhopal, M.P, India, International Journal of Ambient Energy, DOI: 10.1080/01430750.2015.1023834 To link to this article: http://dx.doi.org/10.1080/01430750.2015.1023834
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Publisher: Taylor & Francis Journal: International Journal of Ambient Energy DOI: 10.1080/01430750.2015.1023834
Mathematical Modeling of Solar Radiation incident on Tilted Surface for Photovoltaic Application at Bhopal, M.P, India K N Shukla1*, Saroj Rangnekar2, K. Sudhakar3 Electrical &Electronics, Lakshmi Narain College of Technology, Bhopal-462021, India 2, 3 Department of Energy, Maulana Azad National Institute of Technology Bhopal-462051, India *Corresponding author: [email protected]
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Abstract In general, solar radiations are the combination of beam plus diffuse and ground reflected radiation. The availability of recorded data on tilted surface is very rare due to lake of measuring equipment and techniques involved. In this study a standard procedure is adopted for estimation of solar radiation on tilted surface for a location in Central region of India. Solar radiation is estimated for three tilted positions: First, solar collector tilt equal to latitude angle. Second, solar collector tilt equal to latitude angle +15° and Third, solar collector tilt at latitude -15°. Total global solar radiation estimated on the inclined surface for various PV modules was used to obtain the annual energy yield based on the estimated value. It was found that on an average, 14 kWh/m2 of annual energy output can be obtained for monocrystalline solar PV module corresponding to the inclination of 23.26° latitude at Bhopal.
1.
Introduction:
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Key words: Extraterrestrial radiation, Global radiation, tilted surface models, sunshine hour, clearness index, Bhopal.
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From the beginning of 19th century dwelling of fossil fuels is increasing continually toward the development industrialization and modern life style. The fossil fuels are being used for domestic to industrial applications on the cost of pollution, health hazards and ecology of earth. Excessive exploitation of conventional fuels directly and indirectly assist in global warming and many more factors which drive the planet towards dark future [1].
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To overcome the dependency on conventional fuels researchers and many organizations are working on alternative fuels, which should be commercially viable, easy to use, less pollutant and must be abundant in nature. In this direction renewable energies like solar energy tidal energy, wind energy, bio fuels and so forth are more suitable then conventional sources of energy. These non conventional forms are not only renewable but also maintain ecology and environment as they are eco friendly and do not contribute to global warming and production of green house gases and so forth [1,2]. Importance of renewable energy source in the world grows rapidly because of depletion of fossil fuel reserves, it is feared that the world will soon run out of its energy resource. This is matter of concern for the India and the developing countries whose economy heavily lean on its use of energy. Under the circumstances it is highly desirable that alternate energy resources should be utilized with maximum conversion efficiency to cope with the ever increasing energy demand [2].Currently renewable energy resources supply about 14% of total world energy demand and their future potential is remarkable [3].
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1
India is blessed with an abundance of nondepleting and environment friendly renewable energy resources. The central region of India, where solar energy and wind energy are profusely available throughout the year in comparison to the rest of India has higher potential to exploit renewable energies for domestic and industrial applications [1,3]. India is the only country in the world that has separate ministry of new and renewable energy (MNRE) earlier known as the ministry of non conventional energy source [1]. Among renewable source, solar energy is one of the most promising now days [2] and is predicted by numerous analyses to becomes the mostly used energy resources by 2050 [5]. Solar systems are practicable form of power supply where the grid connections are not available and the extension of power transmission lines is expensive [5]. However, their proper design and sizing is ultimately requires long term recorded data of solar radiation [6]. The local metrological measurements provide more perfect estimation, as compared observed thought satellites because it holds the site specific characteristics. Photovoltaic panels (and other solar system e.g. solar collectors) still have
weak efficiency and high cost of production and in order to enlarge their power production gain they are after placed in a tilted position [7]. E.g., authors in [8] use solar irradiance prediction (on a daily basis) to calculated the optimal positioning trajectory for photovoltaic panels in order to maximize their power production considering positioning system energy consumption. Recent development on PVs and thus to understand the importance of the overall output of PVs [9-13].
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Metrological stations usually measure global and diffuse solar irradiance received on horizontal surface. The availability of recorded data on tilted surface is very rare. Therefore the tilted surface radiation in most cases is calculated from horizontal surface radiation by means of empirical models [6, 7]. Although a large number of empirical models exist but they are validated using the data collected from the meteorological station of United Nation, Canada, Australia and northern European countries. Furthermore , the existing models were formulated based on different procedures using different elements [15].It is prime need to evaluate the models and verify their suitability according to the local environmental condition before application for the design and development of solar system. The purpose of this study is to estimate solar radiation on horizontal and tilted surface for Bhopal Madhya Pradesh in order to utilize the solar radiation for Photo Voltaic applications.
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Quantitative assessment of solar irradiance incident on tilted surface is very important to engineers who design advanced control and/or monitoring of power electronics convertors connected to photovoltaic panels or optimal tilt and azimuth angle positioning [8, 14]. The usage goes of course beyond photovoltaic system and applied to different system where input energy comes from sun. Tilted surface is important for system control, e.g., input solar irradiance on different outer building surfaces is very important for energy efficient control of indoor building climate.
2. Methodology: 2.1 Study location:
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On average, the temperatures are always high. Most rainfall is seen in June, July, August and September. It has dry periods in January, February, March April and December. The warmest month is May. The coolest month is December. The wettest month is August.
2.2 Solar Radiation on Horizontal Surface:
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2.2.1. Estimation of Monthly Average Daily Extraterrestrial solar radiation (Ho):
The monthly mean daily extraterrestrial solar radiation (Ho) on the horizontal surface is computed by taking the values of single day (closed to monthly mean values) for every month of the year by using days suggested by klein [34] which are representing the individual month. The proposed days were 17th of January and July, 16th of February, March and August, 15th of April, May, September, and October ,14th of November, 11th of June, and 10th of December[15,34]. The monthly average daily extraterrestrial solar radiation (Ho) on the horizontal surface is determined by the following empirical relationship. ISC× 3600(1 + 0.033 cos
)(
sin ∅ sin + cos ∅ cos sin
d
H O=
S
) kJ/m2-day
(1)
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Where, Isc is solar constant 1.367 kW/m2, N is day of the year (N=1 for 1st January and N=365 for 31st December), ωs is sunset hour angle for the mean day of the month (degrees), Φ is latitude angle (degrees) and δ is Declination angle (degrees).
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The declination angle (δ) can be mathematically presented by the Cooper’s (1969 equation δ =23.34sin
(284+N)
(2)
Where, N is the Nth day of the year starting from January as shown in Table 1
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The geographical location of the Bhopal City lies within North Latitude 23°16' and East Longitude 77°36'. The location of Bhopal falls in the north western portion of Madhya Pradesh. It seen in the Map of India, Bhopal occupies the central most region of the country. The total area of the city of Bhopal is 697 sq km and the total number of inhabitants roughly equals 30, 00,000 .The climate of Bhopal is subtropical, with hot and humid summer and a cool but dry winter. The average temperature during the day is around 30℃, whereas in the month of May, it rises to 40℃. Humidity always remains high during this time and hence the atmosphere remains sweaty. Monsoons usually start from June and last till September end. The total rainfall of the city does not exceed 1200 mm, accompanied by frequent thunderstorms and occasional floods. In brief about the Bhopal district:
The sunshine hour angle (ωs) for a location is a function of solar declination angle and the latitude [17] is given by ωs=cos (− tan
tan ∅ )
(3)
2.2.2. Estimation of Monthly average hourly extraterrestrial solar radiation (Io): Monthly average hourly extraterrestrial solar radiation on horizontal surface is estimated by the equation: Io= Isc× 3600 1 + 0.033 cos Where,
(sin ∅ sin + cos ∅ cos cos
) kJ/m2h
is hour angle and the other symbols have the same meaning as given earlier.
(4)
The hour angle is an angular measure of time and is equivalent to 15° per hour. It also varies from -180° to +180°. we adopt the convention of measuring it from noon based on local apparent time (LAT), being positive in the morning and negative in the afternoon. Local Apparent Time (LAT): The time used for calculating the hour angle ω is the local apparent time. This can be obtained from the standard time observed on a clock by applying two corrections: The first correction arises because of the difference between the longitude of the location and the meridian on which the standard time is based. The correction has a magnitude of 4 minutes for every degree difference in longitude. The second correction, called the equation of time (EOT) is due to the fact that the earths orbit and rate of rotation are subject to small variations [18]. Thus,
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Local Apparent Time (LAT) = standard time (clock time)±4( standard time longitude –longitude of location)+ Equation of time correction(EOT) (5)
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Equation of Time (EOT): Equation of time in Minutes can be calculated from the following empirical relations [19.] = 229.18(0.000075 + 0.001868 cos )
, N is the day of year
So, Hour angle = 15[12 −
− 0.014615 cos 2 − 0.04089 sin 2
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(
=
Where,
− 0.032077 sin
]
(6)
(7)
2.2.3 Estimation of Monthly average daily global solar radiation ( Hg):
+ (
)
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=
d
The monthly average daily global solar radiation on a horizontal surface Hg is given by the angstrom equation: [20] (8)
Where, S is monthly average daily hours of bright sunshine, Smax is monthly average of the maximum possible daily hours of bright sun shine i.e the day length on a horizontal surface (h) and a,b are constants known as angstrom constants and they are empirical and obtained by the fitting data.
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= 0.409 + 0.5016 sin(
= 0.6609 + 0.4767 sin(
− 60) − 60)
(9)
The value of constants a & b are given by Lof. et al. (1966) [21] for many cities of the world and by Modi and Sukhatme (1979) for many Indian cities. (Bhopal a =0.26, b = 0.5) [26]
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Negative sign, in first correction is applicable for the eastern hemisphere, while positive sign is applicable for the western hemisphere.
Gopinathan has also suggested the correlation [22]. = a1+b1(
)
(10)
Equation (10) based on the data of 40 locations around the world. The constants a1 and b1 are related to three parameters: The latitude, the elevation and the sunshine hours as follows:
a1 = -0.309+ 0.539cos ∅ − 0.0693EL +0.290(
)
b1 = 1.527-1.027cos ∅ + 0.0926EL-0.359(
)
(11)
Where, ∅ is latitude (in degrees) and EL is elevation of the location above mean sea level (in kilometers) Equation (11) is recommended for predicting the daily global radiation at locations all over the world including location in India. 2.2.4 Estimation of Monthly average hourly global solar radiation (Ig): A number of studies have also been conducted with the objective of obtaining relations for predicting the diurnal variation of the monthly average hourly global radiation at a location.
)
(12)
is hour angle both evaluated from equation (9) and (7)
Ig = Hg [
( +
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so
cos
cos )]
(13)
(
= =
Where,
+ 0.5 [
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Gueymard (1986) [24] modified equation (12) suggested by Collares – Pereira and Rabl [23] by incorporating a normalizing factor fc. Thus equation (12) becomes )
(14)
]
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Subsequently Gueymard [24]has reviewed a number of predictive models using a large data set for 135 locations and has concluded that equation (14) is the simplest and most satisfactory correlation for predicting monthly average hourly global radiation for sites all over the world with in latitude 65° N to 65° S. The rms difference ) ranged only between 2.6 and 5.5 percent for 13 of the 14 between the predicted and measured values of ( location. A significant difference of 10.4 percent was obtained only at one location. 2.2.5 Estimation of Monthly average daily diffuse radiation (Hd):
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Based on a study of data for a few countries, Liue and Jorden [25] showed that the daily diffuse- to- global radiation ratio could be correlated against the daily global- to- extraterrestrial radiation ratio. The correlation was expressed by the following cubic equation. = 1.390 − 4.027
+ 5.531(
)2 -3.108(
)3
(15)
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Where, a and b are constants,
( +
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=
t
Collares-Pereira and Rabl [23] have developed the following relation.
Where, Hd is Monthly average of the daily diffuse radiation on a horizontal surface (kJ /m2-day) the other symbols have the same meaning as given earlier. The ratio ( ) is often denoted by the symbol KT and is called the monthly average clearness index. As in the case of monthly average daily global radiation, many investigators have developed empirical equations for estimating the diffuse-to-global radiation ratio for various parts of the world. Gopinathan and Soler [22] examined radiation data for 40 widely spread locations all over the world in the latitude range 36° S to 36° N. They have proposed the following equation involving the clearness index and the sunshine ratio. = 0.87813 − 0.33280 KT -0.53039(
)
(16)
Equation (16) is based on more recent data then that available to Liu and Jordan [25] and is recommended for use for predicting the daily diffuse radiation at location across the world.
When available Indian data was analyzed, the following linear equation was obtained by Modi and Sukhatme. [26] = 1.411 − 1.696(
)
(17)
Garg and Garg [27] have examined radiation data for 11 Indian cities and proposed the equation = 0.8677 − 0.7365(
)
(18)
Equation (17) and (18) agree well with each other. Either one of the equation may be used for Indian locations
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2.2.6. Estimation of Monthly average hourly diffuse radiation (Id):
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In manner similar to that adopted for developing equation (12). Liue and Jorden [25] have suggested the following relation for estimating the monthly average hourly diffused radiations.
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(19)
=( ′+ Where ′
=0 .4922+ 0.27
′
cos
for 0.1≤
)
(20)
≤ 0.7
(21)
for 0.7 ≤
,
≤ 0.9
(22)
d
′ = 0.76+ 0.113
,
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Satyamurty and Lahiri [28] have also tested the prediction of equation (19) against the measured data for 14 locations in India. In this case relatively poor agreement is obtained, the rms difference between the predicted and measured values of ( ) ranging between 5.7 and 13.4%. Satyamurtiy and Lahiri [28] therefore suggested the following improved relation.
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and ′
= 2(1 − ′)(
.
)
(23)
2.3 Solar Radiation on the tilted Surface:
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2.3.1 Estimation of Monthly Average Daily Incident Solar Radiation (HT): The incident solar radiation on a tilted surface is the sum of the set of radiation streams including direct or beam radiation, the three components of diffused radiation from the sky, and the radiation reflected from the various surfaces seen by the tilted surface. The total incident solar radiation on the tilted surface (HT) can be written as in the following forms
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=
HT= HT,b + HT,d +HT,r
(24)
Where, HT is monthly total daily incident solar radiation, HT,b is beam radiation , HT,d is diffused radiation and HT,r is ground reflected radiation on tilted surface. Beam radiation on tilted surface is given by HT,b = Hb Rb Where, Hb is monthly average daily beam radiation on horizontal surface and Rb is the ratio of mean daily beam radiation on the tilted surface to that on horizontal.
,
Basically Rb is a function of transmittance of atmosphere, which is equal to ( ) and be determined by the following expression for the surface that are sloped towards the equator in the northern hemisphere or 180° in the southern hemisphere ( most favorable azimuth angle = 0, for collector of PV module ) [29] therefore the value of Rb is computed by (∅
=
Rb =
)
∅
Where, is declination angle, ∅ is Latitude angle, degrees)
(∅
)
(25)
∅
is inclination of tilted surface and
is the hour angle. (All is in
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HT,b= Hd,iso Rd +Hd,cs Rb + Hd,hzRhz
(26)
(
Rd = and Hd is Computed from equation (18) HT,d = Hd. Rd
)
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If the diffuse radiation is considered to be only isotropic. Then it is the ratio of diffuse on the tilted surface with slop ( ) to that on the horizontal surface denoted by Rd since
)
(27)
(28)
d
HT,d = Hd(
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Reflected Radiation is the part of total solar radiation that is reflected by the surface of the earth and by any other surface intercepting object such as trees, terrain or buildings on to a surface exposed to the sky is termed as ground reflected radiation or Albedo [6] so reflected radiation on tilted surface is
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HTr = Hr Rr
(29)
Where, Hr is monthly average daily reflected radiation on horizontal surface, Rr is the ratio of mean daily reflected radiation on the tilted surface to that on horizontal surface. Rr is given by
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Diffused radiation (Hd) is that fraction of total solar radiation which is received from the sun when its direction has been changed by atmospheric scattering [30].The direction of diffused radiation is highly variable and difficult to determine [31]. It is function of condition of cloudiness and atmospheric clearness which are extremely unpredictable. The diffused radiation fraction is also the combination of three components namely isotropic, circumsolar and horizon brightening [6].The isotropic diffuse radiation component is received evenly from the entire sky dome. The circumsolar diffuse part received from onward dispersion of solar radiation and concentrated in the section of the sky around the sun [32]. The horizon brightening component is concentrated near the horizon and it is most obvious in the clear skies [33]. In general the diffuse fraction of radiation on inclined surface is composed of isotropic, circumsolar and horizon brightening factors as given by:
Rr =
(
)
(30)
Where, is slop of tilted surface, is reflectivity of the surrounding in which the collector is located. Normally a value = 0.2 is taken in a condition that the mean monthly temperature is greater than 0℃ and the measuring station is located on a roof top with low reflectance. Its value could be taken as 0.7 if the temperature is less than 5℃[33]. Then total incident radiation on a tilted surface HT rewritten as HT = HbRb +Hd Rd +Hr Rr HT = Hb Rb + Hd (
) +Hr (
)
(31)
Liue and Jorden [25] have proposed that the ratio of daily radiation falling on tilted surface (HT) to the daily global radiation on a horizontal surface is given by = 1−
+
+
(32)
and Rr = (
Where, Rb is on the representative day, Rd =
).
Equation (32) can also be used for calculating the monthly average daily radiation falling on a tilted surface if the values required are calculated for the representative day of the month.
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2.3.2 Estimation of Monthly average hourly incident solar radiation (IT):
+
Where, Rb, Rd and Rr have the same meaning in equation (32)
(33)
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+
Equation (33) can also be used for calculating the monthly average hourly incident solar radiation (IT) if the calculations are the done for the representative day of the month.
3.1 Regression Constant for Bhopal
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3. Result and Discussion:
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Input parameters for estimation of solar radiation on horizontal surface and tilted surface are shown in Table 2. From this it is observed that declination angle ( ) varies according to the cooper’s model (1969), -23.04° (December solstice) and +23.08° (June solstice). Twice in year the value of declination angle becomes zero on two equinoxes (in March and September). Sunrise and sunset hour angle varies according to the latitude and both will be the same due to symmetry. For Bhopal location average sunshine hour angle (ωs) is observed approximately 87° which is very good for estimation of solar radiation in this location. From the same Table 2, it is found that percentage sunshine duration (s/smax) is about 79% thought the year. Employing these parameters the regression constant a and b are obtained from the angstrom equation [20] as a=0.27 and b=0.50 for Bhopal. 3.2 Variation of extraterrestrial solar radiation:
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Input parameters like declination angle δ, sunshine hour angle ωs and day length Smax are inserted in equation (1) and (4) to estimate the extraterrestrial solar radiation in daily basis and hourly basis (HO, IO) as shown in Fig.2 and Fig. 3. HO is observed to be maximum in May 39653.61kJ/m2-day and minimum in December 23919.78 kJ/m2-day. Similarly variation of solar radiation in hourly basis (Io) ranges from 3929.75 kJ/m2-h to 2593.21 kJ/m2-h. 3.3 Variation of global solar radiation for horizontal surface:
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= 1−
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Again according to Liue and Jorden [25] the ratio of flux falling on a tilted surface at any instant (IT) to that on horizontal surface (Ig) is given by an equation having a form similar to equation (32).
Global solar radiation on monthly average daily (Hg) and monthly average hourly (Ig) basis is estimated with the help of angstrom equation and regression constant for Bhopal (a=0.27 and b=0.50).Estimated value of Hg and Ig are compared with the HO and IO. It is found that Hg and Ig is lower than HO and IO. as shown in Fig 2 and Fig 3. With the help of Angstrom equation [20] and Collares-Pereira & Rabl correlation [23] ,monthly average daily global radiation Hg and monthly average hourly global radiation Ig are estimated as16022.33kJ/m2-day and 1414.00 kJ/m2-h as shown in Fig. 2 and Fig 3. 3.4 Variation of diffused solar radiation on horizontal surface: The diffused solar radiation based on Liue and Jorden [25] is commonly recommended for predicting daily diffused radiation at location across the world. However in Indian context Modi and Sukhtame [26], Garg and Garg [27] proposed the modified equation. Hence for estimation of monthly average hourly diffused radiation on daily basis Garg and Garg model is adopted in this study .From the estimated result it is seen that Hd is 5660.47 kJ/m2-day
which is 35% of total global radiation. Monthly average hourly diffused radiation Id is 40% above than monthly average hourly global radiation (Ig). That much availability of average hourly solar radiation is encouraging from utilization point of view as shown in Fig. 2 and Fig 3. 3.5 Sky Condition: Bhopal
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Clearness index is the parameter which indicates the transparency of the atmosphere and indicated by fraction of extraterrestrial radiation that reaches the earth surface as global solar radiation. It is measurement of the . From the estimated value of HO and Hg degree of clearness of the sky. Clearness Index KT is defined as KT = for Bhopal, KT is calculated and it is very encouraging to note that the sky over Bhopal is very clear almost throughout the year (KT >0.66) as shown in Fig 4. The transmission through atmosphere KT along with the diffused radiation and global radiation is shown in Fig. 4. The dip in the value of KT is accordance with the high value of Hd/Hg for the same month. The sky is fairly clear during winter months when the solar radiation is demand for utilization purpose for photovoltaic application. Empirical coefficients KT, and for Bhopal are shown in Table
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3.6 Variation of total solar radiation on tilted surface:
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Liu and Jorden model [25] is adopted for estimation of total solar radiation on the tilted surfaces, equal to latitude (23.26°), latitude +15(38.26°) and latitude-15(8.26°). Maximum daily average of monthly solar radiation available on the titled surface at Bhopal varies between 14461.23 kJ/m2-day to 26762.07 kJ/m2- day throughout the year as shown in Table 6.It is revealed from the results, that solar energy incident on tilted surface is more than on the horizontal surface due to low incident angle of solar radiation in these months. This model predicted less amount of radiation in good weather condition due to high angle of incidence of solar radiation. For various tilt angle, average daily and average hourly radiation obtained are as follows (a) = 23.26° HT(lat.)=22383.6 kJ/m2-daly and I(lat.)=1500 =38.26° ,H(lat.+15)=21875.6 kJ/m2-day and I(lat+15)=1565.78 kJ/m2-day (c) =8.26°, H(latkJ/m2-h, (b) 2 2 =22005.01kJ/m -day and I =1601.01kJ/m -day.These values are shown in Table 6. 15) (lat-15) 3.7 Variation in Annual energy output for various solar PV applications:
ce
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Annual energy output for various solar PV module for three titled collector positions: β= Latitude, β = Latitude +15 and β=Latitude -15 are shown in Table 5, 6 and 7. From these it is observed that for tilted angle = 23.26° monocrystalline solar cell yield 13.39kWh/m2 of annual energy output as compared to polycrystalline 11.90kWh/m2, amorphous 7.44kWh/m2 and thin film 8.41kWh/m2 . Similarly for tilted angle =38.26°, annual energy output for monocrystalline is expected to be 3.08 kW/m2 as compared to polycrystalline 11.63 kWh/m2 , amorphous 7.27 kWh/m2 and thin film 7.99 kWh/m2 and for tilted angle =8.26° annual energy output for monocrystalline is estimated as 13.16 kWh/m2 as compared to polycrystalline 11.70 kWh/m2 amorphous 7.31 kWh/m2 and thin film 8.04 kWh/m2. 4. Discussion:
Photovoltaic panel (and other solar system e.g. solar collectors) still has weak efficiency and high cost of production and in order to enlarge their power production gain they are after placed in a tilted position. Metrological stations usually measure global and diffuse solar irradiation received on horizontal surface. The availability of recorded data on tilted surface is very rare. Therefore the tilted surface radiation in most cases is calculated from horizontal surface radiation by means of empirical models.. Tilted surface is important for system control, e.g., input solar irradiation on different outer building surface is very important for energy efficiency control of indoor building climate . For estimation of diffused radiation in daily basis for horizontal surface in Indian context Modi and Sukhtame and Garg and Garg methods are in very good agreement where as Angstrom equation and Collares-Pereira and Rabl correlation adopted for calculation of monthly average daily global solar radiation. For estimation of total solar radiation on tilted surface Liu and Jorden model is utilized and found that solar collector tilted at latitudinal position got the sufficient radiation for solar photovoltaic applications. However the present work employing Angstrommodel and Liu and Jorden model and Garg and Garg model for global and diffused solar radiation for Bhopal serves the purpose very effectively.
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8
5. Conclusion:
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Mathematical study of the estimation of solar radiation in central part of the India, Bhopal for horizontal and tilted solar collector is carried out with considering different input parameters, inclination angle, sunshine hour and day length. Since no research regarding the potential of solar energy has been done prior to this work, this work will be very helpful to use this resource at Bhopal. For each type of module annual energy output is calculated and found that in all three tilted position Monocrysatlline PV can yield more output energy (aprox. 14 kW/m2) at latitudinal tilted position of solar collector at Bhopal. Linear and quadratics regression could be developed, if the measured data for the location under study is available . Estimated values of solar radiation on the tilted surface reveal that Bhopal, Madhya Pradesh, India can be very ideal location for utilization of solar energy efficiently. The estimated value of global and diffused radiation reveals that solar radiation can be very efficiently used for photo voltaic application to compensate for the energy deficit. The wind energy potential (3.42 m/s) average throughout the year is also encouraging at Bhopal location. Therefore a combination of solar and wind energy availability will be very helpful in future to use this tremendous amount of sunshine and high wind energy potential
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1. C.K Pandey and A.K Katiyar, “Solar Radiation Models and Measurement Techniques’ Review Article, Hindwai Publishing Corporation Journal of energy Vol, 2013 Article ID 305207. 2. M.A. Ahmed, Firoz Ahmed and M. Wasim Akhtar, “ Estimation of Global and Diffuse Solar Radiation for Hyderabad, Sindh, Pakistan” Journal of Basic and Applied Sciences Vol.5, NO2, PP 73-77,2009.
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3. E. Cuce and P.M. Cuce, “A Comparehnsive Review on Solar Cookers”. Applied Energy 2013; 102 1399-1421. 4. J.L Sawin, “Renewables 2013: Global status report” REN21 secretariat, 2013. 5. World in Transition: A Social Contract for Sustainability, “German Advisory Council on Global Change, 2011. 6. A. Q. Jakhrani, S. Raza Samo A.R.H Rigit and S.A. Kamboh, “Selection of Modeles for Calculation of Incident Solar Radiation on Tilted Surface.” World Applied Sciences Journal Vol.22, No9, PP.1334-1343, 2013.
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7. J.Kaldellis, K.Kavadias, and D.Zafirakis, “Experimental Validation of the Optimum Photo Voltaic Panels Tilt Angle for Remote Consumers” Renewable Energy”. Vol. 46, NO 0, PP. 179-191, October 2012 8. M.Gulin, M. Vasak, and Peric, “Dynamical Optimal Positioning of a Photo Voltaic Panel in all Weather Conditions.” Applied Energy, Vol.108, NO.0, PP. 429-438, August 2013.
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9. E. Cuce, PM Cuce and T. Bali, “An Experimental Enalysis of Elimination Intensity and Temperature Dependency of Photovoltaic Cell Parameters” Applied Energy 2013; 111:378-382. 10. PM Cuce and E. Cuce, comments on “Analytical Expression for Electrical Efficiency of PV/T Hybrid Collector.” By S. Dubey, G.S. Sandhu, and G.N. Tiwari. International Journal of Ambient Energy 2014; 11. E. Cuce and PM Cuce, “Improving Thermodynamic Performance Parameters of Silicon Photovoltaic Cells via Air Cooling.”International Journal of Ambient Energy 2014;
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12. E. Cuce, T. Bali and SA Sekucoglu, “Effect of Passive Cooling on Performance of Silicon Photovoltaic Cells.” International Journal of Low-Carbon Technologies 2011;6 (4):299-308. 13. P.M Cuce and E. Cuce, “A Novel Model of Photovoltaic Module for Parameters Estimation and Hermodynamic Assessment.” International Journal of Low-Carbon Technologies 2012;7 (2):159-165. 14. E.D Mehleri, P.L Zervas, H. Sarimveis, J.A. Palyvos, and N.C Markatos, “ Determination of the Optimal Tilt Angle and Orientation for Solar Photovoltaic Arrays,” Renewable Energy, vol. 35, NO11, PP. 2468-2475, November 2010.
15. A.Q Jakhrani, A.K Othman, ARH Rigit, S.R Samo and S.A Kamboh, “Life Cycle Cost Analysis of a Standalone PV System”. IEEE International Conference in Green and Ubiquitous Technology, 7-8 July 2012, Bandung, Indonesia. 16. A.Q. Jakhrani, A.K. Othman, A.R.H. Rigit, S.R. Samo and S.A Kamboh, “Estimation of Incident Solar Radiation on Tilted Surface by Different Empirical Models.”International Journal of Scientific and Research Publications, Vol. 2, Issue12, Dec. 2012. 17. C.S. Solanki “Solar Photo Voltaic Fundamental, Technologies and Applications” 2nd Edition PHI Learning Pvt. Ltd. New Delhi, PP 301, 2011.
19. M. Iqbal, An Introduction to Solar Radiation, Academic Press Canada, 1983.
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18. S.P Sukhatme and J.K Nayak, “Solar Energy Principles of Thermal Collection and Storage.” TMH Education Pvt.Ltd. New Delhi, 3rd Edition 2008, PP.87-88.
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21. G.O.G. Lof., J.A. Diffie and C.O.Smith “World Distribution of Solar Radiations” Solar Energy, vol.10, P P.27. 1966. 22. K.K. Gopinatan, and A. Soler, “Diffuse Radiation Models and Monthly Average Daily Diffuse Data for a Wide Latitude Range.” Energy 02:657, 1995.
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23. M. Collares –Pereira, and A. Rabl, “The Average Distribution of Solar Radiation Correlation Between Diffuse and Hemispherical and Between Daily and Hourly Insolation Values.” Solar Energy 22:155, 1979. 24. C. Gueymard, “Mean Daily Average of Beam Radiation Received by Tilted Surfaces as Affected by Atmosphere.” Solar Energy, 37:261, 1986.
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25. B.Y.H. Liu, R.C. Jordan, “The Interrelationship and Characteristics Distribution of Direct, Diffuse and Total Solar Radiation”, Solar Energy 7, 53-65, 1968.
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26. V. Modi,and S.P. Sukhatme , “Estimation of Daily Total and Diffuse Insolation in India for Weather Data” Solar Energy, vol. 22, PP.407, 1979. 27. H.P Garg and S.N Garg, “Correlation of Monthly Average Daily Global, Diffuse and Beam Radiation with Bright Sunshine Hours.” Energy Conservation and Management, 25: 409, 1985.
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28. V.V Satyamurty, and P.K Lahiri, “Estimation of Symmetric and Asymmetric Hourly Global and Diffuse Radiation from Daily Values, Solar Energy, 48:7, 1992. 29. F. Kreith, and D.Y Goswami, “Principles of Sustainable Energy”. Vol.46 CRC Press, Bola Raton., FL, USA, PP. 373-420, 2011.
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20. A. Angstrom, Solar and Terrestrial Radiation Q.J.T Met Soc, 50(1924), 121-126.
30. K.A.I Kondratev , “Radiation in the Atmosphere.” Academic Press.12:3-11, 1969. 31.Y.Q. Tian, R.J. Davies- colley, P. Gong and B.W. Thorrold “ Estimating Solar Radiation on Slopes of Arbitrary Aspect Agriculture for Meteorology,109:67-74. 32. J. Widen, “Distributed Photovoltaic in the Swedish Energy System. Model Development and Simulation.” Licentiate Thesis, Uppsala University Sweden, PP:1-89, 2009. 33. D. Robinson, and A. Stone, “solar radiation modeling in the Urban context.” Solar energy 77(3): 295-309, 2004. 34. S.A. Klein, “Calculation of Monthly Average Insolation on Tilted Surface” Solar Energy 19, 325, 1977.
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35. A. Martin, Green, Keith Emery,Y. Hishikawa and W. Warta, “Solar Cell Efficiency Tables (Version 37)” Prog. Photovolt: Res. April. 2011, 19, PP.84-92
16 14 12 10 S (h)
4
Smax (h)
2
S/Smax (%)
0
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Fig. 1 Input parameters S,Smax and S/SMAX for estimation of global solar radiation
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Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
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6
t
8
45000 40000 35000 30000
Ho (kJ/m2-day)
15000
Hg (kJ/m2-day)
10000
Hd (kJ/m2-day)
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20000
5000
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0
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Fig.2 Monthly average daily solar radiation (HO,Hg,Hd ) on horizontal surface at bhopal
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t
25000
4500 4000 3500 3000 2500 2000
Io (kJ/m2-h)
1500
Ig
1000
(kJ/m2-h)
Id (kJ/m2-h)
t
500
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Fig.3 Monthly average hourly solar radiation (IO ,Ig ,Id ) on horizontal surface at Bhopal.
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0
0.8 0.7 0.6 0.5 0.4
KT= Hg/Ho
0.3
Hd/Ho
0.2
Hd/Hg
0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
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t
0.1
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Fig.4 Monthly variation of clearness index KT=Hg/Ho, Hd/Ho and Hd/Hg at Bhopal.
Day of the year (N)
Jan.
17
17
Feb.
16
47
Mar.
16
75
Apri.
15
105
May
15
135
Jun.
11
162
Jul.
17
198
Aug.
16
228
Sept.
15
Oct.
15
Nov.
14
Dec.
10
258
288 318
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Day
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Month
t
Days on which extraterrestrial radiation is equal to monthly mean value. [34]
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Table:1
344
Table 2 Input parameters for estimation of monthly average daily global solar radiation at Bhopal, Madhya Pradesh, India.
Hours
Hours
80.59
10
10.24
0.8770
Feb.
-12.95 84.60
11
11.28
0.8351
Mar.
- 2.41
88.96
11
11.86
0.7942
Apr.
9.41
135.15
12
11.45
0.8227
May
18.79
98.39
13
Jun.
23.08
100.55
10
Jul.
21.18
80.41
5
Aug.
13.45
Sept.
2.21
Oct.
-9.59
Nov.
-18.91
Dec.
-23.04
13.11
0.7180
13.40
0.7062
10.72
0.8787
5
11.21
0.8403
89.07
8
11.87
0.7931
85.84
10
11.44
0.8263
81.53
9
10.87
0.8660
79.47
9
10.59
0.8895
d
84.10
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-20.81
%
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Jan.
Smax
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Degree Degree
S
t
ωs
Month
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δ
Table: 3 View factors, Rd and Rr for tilted surface at Bhopal, Madhya Pradesh, India Latitude ∅ =23.26°N
Ground Reflectivity =
=
0.9593
0.8926
0.00813
0.02148
View factor diffused
0.00104
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)
0.9948
t
For reflected radiation
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− 15
solar
radiation Rd=
Rr= (
=
rip
for
+ 15
= 0.2
Table: 4 Estimation Total solar radiations in Tilted Surface at Bhopal, Madhya Pradesh, India Latitude =23.26 =
Month
Rb
HT (lat.)
=
IT(lat)
kJ/m2-day
kJ/m2-h
Rb
+ 15
=
HT (lat.+15)
IT(lat +15)
kJ/m2-day
kJ/m2-h
Rb
− 15
HT (lat.-15) IT(lat.-15) kJ/m2-h
19950.39
1424.63
22995.21
1608.81
1.49
24638.46
1384.64
Feb.
1.24
23643.02
1634.77
1.29
24323.94
1661.97
1.10
21579.84
1519.46
Mar.
1.11
17397.30
1604.66
1.09
16970.73
1548.14
1.06
20541.52
1600.58
Apr.
0.99
15467.97
1519.40
0.91
14461.23
1427.74
1.02
15781.39
1556.72
May
0.92
23474.52
1560.56
0.78
21046.41
1418.89
0.98
24746.58
1635.06
Jun.
0.88
22929.41
1617.09
0.73
20199.40
1453.40
0.97
24569.21
1713.48
Jul.
0.89
20077.23
1716.04
0.75
17594.82
1521.32
0.98
21502.79
1827.22
Aug.
0.97
26296.93
1716.40
0.85
24014.22
1576.17
1.00
27205.80
1773.91
Sep.
1.06
24368.29
1656.27
1.01
23401.40
1585.69
1.04
24054.22
1647.62
Oct.
1.38
26379.02
1799.86
1.41
26762.07
1808.39
1.25
24440.96
1693.10
Nov.
1.33
22962.84
1601.74
1.44
24484.85
1714.71
1.14
20305.88
1443.77
Dec.
1.41
22605.17
1573.33
1.56
24610.23
1688.31
1.17
19381.62
1376.57
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1.37
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1.15
kJ/m2-day
Jan.
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Ground Reflectivity =0.2
Table 5: Energy Yield for Various Solar PV Applications at inclination Types of module
Maximum Conversion Annual Energy Input
Annual Energy Output
(kWh/m2)
(kWh/m2)
18
74.40
13.39
Polycrystalline
16
74.40
11.90
Amorphous
10
74.40
7.44
Thinfilm
11
74.40
8.14
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Monocrystalline
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Efficiency (%)
=Latitude
Table 6: Energy Yield for Various Solar PV Application at inclination Types of module
Maximum Conversion Annual Energy Input
Annual Energy Output
(kWh/m2)
(kWh/m2)
18
72.71
13.08
Polycrystalline
16
72.71
11.63
Amorphous
10
72.71
7.27
Thinfilm
11
72.71
7.99
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Monocrystalline
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Efficiency (%)
=Latitude +15
Table 7: Energy Yield for Various Solar PV Application at inclination Types of module
Maximum Conversion Annual Energy Input
Annual Energy Output
(kWh/m2)
(kWh/m2)
18
73.14
13.16
Polycrystalline
16
73.14
11.70
Amorphous
10
73.14
7.31
Thinfilm
11
73.14
8.04
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Monocrystalline
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Efficiency (%)
=Latitude -15
Table 8: Empirical Coefficients for Bhopal, Madhya Pradesh, India
0.1571
0.2217
Feb.
0.6871
0.1736
0.2526
Mar.
0.6671
0.2827
0.4238
April
0.5313
0.2560
0.4818
May
0.6290
0.2131
0.3388
Jun.
0.6213
0.2176
0.3502
Jul.
0.7093
0.1564
0.2205
Aug.
0.6901
0.1717
0.2488
Sep.
0.6667
0.1890
0.2825
Oct.
0.6815
0.1766
0.2591
0.1616
0.2298
0.7147
0.1519
0.2125
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d
Dec.
rip
0.7085
t
KT =
Jan.
Nov.
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Month
Table 9: Empirical Values of Extraterrestrial, Global and diffuse solar radiations Month
Ho
Io kJ/m2-h
kJ/m2-day
Ig kJ/m2-h
Hd kJ/m2-day
Id kJ/m2-h
25216.80
2745.85
17867.30
1295.94
3962.96
431.17
Feb.
29231.12
3129.31
20084.99
1432.01
5075.47
543.34
Mar.
24736.68
3533.40
16502.66
1569.92
6994.83
999.14
April
9471.15
3825.23
15660.26
1353.73
7545.14
979.32
May
39653.61
3929.75
24942.63
1646.26
8452.88
836.83
Jun.
40177.65
4194.10
24963.15
Jul.
30737.41
3917.10
21802.80
Aug.
39260.68
3849.54
27096.17
Sep.
35015.33
3626.074
23348.17
Oct.
30269.71
3238.78
Nov.
26066.38
2825.94 2593.21
pt e ce
rip
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8742.97
911.89
1850.47
4808.33
612.58
1769.42
6741.64
660.68
1610.20
6621.11
685.28
20629.81
1470.08
5345.80
571.46
18332.48
1323.66
4214.47
456.84
17096.88
1234.44
3634.51
393.98
M an
23919.78
1735.51
d
Dec.
t
Jan.
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kJ/m2-day
Hg
International Journal of Ambient Energy Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/taen20
Mathematical Modeling of Solar Radiation incident on Tilted Surface for Photovoltaic Application at Bhopal, M.P, India a
b
K N Shukla , Saroj Rangnekar & K. Sudhakar a
b
Electrical &Electronics, Lakshmi Narain College of Technology, Bhopal-462021, India
b
Department of Energy, Maulana Azad National Institute of Technology, Bhopal-462051, India Accepted author version posted online: 27 Feb 2015.
Click for updates To cite this article: K N Shukla, Saroj Rangnekar & K. Sudhakar (2015): Mathematical Modeling of Solar Radiation incident on Tilted Surface for Photovoltaic Application at Bhopal, M.P, India, International Journal of Ambient Energy, DOI: 10.1080/01430750.2015.1023834 To link to this article: http://dx.doi.org/10.1080/01430750.2015.1023834
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Publisher: Taylor & Francis Journal: International Journal of Ambient Energy DOI: 10.1080/01430750.2015.1023834
Mathematical Modeling of Solar Radiation incident on Tilted Surface for Photovoltaic Application at Bhopal, M.P, India K N Shukla1*, Saroj Rangnekar2, K. Sudhakar3 Electrical &Electronics, Lakshmi Narain College of Technology, Bhopal-462021, India 2, 3 Department of Energy, Maulana Azad National Institute of Technology Bhopal-462051, India *Corresponding author: [email protected]
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Abstract In general, solar radiations are the combination of beam plus diffuse and ground reflected radiation. The availability of recorded data on tilted surface is very rare due to lake of measuring equipment and techniques involved. In this study a standard procedure is adopted for estimation of solar radiation on tilted surface for a location in Central region of India. Solar radiation is estimated for three tilted positions: First, solar collector tilt equal to latitude angle. Second, solar collector tilt equal to latitude angle +15° and Third, solar collector tilt at latitude -15°. Total global solar radiation estimated on the inclined surface for various PV modules was used to obtain the annual energy yield based on the estimated value. It was found that on an average, 14 kWh/m2 of annual energy output can be obtained for monocrystalline solar PV module corresponding to the inclination of 23.26° latitude at Bhopal.
1.
Introduction:
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Key words: Extraterrestrial radiation, Global radiation, tilted surface models, sunshine hour, clearness index, Bhopal.
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From the beginning of 19th century dwelling of fossil fuels is increasing continually toward the development industrialization and modern life style. The fossil fuels are being used for domestic to industrial applications on the cost of pollution, health hazards and ecology of earth. Excessive exploitation of conventional fuels directly and indirectly assist in global warming and many more factors which drive the planet towards dark future [1].
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To overcome the dependency on conventional fuels researchers and many organizations are working on alternative fuels, which should be commercially viable, easy to use, less pollutant and must be abundant in nature. In this direction renewable energies like solar energy tidal energy, wind energy, bio fuels and so forth are more suitable then conventional sources of energy. These non conventional forms are not only renewable but also maintain ecology and environment as they are eco friendly and do not contribute to global warming and production of green house gases and so forth [1,2]. Importance of renewable energy source in the world grows rapidly because of depletion of fossil fuel reserves, it is feared that the world will soon run out of its energy resource. This is matter of concern for the India and the developing countries whose economy heavily lean on its use of energy. Under the circumstances it is highly desirable that alternate energy resources should be utilized with maximum conversion efficiency to cope with the ever increasing energy demand [2].Currently renewable energy resources supply about 14% of total world energy demand and their future potential is remarkable [3].
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1
India is blessed with an abundance of nondepleting and environment friendly renewable energy resources. The central region of India, where solar energy and wind energy are profusely available throughout the year in comparison to the rest of India has higher potential to exploit renewable energies for domestic and industrial applications [1,3]. India is the only country in the world that has separate ministry of new and renewable energy (MNRE) earlier known as the ministry of non conventional energy source [1]. Among renewable source, solar energy is one of the most promising now days [2] and is predicted by numerous analyses to becomes the mostly used energy resources by 2050 [5]. Solar systems are practicable form of power supply where the grid connections are not available and the extension of power transmission lines is expensive [5]. However, their proper design and sizing is ultimately requires long term recorded data of solar radiation [6]. The local metrological measurements provide more perfect estimation, as compared observed thought satellites because it holds the site specific characteristics. Photovoltaic panels (and other solar system e.g. solar collectors) still have
weak efficiency and high cost of production and in order to enlarge their power production gain they are after placed in a tilted position [7]. E.g., authors in [8] use solar irradiance prediction (on a daily basis) to calculated the optimal positioning trajectory for photovoltaic panels in order to maximize their power production considering positioning system energy consumption. Recent development on PVs and thus to understand the importance of the overall output of PVs [9-13].
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Metrological stations usually measure global and diffuse solar irradiance received on horizontal surface. The availability of recorded data on tilted surface is very rare. Therefore the tilted surface radiation in most cases is calculated from horizontal surface radiation by means of empirical models [6, 7]. Although a large number of empirical models exist but they are validated using the data collected from the meteorological station of United Nation, Canada, Australia and northern European countries. Furthermore , the existing models were formulated based on different procedures using different elements [15].It is prime need to evaluate the models and verify their suitability according to the local environmental condition before application for the design and development of solar system. The purpose of this study is to estimate solar radiation on horizontal and tilted surface for Bhopal Madhya Pradesh in order to utilize the solar radiation for Photo Voltaic applications.
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Quantitative assessment of solar irradiance incident on tilted surface is very important to engineers who design advanced control and/or monitoring of power electronics convertors connected to photovoltaic panels or optimal tilt and azimuth angle positioning [8, 14]. The usage goes of course beyond photovoltaic system and applied to different system where input energy comes from sun. Tilted surface is important for system control, e.g., input solar irradiance on different outer building surfaces is very important for energy efficient control of indoor building climate.
2. Methodology: 2.1 Study location:
t
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On average, the temperatures are always high. Most rainfall is seen in June, July, August and September. It has dry periods in January, February, March April and December. The warmest month is May. The coolest month is December. The wettest month is August.
2.2 Solar Radiation on Horizontal Surface:
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2.2.1. Estimation of Monthly Average Daily Extraterrestrial solar radiation (Ho):
The monthly mean daily extraterrestrial solar radiation (Ho) on the horizontal surface is computed by taking the values of single day (closed to monthly mean values) for every month of the year by using days suggested by klein [34] which are representing the individual month. The proposed days were 17th of January and July, 16th of February, March and August, 15th of April, May, September, and October ,14th of November, 11th of June, and 10th of December[15,34]. The monthly average daily extraterrestrial solar radiation (Ho) on the horizontal surface is determined by the following empirical relationship. ISC× 3600(1 + 0.033 cos
)(
sin ∅ sin + cos ∅ cos sin
d
H O=
S
) kJ/m2-day
(1)
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Where, Isc is solar constant 1.367 kW/m2, N is day of the year (N=1 for 1st January and N=365 for 31st December), ωs is sunset hour angle for the mean day of the month (degrees), Φ is latitude angle (degrees) and δ is Declination angle (degrees).
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The declination angle (δ) can be mathematically presented by the Cooper’s (1969 equation δ =23.34sin
(284+N)
(2)
Where, N is the Nth day of the year starting from January as shown in Table 1
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The geographical location of the Bhopal City lies within North Latitude 23°16' and East Longitude 77°36'. The location of Bhopal falls in the north western portion of Madhya Pradesh. It seen in the Map of India, Bhopal occupies the central most region of the country. The total area of the city of Bhopal is 697 sq km and the total number of inhabitants roughly equals 30, 00,000 .The climate of Bhopal is subtropical, with hot and humid summer and a cool but dry winter. The average temperature during the day is around 30℃, whereas in the month of May, it rises to 40℃. Humidity always remains high during this time and hence the atmosphere remains sweaty. Monsoons usually start from June and last till September end. The total rainfall of the city does not exceed 1200 mm, accompanied by frequent thunderstorms and occasional floods. In brief about the Bhopal district:
The sunshine hour angle (ωs) for a location is a function of solar declination angle and the latitude [17] is given by ωs=cos (− tan
tan ∅ )
(3)
2.2.2. Estimation of Monthly average hourly extraterrestrial solar radiation (Io): Monthly average hourly extraterrestrial solar radiation on horizontal surface is estimated by the equation: Io= Isc× 3600 1 + 0.033 cos Where,
(sin ∅ sin + cos ∅ cos cos
) kJ/m2h
is hour angle and the other symbols have the same meaning as given earlier.
(4)
The hour angle is an angular measure of time and is equivalent to 15° per hour. It also varies from -180° to +180°. we adopt the convention of measuring it from noon based on local apparent time (LAT), being positive in the morning and negative in the afternoon. Local Apparent Time (LAT): The time used for calculating the hour angle ω is the local apparent time. This can be obtained from the standard time observed on a clock by applying two corrections: The first correction arises because of the difference between the longitude of the location and the meridian on which the standard time is based. The correction has a magnitude of 4 minutes for every degree difference in longitude. The second correction, called the equation of time (EOT) is due to the fact that the earths orbit and rate of rotation are subject to small variations [18]. Thus,
rip
t
Local Apparent Time (LAT) = standard time (clock time)±4( standard time longitude –longitude of location)+ Equation of time correction(EOT) (5)
us c
Equation of Time (EOT): Equation of time in Minutes can be calculated from the following empirical relations [19.] = 229.18(0.000075 + 0.001868 cos )
, N is the day of year
So, Hour angle = 15[12 −
− 0.014615 cos 2 − 0.04089 sin 2
M an
(
=
Where,
− 0.032077 sin
]
(6)
(7)
2.2.3 Estimation of Monthly average daily global solar radiation ( Hg):
+ (
)
pt e
=
d
The monthly average daily global solar radiation on a horizontal surface Hg is given by the angstrom equation: [20] (8)
Where, S is monthly average daily hours of bright sunshine, Smax is monthly average of the maximum possible daily hours of bright sun shine i.e the day length on a horizontal surface (h) and a,b are constants known as angstrom constants and they are empirical and obtained by the fitting data.
ce
= 0.409 + 0.5016 sin(
= 0.6609 + 0.4767 sin(
− 60) − 60)
(9)
The value of constants a & b are given by Lof. et al. (1966) [21] for many cities of the world and by Modi and Sukhatme (1979) for many Indian cities. (Bhopal a =0.26, b = 0.5) [26]
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Negative sign, in first correction is applicable for the eastern hemisphere, while positive sign is applicable for the western hemisphere.
Gopinathan has also suggested the correlation [22]. = a1+b1(
)
(10)
Equation (10) based on the data of 40 locations around the world. The constants a1 and b1 are related to three parameters: The latitude, the elevation and the sunshine hours as follows:
a1 = -0.309+ 0.539cos ∅ − 0.0693EL +0.290(
)
b1 = 1.527-1.027cos ∅ + 0.0926EL-0.359(
)
(11)
Where, ∅ is latitude (in degrees) and EL is elevation of the location above mean sea level (in kilometers) Equation (11) is recommended for predicting the daily global radiation at locations all over the world including location in India. 2.2.4 Estimation of Monthly average hourly global solar radiation (Ig): A number of studies have also been conducted with the objective of obtaining relations for predicting the diurnal variation of the monthly average hourly global radiation at a location.
)
(12)
is hour angle both evaluated from equation (9) and (7)
Ig = Hg [
( +
us c
so
cos
cos )]
(13)
(
= =
Where,
+ 0.5 [
M an
Gueymard (1986) [24] modified equation (12) suggested by Collares – Pereira and Rabl [23] by incorporating a normalizing factor fc. Thus equation (12) becomes )
(14)
]
pt e
d
Subsequently Gueymard [24]has reviewed a number of predictive models using a large data set for 135 locations and has concluded that equation (14) is the simplest and most satisfactory correlation for predicting monthly average hourly global radiation for sites all over the world with in latitude 65° N to 65° S. The rms difference ) ranged only between 2.6 and 5.5 percent for 13 of the 14 between the predicted and measured values of ( location. A significant difference of 10.4 percent was obtained only at one location. 2.2.5 Estimation of Monthly average daily diffuse radiation (Hd):
ce
Based on a study of data for a few countries, Liue and Jorden [25] showed that the daily diffuse- to- global radiation ratio could be correlated against the daily global- to- extraterrestrial radiation ratio. The correlation was expressed by the following cubic equation. = 1.390 − 4.027
+ 5.531(
)2 -3.108(
)3
(15)
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Where, a and b are constants,
( +
rip
=
t
Collares-Pereira and Rabl [23] have developed the following relation.
Where, Hd is Monthly average of the daily diffuse radiation on a horizontal surface (kJ /m2-day) the other symbols have the same meaning as given earlier. The ratio ( ) is often denoted by the symbol KT and is called the monthly average clearness index. As in the case of monthly average daily global radiation, many investigators have developed empirical equations for estimating the diffuse-to-global radiation ratio for various parts of the world. Gopinathan and Soler [22] examined radiation data for 40 widely spread locations all over the world in the latitude range 36° S to 36° N. They have proposed the following equation involving the clearness index and the sunshine ratio. = 0.87813 − 0.33280 KT -0.53039(
)
(16)
Equation (16) is based on more recent data then that available to Liu and Jordan [25] and is recommended for use for predicting the daily diffuse radiation at location across the world.
When available Indian data was analyzed, the following linear equation was obtained by Modi and Sukhatme. [26] = 1.411 − 1.696(
)
(17)
Garg and Garg [27] have examined radiation data for 11 Indian cities and proposed the equation = 0.8677 − 0.7365(
)
(18)
Equation (17) and (18) agree well with each other. Either one of the equation may be used for Indian locations
t
2.2.6. Estimation of Monthly average hourly diffuse radiation (Id):
rip
In manner similar to that adopted for developing equation (12). Liue and Jorden [25] have suggested the following relation for estimating the monthly average hourly diffused radiations.
us c
(19)
=( ′+ Where ′
=0 .4922+ 0.27
′
cos
for 0.1≤
)
(20)
≤ 0.7
(21)
for 0.7 ≤
,
≤ 0.9
(22)
d
′ = 0.76+ 0.113
,
M an
Satyamurty and Lahiri [28] have also tested the prediction of equation (19) against the measured data for 14 locations in India. In this case relatively poor agreement is obtained, the rms difference between the predicted and measured values of ( ) ranging between 5.7 and 13.4%. Satyamurtiy and Lahiri [28] therefore suggested the following improved relation.
pt e
and ′
= 2(1 − ′)(
.
)
(23)
2.3 Solar Radiation on the tilted Surface:
ce
2.3.1 Estimation of Monthly Average Daily Incident Solar Radiation (HT): The incident solar radiation on a tilted surface is the sum of the set of radiation streams including direct or beam radiation, the three components of diffused radiation from the sky, and the radiation reflected from the various surfaces seen by the tilted surface. The total incident solar radiation on the tilted surface (HT) can be written as in the following forms
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=
HT= HT,b + HT,d +HT,r
(24)
Where, HT is monthly total daily incident solar radiation, HT,b is beam radiation , HT,d is diffused radiation and HT,r is ground reflected radiation on tilted surface. Beam radiation on tilted surface is given by HT,b = Hb Rb Where, Hb is monthly average daily beam radiation on horizontal surface and Rb is the ratio of mean daily beam radiation on the tilted surface to that on horizontal.
,
Basically Rb is a function of transmittance of atmosphere, which is equal to ( ) and be determined by the following expression for the surface that are sloped towards the equator in the northern hemisphere or 180° in the southern hemisphere ( most favorable azimuth angle = 0, for collector of PV module ) [29] therefore the value of Rb is computed by (∅
=
Rb =
)
∅
Where, is declination angle, ∅ is Latitude angle, degrees)
(∅
)
(25)
∅
is inclination of tilted surface and
is the hour angle. (All is in
rip
us c
HT,b= Hd,iso Rd +Hd,cs Rb + Hd,hzRhz
(26)
(
Rd = and Hd is Computed from equation (18) HT,d = Hd. Rd
)
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If the diffuse radiation is considered to be only isotropic. Then it is the ratio of diffuse on the tilted surface with slop ( ) to that on the horizontal surface denoted by Rd since
)
(27)
(28)
d
HT,d = Hd(
pt e
Reflected Radiation is the part of total solar radiation that is reflected by the surface of the earth and by any other surface intercepting object such as trees, terrain or buildings on to a surface exposed to the sky is termed as ground reflected radiation or Albedo [6] so reflected radiation on tilted surface is
ce
HTr = Hr Rr
(29)
Where, Hr is monthly average daily reflected radiation on horizontal surface, Rr is the ratio of mean daily reflected radiation on the tilted surface to that on horizontal surface. Rr is given by
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t
Diffused radiation (Hd) is that fraction of total solar radiation which is received from the sun when its direction has been changed by atmospheric scattering [30].The direction of diffused radiation is highly variable and difficult to determine [31]. It is function of condition of cloudiness and atmospheric clearness which are extremely unpredictable. The diffused radiation fraction is also the combination of three components namely isotropic, circumsolar and horizon brightening [6].The isotropic diffuse radiation component is received evenly from the entire sky dome. The circumsolar diffuse part received from onward dispersion of solar radiation and concentrated in the section of the sky around the sun [32]. The horizon brightening component is concentrated near the horizon and it is most obvious in the clear skies [33]. In general the diffuse fraction of radiation on inclined surface is composed of isotropic, circumsolar and horizon brightening factors as given by:
Rr =
(
)
(30)
Where, is slop of tilted surface, is reflectivity of the surrounding in which the collector is located. Normally a value = 0.2 is taken in a condition that the mean monthly temperature is greater than 0℃ and the measuring station is located on a roof top with low reflectance. Its value could be taken as 0.7 if the temperature is less than 5℃[33]. Then total incident radiation on a tilted surface HT rewritten as HT = HbRb +Hd Rd +Hr Rr HT = Hb Rb + Hd (
) +Hr (
)
(31)
Liue and Jorden [25] have proposed that the ratio of daily radiation falling on tilted surface (HT) to the daily global radiation on a horizontal surface is given by = 1−
+
+
(32)
and Rr = (
Where, Rb is on the representative day, Rd =
).
Equation (32) can also be used for calculating the monthly average daily radiation falling on a tilted surface if the values required are calculated for the representative day of the month.
t
2.3.2 Estimation of Monthly average hourly incident solar radiation (IT):
+
Where, Rb, Rd and Rr have the same meaning in equation (32)
(33)
us c
+
Equation (33) can also be used for calculating the monthly average hourly incident solar radiation (IT) if the calculations are the done for the representative day of the month.
3.1 Regression Constant for Bhopal
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3. Result and Discussion:
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d
Input parameters for estimation of solar radiation on horizontal surface and tilted surface are shown in Table 2. From this it is observed that declination angle ( ) varies according to the cooper’s model (1969), -23.04° (December solstice) and +23.08° (June solstice). Twice in year the value of declination angle becomes zero on two equinoxes (in March and September). Sunrise and sunset hour angle varies according to the latitude and both will be the same due to symmetry. For Bhopal location average sunshine hour angle (ωs) is observed approximately 87° which is very good for estimation of solar radiation in this location. From the same Table 2, it is found that percentage sunshine duration (s/smax) is about 79% thought the year. Employing these parameters the regression constant a and b are obtained from the angstrom equation [20] as a=0.27 and b=0.50 for Bhopal. 3.2 Variation of extraterrestrial solar radiation:
ce
Input parameters like declination angle δ, sunshine hour angle ωs and day length Smax are inserted in equation (1) and (4) to estimate the extraterrestrial solar radiation in daily basis and hourly basis (HO, IO) as shown in Fig.2 and Fig. 3. HO is observed to be maximum in May 39653.61kJ/m2-day and minimum in December 23919.78 kJ/m2-day. Similarly variation of solar radiation in hourly basis (Io) ranges from 3929.75 kJ/m2-h to 2593.21 kJ/m2-h. 3.3 Variation of global solar radiation for horizontal surface:
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= 1−
rip
Again according to Liue and Jorden [25] the ratio of flux falling on a tilted surface at any instant (IT) to that on horizontal surface (Ig) is given by an equation having a form similar to equation (32).
Global solar radiation on monthly average daily (Hg) and monthly average hourly (Ig) basis is estimated with the help of angstrom equation and regression constant for Bhopal (a=0.27 and b=0.50).Estimated value of Hg and Ig are compared with the HO and IO. It is found that Hg and Ig is lower than HO and IO. as shown in Fig 2 and Fig 3. With the help of Angstrom equation [20] and Collares-Pereira & Rabl correlation [23] ,monthly average daily global radiation Hg and monthly average hourly global radiation Ig are estimated as16022.33kJ/m2-day and 1414.00 kJ/m2-h as shown in Fig. 2 and Fig 3. 3.4 Variation of diffused solar radiation on horizontal surface: The diffused solar radiation based on Liue and Jorden [25] is commonly recommended for predicting daily diffused radiation at location across the world. However in Indian context Modi and Sukhtame [26], Garg and Garg [27] proposed the modified equation. Hence for estimation of monthly average hourly diffused radiation on daily basis Garg and Garg model is adopted in this study .From the estimated result it is seen that Hd is 5660.47 kJ/m2-day
which is 35% of total global radiation. Monthly average hourly diffused radiation Id is 40% above than monthly average hourly global radiation (Ig). That much availability of average hourly solar radiation is encouraging from utilization point of view as shown in Fig. 2 and Fig 3. 3.5 Sky Condition: Bhopal
rip
t
Clearness index is the parameter which indicates the transparency of the atmosphere and indicated by fraction of extraterrestrial radiation that reaches the earth surface as global solar radiation. It is measurement of the . From the estimated value of HO and Hg degree of clearness of the sky. Clearness Index KT is defined as KT = for Bhopal, KT is calculated and it is very encouraging to note that the sky over Bhopal is very clear almost throughout the year (KT >0.66) as shown in Fig 4. The transmission through atmosphere KT along with the diffused radiation and global radiation is shown in Fig. 4. The dip in the value of KT is accordance with the high value of Hd/Hg for the same month. The sky is fairly clear during winter months when the solar radiation is demand for utilization purpose for photovoltaic application. Empirical coefficients KT, and for Bhopal are shown in Table
us c
3.6 Variation of total solar radiation on tilted surface:
M an
Liu and Jorden model [25] is adopted for estimation of total solar radiation on the tilted surfaces, equal to latitude (23.26°), latitude +15(38.26°) and latitude-15(8.26°). Maximum daily average of monthly solar radiation available on the titled surface at Bhopal varies between 14461.23 kJ/m2-day to 26762.07 kJ/m2- day throughout the year as shown in Table 6.It is revealed from the results, that solar energy incident on tilted surface is more than on the horizontal surface due to low incident angle of solar radiation in these months. This model predicted less amount of radiation in good weather condition due to high angle of incidence of solar radiation. For various tilt angle, average daily and average hourly radiation obtained are as follows (a) = 23.26° HT(lat.)=22383.6 kJ/m2-daly and I(lat.)=1500 =38.26° ,H(lat.+15)=21875.6 kJ/m2-day and I(lat+15)=1565.78 kJ/m2-day (c) =8.26°, H(latkJ/m2-h, (b) 2 2 =22005.01kJ/m -day and I =1601.01kJ/m -day.These values are shown in Table 6. 15) (lat-15) 3.7 Variation in Annual energy output for various solar PV applications:
ce
pt e
d
Annual energy output for various solar PV module for three titled collector positions: β= Latitude, β = Latitude +15 and β=Latitude -15 are shown in Table 5, 6 and 7. From these it is observed that for tilted angle = 23.26° monocrystalline solar cell yield 13.39kWh/m2 of annual energy output as compared to polycrystalline 11.90kWh/m2, amorphous 7.44kWh/m2 and thin film 8.41kWh/m2 . Similarly for tilted angle =38.26°, annual energy output for monocrystalline is expected to be 3.08 kW/m2 as compared to polycrystalline 11.63 kWh/m2 , amorphous 7.27 kWh/m2 and thin film 7.99 kWh/m2 and for tilted angle =8.26° annual energy output for monocrystalline is estimated as 13.16 kWh/m2 as compared to polycrystalline 11.70 kWh/m2 amorphous 7.31 kWh/m2 and thin film 8.04 kWh/m2. 4. Discussion:
Photovoltaic panel (and other solar system e.g. solar collectors) still has weak efficiency and high cost of production and in order to enlarge their power production gain they are after placed in a tilted position. Metrological stations usually measure global and diffuse solar irradiation received on horizontal surface. The availability of recorded data on tilted surface is very rare. Therefore the tilted surface radiation in most cases is calculated from horizontal surface radiation by means of empirical models.. Tilted surface is important for system control, e.g., input solar irradiation on different outer building surface is very important for energy efficiency control of indoor building climate . For estimation of diffused radiation in daily basis for horizontal surface in Indian context Modi and Sukhtame and Garg and Garg methods are in very good agreement where as Angstrom equation and Collares-Pereira and Rabl correlation adopted for calculation of monthly average daily global solar radiation. For estimation of total solar radiation on tilted surface Liu and Jorden model is utilized and found that solar collector tilted at latitudinal position got the sufficient radiation for solar photovoltaic applications. However the present work employing Angstrommodel and Liu and Jorden model and Garg and Garg model for global and diffused solar radiation for Bhopal serves the purpose very effectively.
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8
5. Conclusion:
rip
t
Mathematical study of the estimation of solar radiation in central part of the India, Bhopal for horizontal and tilted solar collector is carried out with considering different input parameters, inclination angle, sunshine hour and day length. Since no research regarding the potential of solar energy has been done prior to this work, this work will be very helpful to use this resource at Bhopal. For each type of module annual energy output is calculated and found that in all three tilted position Monocrysatlline PV can yield more output energy (aprox. 14 kW/m2) at latitudinal tilted position of solar collector at Bhopal. Linear and quadratics regression could be developed, if the measured data for the location under study is available . Estimated values of solar radiation on the tilted surface reveal that Bhopal, Madhya Pradesh, India can be very ideal location for utilization of solar energy efficiently. The estimated value of global and diffused radiation reveals that solar radiation can be very efficiently used for photo voltaic application to compensate for the energy deficit. The wind energy potential (3.42 m/s) average throughout the year is also encouraging at Bhopal location. Therefore a combination of solar and wind energy availability will be very helpful in future to use this tremendous amount of sunshine and high wind energy potential
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1. C.K Pandey and A.K Katiyar, “Solar Radiation Models and Measurement Techniques’ Review Article, Hindwai Publishing Corporation Journal of energy Vol, 2013 Article ID 305207. 2. M.A. Ahmed, Firoz Ahmed and M. Wasim Akhtar, “ Estimation of Global and Diffuse Solar Radiation for Hyderabad, Sindh, Pakistan” Journal of Basic and Applied Sciences Vol.5, NO2, PP 73-77,2009.
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3. E. Cuce and P.M. Cuce, “A Comparehnsive Review on Solar Cookers”. Applied Energy 2013; 102 1399-1421. 4. J.L Sawin, “Renewables 2013: Global status report” REN21 secretariat, 2013. 5. World in Transition: A Social Contract for Sustainability, “German Advisory Council on Global Change, 2011. 6. A. Q. Jakhrani, S. Raza Samo A.R.H Rigit and S.A. Kamboh, “Selection of Modeles for Calculation of Incident Solar Radiation on Tilted Surface.” World Applied Sciences Journal Vol.22, No9, PP.1334-1343, 2013.
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d
7. J.Kaldellis, K.Kavadias, and D.Zafirakis, “Experimental Validation of the Optimum Photo Voltaic Panels Tilt Angle for Remote Consumers” Renewable Energy”. Vol. 46, NO 0, PP. 179-191, October 2012 8. M.Gulin, M. Vasak, and Peric, “Dynamical Optimal Positioning of a Photo Voltaic Panel in all Weather Conditions.” Applied Energy, Vol.108, NO.0, PP. 429-438, August 2013.
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9. E. Cuce, PM Cuce and T. Bali, “An Experimental Enalysis of Elimination Intensity and Temperature Dependency of Photovoltaic Cell Parameters” Applied Energy 2013; 111:378-382. 10. PM Cuce and E. Cuce, comments on “Analytical Expression for Electrical Efficiency of PV/T Hybrid Collector.” By S. Dubey, G.S. Sandhu, and G.N. Tiwari. International Journal of Ambient Energy 2014; 11. E. Cuce and PM Cuce, “Improving Thermodynamic Performance Parameters of Silicon Photovoltaic Cells via Air Cooling.”International Journal of Ambient Energy 2014;
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References:
12. E. Cuce, T. Bali and SA Sekucoglu, “Effect of Passive Cooling on Performance of Silicon Photovoltaic Cells.” International Journal of Low-Carbon Technologies 2011;6 (4):299-308. 13. P.M Cuce and E. Cuce, “A Novel Model of Photovoltaic Module for Parameters Estimation and Hermodynamic Assessment.” International Journal of Low-Carbon Technologies 2012;7 (2):159-165. 14. E.D Mehleri, P.L Zervas, H. Sarimveis, J.A. Palyvos, and N.C Markatos, “ Determination of the Optimal Tilt Angle and Orientation for Solar Photovoltaic Arrays,” Renewable Energy, vol. 35, NO11, PP. 2468-2475, November 2010.
15. A.Q Jakhrani, A.K Othman, ARH Rigit, S.R Samo and S.A Kamboh, “Life Cycle Cost Analysis of a Standalone PV System”. IEEE International Conference in Green and Ubiquitous Technology, 7-8 July 2012, Bandung, Indonesia. 16. A.Q. Jakhrani, A.K. Othman, A.R.H. Rigit, S.R. Samo and S.A Kamboh, “Estimation of Incident Solar Radiation on Tilted Surface by Different Empirical Models.”International Journal of Scientific and Research Publications, Vol. 2, Issue12, Dec. 2012. 17. C.S. Solanki “Solar Photo Voltaic Fundamental, Technologies and Applications” 2nd Edition PHI Learning Pvt. Ltd. New Delhi, PP 301, 2011.
19. M. Iqbal, An Introduction to Solar Radiation, Academic Press Canada, 1983.
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18. S.P Sukhatme and J.K Nayak, “Solar Energy Principles of Thermal Collection and Storage.” TMH Education Pvt.Ltd. New Delhi, 3rd Edition 2008, PP.87-88.
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21. G.O.G. Lof., J.A. Diffie and C.O.Smith “World Distribution of Solar Radiations” Solar Energy, vol.10, P P.27. 1966. 22. K.K. Gopinatan, and A. Soler, “Diffuse Radiation Models and Monthly Average Daily Diffuse Data for a Wide Latitude Range.” Energy 02:657, 1995.
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23. M. Collares –Pereira, and A. Rabl, “The Average Distribution of Solar Radiation Correlation Between Diffuse and Hemispherical and Between Daily and Hourly Insolation Values.” Solar Energy 22:155, 1979. 24. C. Gueymard, “Mean Daily Average of Beam Radiation Received by Tilted Surfaces as Affected by Atmosphere.” Solar Energy, 37:261, 1986.
d
25. B.Y.H. Liu, R.C. Jordan, “The Interrelationship and Characteristics Distribution of Direct, Diffuse and Total Solar Radiation”, Solar Energy 7, 53-65, 1968.
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26. V. Modi,and S.P. Sukhatme , “Estimation of Daily Total and Diffuse Insolation in India for Weather Data” Solar Energy, vol. 22, PP.407, 1979. 27. H.P Garg and S.N Garg, “Correlation of Monthly Average Daily Global, Diffuse and Beam Radiation with Bright Sunshine Hours.” Energy Conservation and Management, 25: 409, 1985.
ce
28. V.V Satyamurty, and P.K Lahiri, “Estimation of Symmetric and Asymmetric Hourly Global and Diffuse Radiation from Daily Values, Solar Energy, 48:7, 1992. 29. F. Kreith, and D.Y Goswami, “Principles of Sustainable Energy”. Vol.46 CRC Press, Bola Raton., FL, USA, PP. 373-420, 2011.
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20. A. Angstrom, Solar and Terrestrial Radiation Q.J.T Met Soc, 50(1924), 121-126.
30. K.A.I Kondratev , “Radiation in the Atmosphere.” Academic Press.12:3-11, 1969. 31.Y.Q. Tian, R.J. Davies- colley, P. Gong and B.W. Thorrold “ Estimating Solar Radiation on Slopes of Arbitrary Aspect Agriculture for Meteorology,109:67-74. 32. J. Widen, “Distributed Photovoltaic in the Swedish Energy System. Model Development and Simulation.” Licentiate Thesis, Uppsala University Sweden, PP:1-89, 2009. 33. D. Robinson, and A. Stone, “solar radiation modeling in the Urban context.” Solar energy 77(3): 295-309, 2004. 34. S.A. Klein, “Calculation of Monthly Average Insolation on Tilted Surface” Solar Energy 19, 325, 1977.
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35. A. Martin, Green, Keith Emery,Y. Hishikawa and W. Warta, “Solar Cell Efficiency Tables (Version 37)” Prog. Photovolt: Res. April. 2011, 19, PP.84-92
16 14 12 10 S (h)
4
Smax (h)
2
S/Smax (%)
0
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d
M an
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Fig. 1 Input parameters S,Smax and S/SMAX for estimation of global solar radiation
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Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
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6
t
8
45000 40000 35000 30000
Ho (kJ/m2-day)
15000
Hg (kJ/m2-day)
10000
Hd (kJ/m2-day)
rip
20000
5000
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0
ce
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d
M an
Fig.2 Monthly average daily solar radiation (HO,Hg,Hd ) on horizontal surface at bhopal
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t
25000
4500 4000 3500 3000 2500 2000
Io (kJ/m2-h)
1500
Ig
1000
(kJ/m2-h)
Id (kJ/m2-h)
t
500
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ce
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M an
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Fig.3 Monthly average hourly solar radiation (IO ,Ig ,Id ) on horizontal surface at Bhopal.
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0
0.8 0.7 0.6 0.5 0.4
KT= Hg/Ho
0.3
Hd/Ho
0.2
Hd/Hg
0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
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t
0.1
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Fig.4 Monthly variation of clearness index KT=Hg/Ho, Hd/Ho and Hd/Hg at Bhopal.
Day of the year (N)
Jan.
17
17
Feb.
16
47
Mar.
16
75
Apri.
15
105
May
15
135
Jun.
11
162
Jul.
17
198
Aug.
16
228
Sept.
15
Oct.
15
Nov.
14
Dec.
10
258
288 318
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Day
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Month
t
Days on which extraterrestrial radiation is equal to monthly mean value. [34]
Ac
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Table:1
344
Table 2 Input parameters for estimation of monthly average daily global solar radiation at Bhopal, Madhya Pradesh, India.
Hours
Hours
80.59
10
10.24
0.8770
Feb.
-12.95 84.60
11
11.28
0.8351
Mar.
- 2.41
88.96
11
11.86
0.7942
Apr.
9.41
135.15
12
11.45
0.8227
May
18.79
98.39
13
Jun.
23.08
100.55
10
Jul.
21.18
80.41
5
Aug.
13.45
Sept.
2.21
Oct.
-9.59
Nov.
-18.91
Dec.
-23.04
13.11
0.7180
13.40
0.7062
10.72
0.8787
5
11.21
0.8403
89.07
8
11.87
0.7931
85.84
10
11.44
0.8263
81.53
9
10.87
0.8660
79.47
9
10.59
0.8895
d
84.10
pt e ce
rip
-20.81
%
us c
Jan.
Smax
M an
Degree Degree
S
t
ωs
Month
Ac
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δ
Table: 3 View factors, Rd and Rr for tilted surface at Bhopal, Madhya Pradesh, India Latitude ∅ =23.26°N
Ground Reflectivity =
=
0.9593
0.8926
0.00813
0.02148
View factor diffused
0.00104
Ac
ce
pt e
d
M an
us c
)
0.9948
t
For reflected radiation
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− 15
solar
radiation Rd=
Rr= (
=
rip
for
+ 15
= 0.2
Table: 4 Estimation Total solar radiations in Tilted Surface at Bhopal, Madhya Pradesh, India Latitude =23.26 =
Month
Rb
HT (lat.)
=
IT(lat)
kJ/m2-day
kJ/m2-h
Rb
+ 15
=
HT (lat.+15)
IT(lat +15)
kJ/m2-day
kJ/m2-h
Rb
− 15
HT (lat.-15) IT(lat.-15) kJ/m2-h
19950.39
1424.63
22995.21
1608.81
1.49
24638.46
1384.64
Feb.
1.24
23643.02
1634.77
1.29
24323.94
1661.97
1.10
21579.84
1519.46
Mar.
1.11
17397.30
1604.66
1.09
16970.73
1548.14
1.06
20541.52
1600.58
Apr.
0.99
15467.97
1519.40
0.91
14461.23
1427.74
1.02
15781.39
1556.72
May
0.92
23474.52
1560.56
0.78
21046.41
1418.89
0.98
24746.58
1635.06
Jun.
0.88
22929.41
1617.09
0.73
20199.40
1453.40
0.97
24569.21
1713.48
Jul.
0.89
20077.23
1716.04
0.75
17594.82
1521.32
0.98
21502.79
1827.22
Aug.
0.97
26296.93
1716.40
0.85
24014.22
1576.17
1.00
27205.80
1773.91
Sep.
1.06
24368.29
1656.27
1.01
23401.40
1585.69
1.04
24054.22
1647.62
Oct.
1.38
26379.02
1799.86
1.41
26762.07
1808.39
1.25
24440.96
1693.10
Nov.
1.33
22962.84
1601.74
1.44
24484.85
1714.71
1.14
20305.88
1443.77
Dec.
1.41
22605.17
1573.33
1.56
24610.23
1688.31
1.17
19381.62
1376.57
rip
us c
M an
d
pt e
t
1.37
ce
1.15
kJ/m2-day
Jan.
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Ground Reflectivity =0.2
Table 5: Energy Yield for Various Solar PV Applications at inclination Types of module
Maximum Conversion Annual Energy Input
Annual Energy Output
(kWh/m2)
(kWh/m2)
18
74.40
13.39
Polycrystalline
16
74.40
11.90
Amorphous
10
74.40
7.44
Thinfilm
11
74.40
8.14
ce
pt e
d
M an
us c
rip
t
Monocrystalline
Ac
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Efficiency (%)
=Latitude
Table 6: Energy Yield for Various Solar PV Application at inclination Types of module
Maximum Conversion Annual Energy Input
Annual Energy Output
(kWh/m2)
(kWh/m2)
18
72.71
13.08
Polycrystalline
16
72.71
11.63
Amorphous
10
72.71
7.27
Thinfilm
11
72.71
7.99
ce
pt e
d
M an
us c
rip
t
Monocrystalline
Ac
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Efficiency (%)
=Latitude +15
Table 7: Energy Yield for Various Solar PV Application at inclination Types of module
Maximum Conversion Annual Energy Input
Annual Energy Output
(kWh/m2)
(kWh/m2)
18
73.14
13.16
Polycrystalline
16
73.14
11.70
Amorphous
10
73.14
7.31
Thinfilm
11
73.14
8.04
ce
pt e
d
M an
us c
rip
t
Monocrystalline
Ac
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Efficiency (%)
=Latitude -15
Table 8: Empirical Coefficients for Bhopal, Madhya Pradesh, India
0.1571
0.2217
Feb.
0.6871
0.1736
0.2526
Mar.
0.6671
0.2827
0.4238
April
0.5313
0.2560
0.4818
May
0.6290
0.2131
0.3388
Jun.
0.6213
0.2176
0.3502
Jul.
0.7093
0.1564
0.2205
Aug.
0.6901
0.1717
0.2488
Sep.
0.6667
0.1890
0.2825
Oct.
0.6815
0.1766
0.2591
0.1616
0.2298
0.7147
0.1519
0.2125
pt e ce
us c
M an 0.7032
d
Dec.
rip
0.7085
t
KT =
Jan.
Nov.
Ac
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Month
Table 9: Empirical Values of Extraterrestrial, Global and diffuse solar radiations Month
Ho
Io kJ/m2-h
kJ/m2-day
Ig kJ/m2-h
Hd kJ/m2-day
Id kJ/m2-h
25216.80
2745.85
17867.30
1295.94
3962.96
431.17
Feb.
29231.12
3129.31
20084.99
1432.01
5075.47
543.34
Mar.
24736.68
3533.40
16502.66
1569.92
6994.83
999.14
April
9471.15
3825.23
15660.26
1353.73
7545.14
979.32
May
39653.61
3929.75
24942.63
1646.26
8452.88
836.83
Jun.
40177.65
4194.10
24963.15
Jul.
30737.41
3917.10
21802.80
Aug.
39260.68
3849.54
27096.17
Sep.
35015.33
3626.074
23348.17
Oct.
30269.71
3238.78
Nov.
26066.38
2825.94 2593.21
pt e ce
rip
us c
8742.97
911.89
1850.47
4808.33
612.58
1769.42
6741.64
660.68
1610.20
6621.11
685.28
20629.81
1470.08
5345.80
571.46
18332.48
1323.66
4214.47
456.84
17096.88
1234.44
3634.51
393.98
M an
23919.78
1735.51
d
Dec.
t
Jan.
Ac
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kJ/m2-day
Hg