Research Article Exergy, Energy, and Dynamic Parameter...
13
Hindawi Publishing Corporation International Journal of Photoenergy Volume 2013, Article ID 929235, 12 pages http://dx.doi.org/10.1155/2013/929235 Research Article Exergy, Energy, and Dynamic Parameter Analysis of Indigenously Developed Low-Concentration Photovoltaic System Pankaj Yadav, 1 Brijesh Tripathi, 1,2 and Manoj Kumar 2 1 School of Solar Energy, Pandit Deendayal Petroleum University, Gandhinagar 382007, India 2 School of Technology, Pandit Deendayal Petroleum University, Gandhinagar 382007, India Correspondence should be addressed to Manoj Kumar; [email protected] Received 29 May 2013; Revised 26 July 2013; Accepted 11 August 2013 Academic Editor: Mahmoud M. El-Nahass Copyright © 2013 Pankaj Yadav et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Piecewise linear parabolic trough collector (PLPTC) is designed and developed to concentrate solar radiation on monocrystalline silicon based photovoltaic module. A theoretical model is used to perform electrical energy and exergy analysis of low-concentration photovoltaic (LCPV) system working under actual test conditions (ATC). e exergy efficiency of LCPV system is in the range from 5.1% to 4.82% with increasing rate of input exergy rate from 30.81W to 96.12W, when concentration ratio changes from 1.85 to 5.17 Sun. Short-circuit current shows increasing trend with increasing input exergy rate of ≈0.011 A/W. Power conversion efficiency decreases from 7.07 to 5.66%, and open-circuit voltage decreases from 9.86 to 8.24V with temperature coefficient of voltage ≈ −0.021 V/K under ATC. e results confirm that the commercially available silicon solar PV module performs satisfactorily under low concentration. 1. Introduction Silicon based solar photovoltaic (PV) technology is emerging as a potential renewable energy source for future power requirements. ere are several ways by which the cost of this technology can be reduced, for example, improv- ing the efficiency, efficient light trapping, using thinner wafer, thin-film silicon technology, concentrator photovoltaic (CPV) technology, and so forth. In CPV, compared to nonconcentrating solar PV systems, the required area for solar PV module is reduced by the factor of concentration ratio, providing significant reduction in the overall cost of solar PV system. e considerable amount of research is going on in the field of CPV systems with different optics (mirrors or lenses—Fresnel or anidolic), spot sizes and geometries, tracking strategies, cooling systems (active or passive), and cells (Si or III–V compound semiconductors, whether single or multi-junction) [1, 2]. Composite split- spectrum concentrator solar cell having efficiency of forty- three per cent has been reported at laboratory level [3]. e III–V compound based multi-junction solar cells are quite expensive [4], and for bringing them to commercial level, it needs a geometrical concentration ratio (CR) of greater than 500. Generally, the higher the concentration ratio, the greater the accuracy needed in tracking the Sun and the smaller the manufacturing and installation tolerances permitted. is means that high efficiency and high concentration concepts need very accurate systems, including their manufacture, installation, and Sun tracking which increases their cost. In the beginning of this decade, Sala et al. [5] and Aminox Inc. [6] have shown that the efficiency of silicon based photovoltaic system increases with concentration ratio wherein they show that the optimum performance for silicon solar cells lies near to five Sun to extract maximum power. An industrialization potential of silicon based concentrator photovoltaic system with an estimated cost of $0.5/ is reported by Castro et al. [7], where the group uses back contact solar cells under 100 Sun. A detailed review of mod- eling in relation to low-concentration solar concentrating photovoltaic is presented by Zahedi [8]. Li et al. have studied the performance of solar cell array based on a trough concen- trating photovoltaic/thermal system [9]. Recently, Schuetz
Transcript of Research Article Exergy, Energy, and Dynamic Parameter...
Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2013 Article ID 929235 12 pageshttpdxdoiorg1011552013929235
Research ArticleExergy Energy and Dynamic Parameter Analysis ofIndigenously Developed Low-Concentration PhotovoltaicSystem
Pankaj Yadav1 Brijesh Tripathi12 and Manoj Kumar2
1 School of Solar Energy Pandit Deendayal Petroleum University Gandhinagar 382007 India2 School of Technology Pandit Deendayal Petroleum University Gandhinagar 382007 India
Correspondence should be addressed to Manoj Kumar manojkspvgmailcom
Received 29 May 2013 Revised 26 July 2013 Accepted 11 August 2013
Academic Editor Mahmoud M El-Nahass
Copyright copy 2013 Pankaj Yadav et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Piecewise linear parabolic trough collector (PLPTC) is designed and developed to concentrate solar radiation on monocrystallinesilicon based photovoltaicmoduleA theoreticalmodel is used to performelectrical energy and exergy analysis of low-concentrationphotovoltaic (LCPV) systemworking under actual test conditions (ATC)The exergy efficiency of LCPV system is in the range from51 to 482 with increasing rate of input exergy rate from 3081W to 9612W when concentration ratio changes from 185 to517 Sun Short-circuit current shows increasing trend with increasing input exergy rate of asymp0011 AW Power conversion efficiencydecreases from 707 to 566 and open-circuit voltage decreases from 986 to 824V with temperature coefficient of voltage asymp
minus0021VK under ATCThe results confirm that the commercially available silicon solar PV module performs satisfactorily underlow concentration
1 Introduction
Silicon based solar photovoltaic (PV) technology is emergingas a potential renewable energy source for future powerrequirements There are several ways by which the costof this technology can be reduced for example improv-ing the efficiency efficient light trapping using thinnerwafer thin-film silicon technology concentrator photovoltaic(CPV) technology and so forth In CPV compared tononconcentrating solar PV systems the required area forsolar PV module is reduced by the factor of concentrationratio providing significant reduction in the overall cost ofsolar PV system The considerable amount of research isgoing on in the field of CPV systems with different optics(mirrors or lensesmdashFresnel or anidolic) spot sizes andgeometries tracking strategies cooling systems (active orpassive) and cells (Si or IIIndashV compound semiconductorswhether single or multi-junction) [1 2] Composite split-spectrum concentrator solar cell having efficiency of forty-three per cent has been reported at laboratory level [3] TheIIIndashV compound based multi-junction solar cells are quite
expensive [4] and for bringing them to commercial level itneeds a geometrical concentration ratio (CR) of greater than500 Generally the higher the concentration ratio the greaterthe accuracy needed in tracking the Sun and the smallerthemanufacturing and installation tolerances permittedThismeans that high efficiency and high concentration conceptsneed very accurate systems including their manufactureinstallation and Sun tracking which increases their cost
In the beginning of this decade Sala et al [5] andAminox Inc [6] have shown that the efficiency of siliconbased photovoltaic system increases with concentration ratiowherein they show that the optimum performance for siliconsolar cells lies near to five Sun to extract maximum powerAn industrialization potential of silicon based concentratorphotovoltaic system with an estimated cost of $05119882119901 isreported by Castro et al [7] where the group uses backcontact solar cells under 100 Sun A detailed review of mod-eling in relation to low-concentration solar concentratingphotovoltaic is presented by Zahedi [8] Li et al have studiedthe performance of solar cell array based on a trough concen-trating photovoltaicthermal system [9] Recently Schuetz
2 International Journal of Photoenergy
et al [10] have reported design and construction of sim7timeslow-concentration PV system based on compound parabolicconcentrators
Despite all these progresses of the LCPV system thistechnology is unable to get market share among existing PVtechnologies that is monocrystalline Si flat panel and thin-film technologies Low-concentration photovoltaic technol-ogy has been limited due to requirement of special solarcell design perfect concentration geometry and insufficientanalysis of various issues such as exergy thermalizationlosses junction temperature and recombination processesTo surmount such issues in depth understanding of depen-dence of solar cell design parameters on CR and temperaturebetter design of concentration systems and proper systemperformance evaluation is required For LCPV systems suchimportant aspects have been scarcely addressed in detail sofar to the best of our knowledge
Keeping in view the above-mentioned shortfalls we havethe (i) the design and development of linear piecewiseparabolic trough for LCPV application and (ii) presented atheoretical model to perform exergy energy and dynamicbehavior analysis of LCPV system In this paper actualclimatic conditions are taken as reference state
2 Theoretical Modeling
21 Design and Modeling of PLPTC In this section designof piecewise linear parabolic trough collector (PLPTC) ispresented The parabola is designed in such a way thatmaximum energy and exergy can be extracted from theLCPV system A schematic diagram of PLPTC is shownin Figure 1 The design of PLPTC depends on receiverrsquosgeometry acceptance angle subtended by the receiver withparabolic reflector and desired geometric concentration
The level of concentration is restricted by the designparameters which include rim angle (0119903) acceptance angle(120579119888) and effective entrance aperture area (width119882times length119871) In this section theoretical model of a PLPTC withgeometrical CR sim8 Sun is presented [11]
The actual concentration ratio is calculated by
CR = 180 lowast (
sin 0119903 minus sin 120579119888 cos (0119903 minus 120579119888)
120587 (0119903 + 90 minus 120579119888) sin 120579119888) (1)
The amount of light received by solar PVmodule depends onthe reflectivity of mirrors used in the LCPV system
The line of focus for PLPTC can be located using thefollowing
119865 =
119882
2
16119863
(2)
Using focal length and the depth of parabola the rim angle iscalculated from the following
cos 0119903 = (
2119865
radic(05119882)
2+ (119863 minus 119865)
2
)minus 1 (3)
120579c
D
W
Parabolicreflector
Inci
dent
radi
atio
ns
Solarmodule
FocusRmin
0r
Figure 1 Basic geometry of parabolic trough concentrator
For the condition of 119865 = 119863 in (3) the rim angle becomesequal to 90∘ and the receivermakesminimum intercept anglewith radiation reflected from PLPTC The relation between119877min and the acceptance angle is given by
sin 120579119888 =119877min (1 + cos 0119903)
2119865
(4)
The receiver with the width of 119877min (equal to 32 cm in thiscase) is able to intercept all the radiation comingwith an angle20119903 From these equations it is established that the CR can bechanged by changing the effective aperture area of PLPTCIn developed PLPTC the numbers of reflecting mirrors arevaried from 2 to 8 to change the effective exit aperture areawhich gives desirable geometrical CR (sim2 to 8 Sun)
22 Thermodynamic Analysis for Exergetic Calculations Thelaws of thermodynamics are applied for the electrical exergyand energy analysis of LCPV system Energy conservationand energy quantity are generally analyzed by using the firstlaw of thermodynamics Exergy analysis which deals withavailability of energy in the system nature of irreversibilityand quality of energy is presented using the second law ofthermodynamics Exergymeasures not only quantity but alsothe quality of energy which is not conserved but rather isin part destroyed or lost Thermodynamic analysis for theelectrical output of LCPV system is performed using themethod described by many researchers [12ndash15]
The magnitude of the energy rate on the focal plane ofPLPTC (where crystalline solar PV module is placed) can beexpressed as [16]
119876119891 = 120587119891
2[sin2 (120601rim) minus sin2 (120601119904)] 120588mirror119866119887 (5)
where 120588mirror represents the reflectivity of mirror 120601119904 rep-resents the shading angle and 119866119887 represents direct beamsolar radiation on parabola aperture The energy rate
119876119891represents energy flow per unit time at which solar energyreaches the front glass of LCPVmodule The energy received
International Journal of Photoenergy 3
at front glass of LCPV module undergoes radiative andconvective losses which can be expressed in terms of heat losscoefficient 119880119892 (measured in terms of WK) [16]
119880119892 = 119880con + 119880rad (6)
After considering these heat losses the energy rate on thefront glass of LCPV module
119876119892 can be expressed as
119876119892 =
119876119891 minus 119880119892 (119879119892 minus 119879amb) (7)
Since the thickness of the glass is very small the conductionheat loss coefficient could be ignored for further calculationsThe incoming energy rate to LCPV module
119876in is given as
119876in =
119876119892120591 (8)
where 120591 represents transmission coefficient of front glass ofLCPV module
The output energy rate of LCPV module 119876out is calcu-
lated using the following expression [15]
119876out =
119876el + 119876th = 119881OC119868SC +
119876th (9)
where 119876el represents electrical output energy rate and
119876threpresents thermal output energy rate respectively Theenergy efficiency of LCPV system can be defined as theratio of output energy rate to the input energy rate Adetailed calculation of LCPV modulersquos electrical power con-version efficiency starting with terminal equation is given inSection 23
Similar expression for output exergy rate of LCPV systemis given as [15]
119864119909out =
119864119909el + 119864119909th +
119864119909des (10)
where 119864119909des =
119864119909desel + 119864119909desopt +
119864119909desΔ119879sun +
119864119909desΔ119879mod
which includes electrical exergy destruction rate (
119864119909desel)caused by series and shunt resistance losses [15] opticalexergy destruction rate (
119864119909desopt) caused by optical losses inLCPV module surface [17 18] thermal exergy destructionrate (
119864119909desΔ119879sun) caused by temperature difference between
LCPV module surface and the sun surface temperature [17ndash20] and thermal exergy destruction rate (
119864119909desΔ119879mod) caused
by temperature variation of LCPV module with respect toreference environmental state [19 20] The electrical exergydestruction rate is given as [15]
119864119909desel = 119881OC119868SC minus 119881mp119868mp (11)
In case of LCPVT systems thermal losses become thermalgain which is not in the scope of this paper (which deals withonly electrical energy and exergy analysis of LCPV system)Under this scenario in (10) the term representing exergydestruction rate is insignificant compared with electricalexergy rate (
119864119909el) and thermal exergy rate (
119864119909th) so the
effective expression for output exergy rate is given as [15]
119864119909out =
119864119909el plusmn 119864119909th
= 119881mp119868mp minus 119880119892119860 (119879119862 minus 119879amb) (1 minus119879amb119879119862
)
(12)
where the first term represents electrical exergy rate (119881mpand 119868mp being a voltage and current resp at maximumpower point of LCPV module) and the second term repre-sents thermal exergy rate due to the temperature differencebetween cell temperature and ambient temperature Thenegative sign with the second term in (12) corresponds tothe lost thermal exergy which would have been a gain incase of LCPVT system with a positive sign The inputexergy includes solar radiation intensity exergy which can beestimated by maximum efficiency ratio 120595 given by Petalarsquostheorem [16]
120595 = 1 +
1
3
(
119879amb119879sun
)
4
minus
4
3
119879amb119879sun
(13)
The input exergy rate to the PLPTC is found as [16]
119864119909in = 119866119887119860120595 (14)
The exergy efficiency of LCPV system is defined as ratio ofoutput exergy rate to the input exergy rate of the system [15]
120578ex =
119864119909out
119864119909in
=
119881mp119868mp minus 119880119892119860 (119879119862 minus 119879amb) (1 minus 119879amb119879119862)
1198661198871198601 + (13) (119879amb119879sun)4minus (43) (119879amb119879sun)
(15)
23 Model for Electrical Energy Analysis When a solar PVmodule is exposed to solar radiation it shows nonlinearcurrent-voltage characteristics The output current-voltagecharacteristic of solar PV module is mainly influenced bythe solar insolation and cell temperature There exist manymathematical models used for computer simulation whichdescribe the effect of solar insolation and cell temperatureon output current-voltage characteristics of solar PV module[21ndash23]
A crystalline silicon wafer-based solar photovoltaic (PV)cell of size 125mm times 125mm typically produces around25W at a voltage of 560mV These cells are connected inseries andor parallel configuration on a module to producerequired power The equivalent circuit for solar PV modulehaving 119873119875 numbers of cells arranged in parallel and 119873119878
number of cells arranged in series is shown in Figure 2The terminal equation for current and voltage of the
solar PV array is mentioned as follows as described by otherresearchers [25ndash28]
119868 = 119873119875119868PH minus 119873119875119868119878 [exp(119902 (119881119873119878 + 119868119877119878119873119875)
119896119861119879119862119860
) minus 1]
minus
(119873119875119881119873119878 + 119868119877119878)
119877SH
(16)
Ideally a solar PV module offers a low series resistance andhigh shunt resistance for higher solar energy conversion Insolar PV modules the PV cells are generally connected inseries in order to obtain adequate working voltage The solar
4 International Journal of Photoenergy
+
minus
RS
NS
NP
RSHNS
NP
NS
NP
NPIPH
I
Figure 2 The general model for solar PV module
PVmodules can be arranged in series-parallel combination tomake an array which produces desired power The current-voltage characteristic of such array is described by (16)Generally for the solar PVmodule 119868PH ≫ 119868119878 in (16) the smalldiode and ground-leakage currents can be ignored underzero-terminal voltage Therefore the short-circuit current isapproximately equal to the photocurrent The expression for119868PH is given by
119868PH = [119868SC + 119870119868 (119879119862 minus 119879Ref)] 120582 (17)
where 120582 = 120588mirror times CR times 119866119887 in Wm2 120588mirror representsreflection coefficient of mirrors
The photocurrent (119868PH) mainly depends on the solarinsolation and cellrsquos working temperature The saturationcurrent of a solar cell varies with the cell temperature whichis described by
119868119878 = 119868RS(119879119862
119879Ref)
3
exp[119902119864119892 (1119879Ref minus 1119879119862)
119896119861119860
] (18)
Reverse saturation current of the cell at reference temperaturedepends on the open-circuit voltage (119881OC) and can beapproximately obtained by following equation as given byTsai et al [29]
119868RS =119868SC
[exp (119902119881OC119873119878119896119861119860119879119862) minus 1]
(19)
The maximum power output of LCPV module is related tothe 119868SC and 119881OC by following
119875MAX = FF times 119881OC times 119868SC (20)
The values of 119868SC 119881OC and FF can be determined from the119868-119881 characteristics obtained by (16) The electrical powerconversion efficiency (120578) of LCPV module can be calculatedby the ratio of maximum output power generated by LCPVmodule to the input power carried by solar radiation (ie 120578 =
119875MAX120582)A solar PV module mainly consists of three types of
resistance series resistance (119877119878) shunt resistance (119877SH) anddynamic resistance (119903119889) The series resistance 119877119878 can be
determined by various illumination conditions such as darkconstant illumination and varying illumination and theyyield different results [30] The output impedance of solarPV module that is dynamic resistance is usually composedof the series resistance and shunt resistance In this paperdynamic resistance of LCPV module is quantified by usingdirect estimation method reported by Wang et al [31] Theequivalent circuit for solar PV module is shown in Figure 2
In order to estimate the dynamic resistance which isdefined as the negative reciprocal of 119889119868119889119881 (16) is differenti-ated with respect to 119881 that is
119889119868
119889119881
= minus
119873119875
119873119878119877SHminus
119889119868
119889119881
sdot
119877119878
119877SH
minus
119873119875119868119878119902
119896119879119862119860
[
1
119873119878
+
119889119868
119889119881
sdot
119877119878
119873119875
]
times exp [119902
119896119879119862119860
sdot (
119881
119873119878
+
119868119877119878
119873119875
)]
(21)
For the open-circuit condition and short-circuit conditions ofLCPVmodule the following two expressions are given usingthe slope of one 119868-119881 characteristics at the points (119881OC 0) and(0 119868SC) by
1198771199040 = minus(
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
)
minus1
(22)
119877sh0 = minus(
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
)
minus1
(23)
respectively When the load is disconnected from the LCPVmodule and the output current (119868) is equal to zero (21) canbe expressed by
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
= minus
119873119875
119873119878119877SHminus
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
sdot
119877119878
119877SH
minus
119873119875119868119878119902
119896119879119862119860
[
1
119873119878
+
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
sdot
119877119878
119873119875
]
times exp [119902
119896119879119862119860
sdot
119881
119873119878
]
(24)
Equation (24) is further simplified to
minus
1
119873119875119868119878
119896119879119862119860
119902
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
exp [minus119902
119896119879119862119860
sdot
119881OC119873119878
]
cong
1
119873119878
+
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
sdot
119877119878
119873119875
(25)
Therefore series resistance 119877119878 is expressed by
119877119878 =1198771199040119873119875
119873119878
minus
119896119879119862119860
119902119868119878
exp [minus119902
119896119879119862119860
sdot
119881OC119873119878
] (26)
International Journal of Photoenergy 5
Table 1 Simulation parameters for desired CR in developed LCPV system
Number ofmirrors Width119882 (m) Rim angle (0119903) Acceptance angle (120579119888) Length 119871 (m) Effective 119860119886 (m
2) CR Solar radiation (Wm2)
2 mirrors 027 1351∘ 317∘ 030 0054 185 12254 mirrors 045 2502∘ 307∘ 030 0108 356 22546 mirrors 062 3378∘ 294∘ 030 0159 472 32348 mirrors 079 4198∘ 280∘ 030 0211 517 3822
For short-circuit condition the output voltage of LCPVmodule is zero so (21) is reduced to
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
= minus
119873119875
119873119878119877SHminus
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
sdot
119877119878
119877SH
minus
119873119875119868119878119902
119896119879119862119860
[
1
119873119878
+
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
sdot
119877119878
119873119875
]
times exp [119902
119896119879119862119860
sdot (
119868SC119877119878119873119875
)]
(27)
Equation (27) can be further simplified as
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
= minus
119873119875
119873119878119877SHminus
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
sdot
119877119878
119877SH (28)
Therefore the shunt resistance can be expressed by
119877SH = minus
119873119878
119873119875
(
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
)
minus1
119877SH =
119873119878
119873119875
119877sh0
(29)
By analysis of (21) we conclude that the dynamic resistance ofLCPVmodule is dependent on the solar irradiance and solarPV module temperature
24 Statistical Analysis To compare the theoretical andobtained experimental results the correlation coefficient(119903) and root-mean square percent deviation (119890) have beenevaluated by using the following expressions [32]
119903 =
119873sum119883119894119884119894 minus (sum119883119894sum119884119894)
radic119873sum1198832119894minus (sum119883119894)
2radic119873sum119884
2119894minus (sum119884119894)
2
119890 =radic(sum 119890119894)
2
119873
(30)
where 119890119894 = [(119883119894 minus 119884119894)119883119894] times 100 The variables 119883119894 and 119884119894
represent theoretical and experimental data respectivelyThelinear coefficient of correlation (119903) which ranges betweenminus1 and 1 measures strength and the direction of a linearrelationship between two variables that is 119883119894 and 119884119894 The 119903value close to 1 indicates that two variables are in a strongpositive linear correlation
Figure 3 The constructed model of concentrator photovoltaic(CPV) system
3 LCPV Development and Validation of theProposed Model
31 System Development A MATLABSimulink computercode is developed using the mathematical model discussedin Section 2 to simulate LCPV system Table 1 shows theparameters used for calculating CR of the developed PLPTCThe CR depends on the effective aperture area which isgoverned by the number of mirrors used as reflectors FromTable 1 it is clear that by changing the number of mirrorsfrom 2 to 8 the geometric CR changes from sim2 to 8 Sun
A piecewise linear parabolic LCPV system is developed asshown in Figure 3 by using the modeling parameters listed inTable 1 The effective aperture area available using 8 mirrorsis 0211m2 and the effective receiver area is 0027m2 whichgives the geometric concentration ratio of sim8 The receiver ismade of a solar PV module fabricated by a string of sixteencommercially available silicon cell pieces (material mono-crystalline silicon size 14mm times 64mm efficiency sim14)The reason behind the selection of this specific size of thecells is to solve the current handling problem of the solarcells under concentration A typical solar cell of size 125mmtimes 125mm producing 25W at a voltage of 560mV wouldhave a current handling capability of around 45 A This cellwhen used under 10 Sun concentration may produce 45Acurrent by assuming a linear relationship between the currentincrement and CR But if the size of the cell is reduced to110th normal size then the current generated under 10 Sunconcentration would be less than or equal to 45 A thenit will be easily handled without damaging the solar cellcontacts The incident solar radiation is reflected by PLPTCand concentrated on the focal plane havingwidth of 064mm
6 International Journal of Photoenergy
Table 2 The parameters used for simulation under 1 Sun
Parametersunits 119877119878 (Ω) 119864119892 (eV) 119873119878 119873119875 119860 119879119862 (K) 119879ref (K) 119896119861 (JK) 119870119868 119902 (C) 119868SC (A) 119868RS (A) 119881OC (V)
For 1 Sun 0071 112 16 1 15 298 298 138 times 10
minus23065 times 10
minus31602 times 10
minus19 0259 086 times 10
minus12 986
Table 3 The value of 119877 119862 and corresponding 120591 obtained fromthe measured impedance spectra under different bias voltage con-ditions
Appliedvoltage(V)
Resistance inequivalent circuit
119877 (kΩ)
Capacitance inequivalent circuit
119862 (nF)
Timeconstant 120591
(ms)minus05 70 49 343minus02 55 514 2830 45 362 16302 37 351 13005 28 321 090
An active cooling mechanism is employed by flowing waterbehind the encapsulated solar PV module which is shown inFigure 3 By employing this mechanismmodule temperaturecould be lowered down to 45∘C A light dependent resistor(LDR) based one axis tracking system is developed for Suntracking with a provision of manual tracking on second axiswith an accuracy of plusmn3∘ as shown in Figure 3
32 Theory Validation and Characterization of LCPVModuleThe module characterization was done under standard testconditions (STC) by 119868-119881 characteristics impedance spec-troscopy (IS) and capacitance-voltage (CV) measurementand detailed parameters are given in Tables 2 and 3 Theconcentrated light is received by the solar PV module whichis placed at the focal plane of the PLPTC To simulate theelectrical power generated from this PV module the inputparameters are series resistance energy band gap number ofcells connected in series number of strings connected parallelto each other cell temperature ambient temperature short-circuit current ofmodule open-circuit voltage of themoduleand so on These input parameters are listed in Table 2
In this LCPV system a solar PV module manufacturedat WAAREE Energies Pvt Ltd module production line isused The open-circuit voltage and short-circuit current ofthis module aremeasured as119881OC = 986V and 119868SC = 0259Arespectively under AM15 spectrum at 29814 KThe current-voltage output characteristics of generalized solar PVmoduleunder AM15 solar spectrum are shown in Figure 4 In thesimulation short-circuit current open-circuit voltage seriesresistance and cell temperature measured under standardtest conditions (STC) by manufacturer are taken as inputparameters The current-voltage characteristic generatedfrom simulation programmatches well with the experimentalcurrent-voltage characteristic
Looking at the current-voltage curve it can be identifiedthat the photovoltaic module is a constant current source atlower values of voltage with current equal to the short-circuitcurrent (119868SC) With the further increase in voltage values the
0 2 4 6 8 100
005
01
015
02
025
03
Voltage (V)
Curr
ent (
A)
TheoreticalExperimental
e = 025 r = 0999
Figure 4 Current-voltage characteristics of the designed solar PVmodule under 1 Sun AM15 at 29814 K
current starts decreasing exponentially at certain point Thevalue of current becomes zero at open-circuit voltage (119881OC)The point where themodule operates at the highest efficiencyis called maximum power point (119875MAX)
For impedance measurements an ac signal having fre-quency in the range from 1 Hz to 01MHz with amplitudeof 5mV is used The impedance spectra were plotted in acomplex plane (ie 1198851015840 versus 119885
10158401015840 also known as Nyquistor ColendashCole plot [33]) which can provide information onany system that is composed of combination of interfacialand bulk process The measurements were carried out onthe developed LCPVmodule under forward and reverse bias(+05 V to minus05 V) conditions in the dark Figure 5 shows theimpedance spectrum of the LCPVmodule under reverse biasconditions (from 0 to minus05 V) The radius of the semicircleincreases with the increase in bias voltage as compared tozero bias demonstrating the bias dependence of resistanceand capacitance [33] The increase in the radius of semicircleduring reverse bias is observed due to expansion of depletionregion of the solar cell which increases the resistance offeredby the cell
Figure 6 shows the impedance spectrum under the for-ward bias conditions (from0 to 05V)where in contrast to thereverse bias opposite behavior is observed Here the radiusof the semicircle decreases with increasing positive bias fromits maximum value at zero bias The decrease in the radius ofsemicircle during forward bias is observed due to shrinking
International Journal of Photoenergy 7
0 2 4 6 8
times104
times104
0
05
1
15
2
25
3
35
Bias = 0VBias = minus02VBias = minus05V
Z998400 (Ohm)
Z998400998400
(Ohm
)
Figure 5 Impedance spectra of LCPV module under reverse biasconditions
times104
times104
0
05
1
15
2
25
Z998400 (Ohm)
Z998400998400
(Ohm
)
Bias = 0V
0 1 2 3 4 5
Bias = 02VBias = 05V
Figure 6 Impedance spectra of LCPV module under forward biasconditions
of depletion region of the solar cell which decreases theresistance offered by the cell
The ac equivalent circuit of the n+-p-p+structure underconsideration is shown in Figure 7 which incorporates thecapacitive effect owing to the excess minority carriers (119862119889commonly known as the diffusion capacitance) in parallelwith the depletion layer capacitance 119862119905 (Figure 7) Resistiveeffects arising from the minority carrier recombination areshown as the diffusion resistance (119877119889) in parallel with a shunt
RS
C = (Cd + Ct)
R = (RSH Rd)
Figure 7 The ac equivalent circuit of LCPV module to explainobserved impedance spectra
(119877SH) resistance and a series resistance 119877119878 connected in thecircuit [33]
Under forward bias condition due to the accumulationof minority carriers in the bulk the magnitude of thediffusion capacitance is large compared to the depletionregion capacitance [34] The ac impedance of the circuit isgiven by
119885 (120596) = 119885
1015840(120596) minus 119895119885
10158401015840(120596) (31)
where 119885
1015840 and 119885
10158401015840 are the magnitudes of the real andimaginary parts of impedance and a minus sign arises dueto capacitive reactance involved in the circuit On analyzingthe circuit 1198851015840 and 119885
10158401015840 can be written as
119885
1015840(120596) = 119877119904 +
119877
1 + (120596119877119862)
2
119885
10158401015840(120596) =
120596119862119877
2
1 + (120596119877119862)
2
(32)
For the case of very low 119877119878 when 119885
1015840 and 119885
10158401015840 are plotted ina complex plane by varying the frequency (120596) a semicircleof radius 1198772 with its center at (1198772 0) is obtained Furtherbecause of the semicircular geometry the maximum valueof 11988510158401015840 arises when 120596119898119877119862 = 1 where 120596119898 is the frequencyat which 119885
10158401015840 becomes maximum Thus we have that 119862 =
1120596119898119877 and the presence of 119877119878 shifts the semicircle byits value on the 119909-axis The analysis of the impedancediagram on the complex plane therefore gives values ofall the three parameters that is 119877 119862 and 119877119878 used in theequivalent circuit The product of resistance and capacitance(119877119862) represents the time constant (120591) The value of 119877 119862and corresponding 120591 obtained from themeasured impedancespectra under different bias voltage conditions is listed inTable 3These values are in good agreement with the existingliterature for silicon solar cells [33 35]
Capacitance-voltage (119862-119881) measurement is an importanttool to understand the transient behavior of a semiconductordevice Generally capacitance is measured in the reversedbias (Mott-Schottky) condition to determine barrier poten-tial and effective doping concentration Capacitance-voltagecharacterization is done for the developed LCPV module asshown in Figure 8
8 International Journal of Photoenergy
minus08 minus06 minus04 minus02 0 02 04 06 08Voltage (V)
times1014
0
05
1
15
2
25
3
1C
2(1F2)
Figure 8 The capacitance-voltage characterization of LCPV mod-ule
The dependence of barrier potential and doping concen-tration on the depletion region capacitance per unit area isgiven by [30]
1
1198622=
2
1199021198701205760119873
(119881bi minus 119881 minus
2119896119861119879
119902
)
119889 (1119862
2)
119889119881
= minus
2
1199021198701205760119873
(33)
where 119902 is the electron charge 119870 is dielectric constant ofsilicon 1205760 is the permittivity of free space 119881bi is barrierpotential 119896119861 is Boltzmannrsquos constant119879 is equal to 29814 K119873is doping concentration and 119881 represents applied potential
The slope and its intersection on the abscissa in theMott-Schottky plot shown in Figure 8 for the LCPV module givesthe doping concentration (119873) and barrier potential (119881bi)respectivelyThe119873 value is found as 779 times 1016 cmminus3 and thevalue of119881bi minus2119896119879119902 is equal to 056 eV which corresponds to119881bi = 061 eV The calculated values are in good agreementwith the reported values for commercially available siliconsolar cells [36 37]
4 LCPV Experiment under ATC
The experiments were carried out in the campus of Schoolof Solar Energy located in Gandhinagar India (Lat 2322∘Long 7268E) in the month of December (Year 2012) Themodule temperature was measured with the digital ther-mometer having an accuracy of plusmn01∘C during experimentswind speed was measured by anemometer as 085ms withan accuracy of plusmn5 Solar radiation and ambient temperaturewere recorded at the weather station located in the universitycampus The following parameters were measured duringexperiments ambient temperature solar radiation LCPVmodule and ambient temperature load current load voltageshort-circuit current and open-circuit voltage During theexperiments the module temperature was varied in the
range of 300ndash350K by controlling the flow rate of waterbehind the LCPV module Since the aim of this paper is toextract maximum electrical output from LCPV systems thethermodynamic analysis of flowingwater is avoided hereThecurrent-voltage measurements of an LCPV system are takenby Agilent SMU 6632B and by using multimeters and loadrheostat The sensitivity of the current-voltage measurementinstrument is given as plusmn3 The developed LCPV system isstudied by varying the number of reflecting mirrors arrangedin PLPTC
5 Result and Discussion
51 Exergy and Energy Analysis The effect of the lightconcentration and module temperature on the input exergyrate electrical exergy output rate and thermal exergy outputrate of LCPV module is estimated from the proposed modelin Section 2 It is found that with the increase in CR the inputexergy rate increases which results in increased amount ofenergy available to do useful work by the system The datalisted in Table 4 shows that the exergy efficiency decreaseswith the increase in the input exergy rate This decrease ismainly due to the increase in cell temperature which resultsin electrical exergy destruction with a rate of ldquo119881OC119868SC minus
119881mp119868mprdquo [38] Further the increase in the cell temperatureaffects 119881OC with a negative temperature coefficient as shownin the Figure 9 Figure 9 shows that 119881OC decreases from848V to 824V with increase in input exergy rate from3081W to 9612W when the cell temperature changesfrom 321 K to 3325 K The influence of the cell temperatureon exergy efficiency is clearly observed (Table 4) whichdecreases with the increase in the cell temperature Similareffect is observed by other researchers [15 38] Since the celltemperature changes with the increase in the input exergyrate it is imperative to design the LCPV system based on thisinformation so that useful exergy can bemaximized For thispurpose it is very important to track maximum power pointwhich depends on dynamic resistance of LCPV system
The proposed model in Section 2 is used to performenergy analysis of the LCPV module having 16 cells con-nected in series The static parameters (119868SC 119881OC 119875MAX and119877119878) of the LCPV module are measured in ATC conditionsas well as calculated by the proposed theoretical model Themeasured and simulated current-voltage characteristics ofLCPVmodule is shown in Figure 9 with varying input energyrate and corresponding temperature
It can be seen from Figure 9 that there is good agreementbetween the experimental and theoretical current-voltagecharacteristics which include 119868SC 119881OC 119875MAX 119877119878 FF 119903119889and efficiency The mean square of percentage deviation (119890)
is in the range of 274ndash843 and the linear coefficient ofcorrelation (119903) is in the range of 0995ndash0999
The measured values of solar irradiation 119868SC 119881OC 119875MAX119877119878 temperature FF 119903119889 and efficiency are listed in Table 5Generally the output current of the solar PV modulesincreases with the increase in input energy rate (ie solarirradiance received at focal point of PLPTC) With increasein the solar irradiance the higher number of photons strikes
International Journal of Photoenergy 9
Table 4 Exergy analysis of LCPV system
Solar irradiation(Wm2)
Cell temperature 119879119862 (K) Input exergy rate (W)Output exergy rate (W)
Exergy efficiency 120578ex ()Electricalexergy rate (W)
Thermal exergyrate (W)
1225 321 3081 2 043 5102254 328 5668 355 070 5033234 331 8133 491 083 5013822 3325 9612 554 091 482
Table 5 Parameter estimated from 119868-119881 curves plotted under various CR
Solarirradiation(Wm2)
Celltemperature
119879119862 (K)
Short-circuitcurrent 119868SC
(A)
Seriesresistance 119877119878
(Ω)
Dynamicresistance 119903119889
(Ω)
Open-circuitvoltage 119881OC
(V)
Maximumpower 119875MAX
(W)
Fill factor FF()
Energyefficiency 120578
()1000 298 025 112 1799 986 191 7458 7071225 321 033 120 1923 848 207 7397 6262254 328 063 129 2073 839 372 7037 6113234 331 091 139 2227 831 500 6700 5733822 3325 107 155 2484 824 584 6623 566
0 2 4 6 8 10Voltage (V)
Curr
ent (
A)
0
02
04
06
08
1
12
Simulation (2 mirrors)Experimental (2 mirrors)Simulation (4 mirrors)Experimental (4 mirrors)
Simulation (6 mirrors)Experimental (6 mirrors)Simulation (8 mirrors)Experimental (8 mirrors)
Figure 9 Simulated and experimental 119868-119881 characteristics of LCPVsystem under ATC
the solar PVmodule which results in enhanced electron-holepair production and higher photocurrent [39] The valuesof the dynamic resistance at MPP are computed using thevalues of 119868PH 119868SC and 119877119878 The dynamic resistance of LCPVmodule is calculated in an effective manner using (21) andis listed in Table 5 Approximate error between experimentaland theoretical dynamic resistance of the LCPV module isfound as sim13ndash21 which shows the uncertainty is wellwithin the practically acceptable limits
The plot shown in Figure 9 and extracted data listed inTable 5 describe the dependence of FF and efficiency of LCPV
module on the change in input energy rate and moduletemperature From the observed results it can be concludedthat the FF and efficiency of LCPV module decrease as theinput energy rate increasesThe decrease in FF and efficiencyof solar PV module with the increasing energy rate is highlydependent on the increase in electrical exergy destructionof LCPV module due to the increase in input energy rateand temperature As a result of increased input energy ratedynamic resistance offers greater resistive power losses inLCPV module and thus reduces its performance by reducingthe FF and efficiency The increase in the dynamic resistanceand reduction in the FF of LCPV module are foremostparameters for the decrease in the electrical energy efficiency
The effects of the cell temperature (119879119862) on 119868-119881 curveof LCPV module is estimated from the proposed model asshown in Figure 10 As the device temperature increasessmall increase in short-circuit current is observed how-ever the open-circuit voltage rapidly decreases due to theexponential dependence of the saturation current on thetemperature as given by (18) [39] In the actual experimentssimilar effect of temperature on open-circuit voltage (119881OC) isobserved and it is found that the 119881OC decreases from 986 to824V with temperature coefficient of voltage asymp minus0021 VKunder ATC as shown in Figure 9
A decrease in the 119875MAX with the increase in 119879119862 isobserved because with the increase in temperature the bandgap of the intrinsic semiconductor shrinks The increasedtemperature causes reduction in open-circuit voltage (119881OC)and the increase in the photocurrent for a given irradiancebecause of high injection of electrons from valance band toconduction band of semiconductor material [39]
52 Economical Analysis of LCPV System Net Present Value(NPV) method allows analyzing the economic aspects of anyengineering system and is used for the economic analysis of
10 International Journal of Photoenergy
Table 6 Cost of various components of LCPV system (asymp1 kWP) to find initial investment cost (numbers provided here are in accordancewith the current market price)lowast
Components Module BOSBattery Charge controller Support structure Tracker Cabling
Cost (in US$) 206 800 48 320 590 120Total initial investment cost (in US$) 2084
lowastThe price is based on market survey which may vary depending on specific location or company
Table 7 Economical analysis of LCPV system (having a lifetime of 25 years [24])
Period (year) 0 1 2 3 4 5 6 7 8Initial investment cost minus2084
Benefitslowastlowast 29043 29043 29043 29043 29043 29043 29043 29043O and M costlowastlowastlowast minus218 minus230 minus243 minus257 minus272 minus288 minus304 minus321
Discount rate 001 001 001 001 001 001 001 001 001Net cash flow 28825 28813 287995 28786 28771 28755 28739 28721119886 099 099 098 097 096 095 094 093 092Discounted net cash flow 28539 28245 27953 27662 27374 27089 26805 26524NPV minus17986 minus15162 minus12366 minus960 minus68626 minus41537 minus14732 11792lowastlowastBenefits are based on the tariff policy of Gujarat Electricity Regulatory Commission released for projects commissioned in 2012 [24]lowastlowastlowastEscalation in operating cost is taken as 572 annually [24]
300K325K
350K375K
0 2 4 6 8 100
005
01
015
02
025
03
Voltage (V)
Curr
ent (
A)
Figure 10 Variation of current-voltage characteristics with the celltemperature 119879119862
developed LCPV system of 1 kWP As the system presented inthis paper is very small for economic analysis the calculationsare done for 1 kWP system NPV method allows accountingfor the present value of annual capital expenditures andsavings during the lifetime of the system Net present value(NPV) includes sum of all the current values (costs are shownas negative and net savings are shown as positive) Foracceptance of any engineering project the positive NPV is
desiredThe formulas for calculatingNPVand correspondingfactor are given as [16]
NPV =
119899
sum
119894=1
(119861 minus 119862)119894
119886 =
1
(1 + 119894)
119901
(34)
where ldquo119886rdquo represents net present value factor ldquo119861rdquo representsgain ldquo119901rdquo represents the period and ldquo119894rdquo represents discountrate in the equation given previously
The initial investment cost is required in order to calculateNPV which includes module cost and balance of systems(BOS) cost The components of BOS include battery storagecharge controllers support structure tracking system andtransmission cables Cost of all these components is listedin Table 6 Using the initial investment cost and the formulaoutlined in (34) the NPV is calculated (Table 7) Operationandmaintenance (O andM) cost is taken as 075 of the totalinvestment cost with escalation in operating cost as 572 perannum [24] The feasibility of this project is demonstrated bya positive value of NPV obtained within 8 years
6 Conclusions
A theoretical model is used to perform electrical energy andexergy analyses of low-concentration photovoltaic (LCPV)system working under actual test conditions (ATC) Theexergy efficiency of LCPV system is in the range from51 to 482 with increasing rate of input exergy ratefrom 3081W to 9612W when concentration ratio changes
International Journal of Photoenergy 11
from 185 to 517 Sun Short-circuit current shows increasingtrend with increasing input exergy rate of asymp0011 AW Powerconversion efficiency decreases from 707 to 566 and open-circuit voltage decreases from986 to 824Vwith temperaturecoefficient of voltage asymp minus0021 VK under ATC The resultsconfirm that the commercially available silicon solar PVmodule performs satisfactorily under low concentration
Nomenclature
CR Concentration ratio119882 Width of the profile119863 Depth of the profile0119903 Rim angle120579119888 Acceptance angle119865 Focus point120588mirror Reflectivity of mirrors119877min Half width of the solar panel119871 Parabolic trough length120572 Absorption coefficient119860119886 Aperture area119896119861 Boltzmannrsquos constant (138 times 10minus23)119868PH Light generated current119868119878 Cell saturation or dark current119902 Electron charge (16 times 10minus19 C)119860 Ideality factor119880rad Radiative heat loss coefficient119880con Convective heat loss coefficient119879119862 Working temperature of solar cell (Kelvin)119877SH Shunt resistance119877119878 Series resistance119873119878 Series number of cells in a PV module119873119875 Parallel number of modules for a PV array119868SC Cellrsquos short-circuit current at 29814 K and
1 kWm2119870119868 Cellrsquos short-circuit current temperature
coefficient119879Ref Cellrsquos reference temperature120582 Solar insolation in kWm2119868RS Cellrsquos reverse saturation current at a
reference temperature and solar radiation119864119892 Band gap energy of the semiconductor119868mp Current at maximum power point119881mp Voltage at maximum power point
Acknowledgments
The authors acknowledge the financial support providedby Gujarat Energy Development Agency (GEDA) todevelop CPV system by Grant no GEDAECRECMarch-201039174 Authors also acknowledge WAAREE EnergiesPvt Ltd India for providing encapsulated crystallinesilicon solar PV modules for this study
References
[1] G Sala D Pachon I Anton and Test Test Rating andSpecification of PV Concentrator Components and Systems
(C-Rating Project) Book1 Classification of PV ConcentratorsUniversidad Politecnica de Madrid Madrid Spain 2002httpwwwies-defupmesiesCRATINGDocumentshtm
[2] M Yamaguchi andA Luque ldquoHigh efficiency and high concen-tration in photovoltaicsrdquo IEEE Transactions on Electron Devicesvol 46 no 10 pp 2139ndash2144 1999
[3] M A Green and A Ho-Baillie ldquoForty three per cent compositesplit-spectrum concentrator solar cell efficiencyrdquo Progress inPhotovoltaics vol 18 no 1 pp 42ndash47 2010
[4] H Cotal C Fetzer J Boisvert et al ldquoIII-V multijunction solarcells for concentrating photovoltaicsrdquo Energy and Environmen-tal Science vol 2 no 2 pp 174ndash192 2009
[5] G Sala I Anton J Monedero et al ldquoThe euclides-thermieconcentrator power plant in continuous operationrdquo in Proceed-ings of the 17th European Photovoltaic Solar Energy Conference(EUPVSEC rsquo01) pp 488ndash491 Munich Germany 2001
[6] V Garboushian S Yoon G Turner A Gunn and D FairldquoNovel high-concentration PV technology for cost competitiveutility bulk power generationrdquo in Proceedings of the 24th IEEEPhotovoltaic Specialists Conference Part 2 (of 2) pp 1060ndash1063December 1994
[7] M Castro I Anton and G Sala ldquoPilot production of concen-trator silicon solar cells approaching industrializationrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1697ndash17052008
[8] A Zahedi ldquoReview of modelling details in relation to low-concentration solar concentrating photovoltaicrdquoRenewable andSustainable Energy Reviews vol 15 no 3 pp 1609ndash1614 2011
[9] M Li X Ji G Li S Wei Y Li and F Shi ldquoPerformancestudy of solar cell arrays based on a trough concentratingphotovoltaicthermal systemrdquoApplied Energy vol 88 no 9 pp3218ndash3227 2011
[10] M A Schuetz K A Shell S A Brown G S Reinbolt RH French and R J Davis ldquoDesign and construction of a sim
7times low-concentration photovoltaic system based on compoundparabolic concentratorsrdquo IEEE Journal of Photovoltaics vol 2no 3 pp 382ndash386 2012
[11] H G Riveros and A I Oliva ldquoGraphical analysis of sunconcentrating collectorsrdquo Solar Energy vol 36 no 4 pp 313ndash322 1986
[12] O A Jaramillo J A Del Rıo and G Huelsz ldquoThermal study ofoptical fibres transmitting concentrated solar energyrdquo Journal ofPhysics D vol 32 no 9 pp 1000ndash1005 1999
[13] O A Jaramillo G Huelsz and J A Del Rıo ldquoA theoretical andexperimental thermal study of SiO2 optical fibres transmittingconcentrated radiative energyrdquo Journal of Physics D vol 35 no2 pp 95ndash102 2002
[14] C Kandilli and K Ulgen ldquoReview and modelling the systemsof transmission concentrated solar energy via optical fibresrdquoRenewable and Sustainable Energy Reviews vol 13 no 1 pp 67ndash84 2009
[15] A S Joshi I Dincer and B V Reddy ldquoThermodynamicassessment of photovoltaic systemsrdquo Solar Energy vol 83 no8 pp 1139ndash1149 2009
[16] C Kandilli ldquoPerformance analysis of novel concentrating solarphotovoltaic combined systemrdquo Energy Conversion and Man-agement vol 67 pp 186ndash196 2013
[17] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part I the concept of net exergyflow and the modeling of solar air heatersrdquo Solar Energy vol 41no 2 pp 127ndash132 1988
12 International Journal of Photoenergy
[18] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part 2 results of optimizationand analysis of sensibility to variations of operating conditionsrdquoSolar Energy vol 41 no 4 pp 309ndash317 1988
[19] S Farahat F Sarhaddi and H Ajam ldquoExergetic optimization offlat plate solar collectorsrdquo Renewable Energy vol 34 no 4 pp1169ndash1174 2009
[20] H Ajam S Farahat and F Sarhaddi ldquoExergetic optimizationof solar air heaters and comparison with energy analysisrdquoInternational Journal of Thermodynamics vol 8 no 4 pp 183ndash190 2005
[21] M J Kerr and A Cuevas ldquoGeneralized analysis of the illumi-nation intensity versus open-circuit voltage of solar cellsrdquo SolarEnergy vol 76 no 1ndash3 pp 263ndash267 2004
[22] E Radziemska and E Klugmann ldquoThermally affected parame-ters of the current-voltage characteristics of silicon photocellrdquoEnergy Conversion and Management vol 43 no 14 pp 1889ndash1900 2002
[23] E E van Dyk B J Scott E L Meyer and A W R LeitchldquoTemperature dependence of performance of crystalline siliconphotovoltaic modulesrdquo South African Journal of Science vol 96no 4 pp 198ndash200 2000
[24] httpwwwgercinorgrenewablepdfSolar20Tariff20Order20120of202012pdf 2013
[25] M Veerachary T Senjyu and K Uezato ldquoVoltage-basedmaximum power point tracking control of PV systemrdquo IEEETransactions on Aerospace and Electronic Systems vol 38 no1 pp 262ndash270 2002
[26] M Veerachary and K S Shinoy ldquoV2-based power tracking fornonlinear PV sourcesrdquo IEE Proceedings-Electric Power Applica-tions vol 152 no 5 pp 1263ndash1270 2005
[27] I S Kim and M J Youn ldquoVariable-structure observer for solararray current estimation in a photovoltaic power-generationsystemrdquo IEE Proceedings-Electric Power Applications vol 152no 4 pp 953ndash959 2005
[28] I S Kim M B Kim and M J Youn ldquoNew maximum powerpoint tracker using sliding-mode observer for estimation ofsolar array current in the grid-connected photovoltaic systemrdquoIEEE Transactions on Industrial Electronics vol 53 no 4 pp1027ndash1035 2006
[29] H L Tsai C S Tu and Y J Su ldquoDevelopment of generalizedphotovoltaic model using MATLABSIMULINKrdquo in Proceed-ings of theWorld Congress on Engineering and Computer ScienceSan Francisco NC USA October 2008
[30] J CThongpron K Kirtikara and C Jivacate ldquoAmethod for thedetermination of dynamic resistance of photovoltaic modulesunder illuminationrdquo Solar Energy Materials and Solar Cells vol90 no 18-19 pp 3078ndash3084 2006
[31] J C Wang J C Shieh Y L Su et al ldquoA novel method for thedetermination of dynamic resistance for photovoltaicmodulesrdquoEnergy vol 36 no 10 pp 5968ndash5974 2011
[32] S Dubey G S Sandhu andG N Tiwari ldquoAnalytical expressionfor electrical efficiency of PVT hybrid air collectorrdquo AppliedEnergy vol 86 no 5 pp 697ndash705 2009
[33] S Kumar P K Singh G S Chilana and S R Dhariwal ldquoGen-eration and recombination lifetime measurement in siliconwafers using impedance spectroscopyrdquo Semiconductor Scienceand Technology vol 24 no 9 Article ID 095001 pp 1ndash8 2009
[34] J Millman and C C Halkias Integrated Electronics McGraw-Hill New York NY USA 1972
[35] S Kumar P K Singh and G S Chilana ldquoStudy of siliconsolar cell at different intensities of illumination andwavelengthsusing impedance spectroscopyrdquo Solar Energy Materials andSolar Cells vol 93 no 10 pp 1881ndash1884 2009
[36] S Kumar V Sareen N Batra and P K Singh ldquoStudy of C-Vcharacteristics in thin n+-p-p+ silicon solar cells and inducedjunction n-p-p+ cell structuresrdquo Solar Energy Materials andSolar Cells vol 94 no 9 pp 1469ndash1472 2010
[37] I Mora-Sero G Garcia-Belmonte P P Boix M A Vazquezand J Bisquert ldquoImpedance spectroscopy characterisation ofhighly efficient silicon solar cells under different light illumina-tion intensitiesrdquo Energy and Environmental Science vol 2 no 6pp 678ndash686 2009
[38] F Sarhaddi S Farahat H Ajam andA Behzadmehr ldquoExergeticoptimization of a solar photovoltaic arrayrdquo Journal of Thermo-dynamics vol 2009 Article ID 313561 11 pages 2009
[39] S M Sze Physics of Semiconductor Devices Wiley New YorkNY USA 2nd edition 1981
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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International Journal ofPhotoenergy
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Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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CatalystsJournal of
2 International Journal of Photoenergy
et al [10] have reported design and construction of sim7timeslow-concentration PV system based on compound parabolicconcentrators
Despite all these progresses of the LCPV system thistechnology is unable to get market share among existing PVtechnologies that is monocrystalline Si flat panel and thin-film technologies Low-concentration photovoltaic technol-ogy has been limited due to requirement of special solarcell design perfect concentration geometry and insufficientanalysis of various issues such as exergy thermalizationlosses junction temperature and recombination processesTo surmount such issues in depth understanding of depen-dence of solar cell design parameters on CR and temperaturebetter design of concentration systems and proper systemperformance evaluation is required For LCPV systems suchimportant aspects have been scarcely addressed in detail sofar to the best of our knowledge
Keeping in view the above-mentioned shortfalls we havethe (i) the design and development of linear piecewiseparabolic trough for LCPV application and (ii) presented atheoretical model to perform exergy energy and dynamicbehavior analysis of LCPV system In this paper actualclimatic conditions are taken as reference state
2 Theoretical Modeling
21 Design and Modeling of PLPTC In this section designof piecewise linear parabolic trough collector (PLPTC) ispresented The parabola is designed in such a way thatmaximum energy and exergy can be extracted from theLCPV system A schematic diagram of PLPTC is shownin Figure 1 The design of PLPTC depends on receiverrsquosgeometry acceptance angle subtended by the receiver withparabolic reflector and desired geometric concentration
The level of concentration is restricted by the designparameters which include rim angle (0119903) acceptance angle(120579119888) and effective entrance aperture area (width119882times length119871) In this section theoretical model of a PLPTC withgeometrical CR sim8 Sun is presented [11]
The actual concentration ratio is calculated by
CR = 180 lowast (
sin 0119903 minus sin 120579119888 cos (0119903 minus 120579119888)
120587 (0119903 + 90 minus 120579119888) sin 120579119888) (1)
The amount of light received by solar PVmodule depends onthe reflectivity of mirrors used in the LCPV system
The line of focus for PLPTC can be located using thefollowing
119865 =
119882
2
16119863
(2)
Using focal length and the depth of parabola the rim angle iscalculated from the following
cos 0119903 = (
2119865
radic(05119882)
2+ (119863 minus 119865)
2
)minus 1 (3)
120579c
D
W
Parabolicreflector
Inci
dent
radi
atio
ns
Solarmodule
FocusRmin
0r
Figure 1 Basic geometry of parabolic trough concentrator
For the condition of 119865 = 119863 in (3) the rim angle becomesequal to 90∘ and the receivermakesminimum intercept anglewith radiation reflected from PLPTC The relation between119877min and the acceptance angle is given by
sin 120579119888 =119877min (1 + cos 0119903)
2119865
(4)
The receiver with the width of 119877min (equal to 32 cm in thiscase) is able to intercept all the radiation comingwith an angle20119903 From these equations it is established that the CR can bechanged by changing the effective aperture area of PLPTCIn developed PLPTC the numbers of reflecting mirrors arevaried from 2 to 8 to change the effective exit aperture areawhich gives desirable geometrical CR (sim2 to 8 Sun)
22 Thermodynamic Analysis for Exergetic Calculations Thelaws of thermodynamics are applied for the electrical exergyand energy analysis of LCPV system Energy conservationand energy quantity are generally analyzed by using the firstlaw of thermodynamics Exergy analysis which deals withavailability of energy in the system nature of irreversibilityand quality of energy is presented using the second law ofthermodynamics Exergymeasures not only quantity but alsothe quality of energy which is not conserved but rather isin part destroyed or lost Thermodynamic analysis for theelectrical output of LCPV system is performed using themethod described by many researchers [12ndash15]
The magnitude of the energy rate on the focal plane ofPLPTC (where crystalline solar PV module is placed) can beexpressed as [16]
119876119891 = 120587119891
2[sin2 (120601rim) minus sin2 (120601119904)] 120588mirror119866119887 (5)
where 120588mirror represents the reflectivity of mirror 120601119904 rep-resents the shading angle and 119866119887 represents direct beamsolar radiation on parabola aperture The energy rate
119876119891represents energy flow per unit time at which solar energyreaches the front glass of LCPVmodule The energy received
International Journal of Photoenergy 3
at front glass of LCPV module undergoes radiative andconvective losses which can be expressed in terms of heat losscoefficient 119880119892 (measured in terms of WK) [16]
119880119892 = 119880con + 119880rad (6)
After considering these heat losses the energy rate on thefront glass of LCPV module
119876119892 can be expressed as
119876119892 =
119876119891 minus 119880119892 (119879119892 minus 119879amb) (7)
Since the thickness of the glass is very small the conductionheat loss coefficient could be ignored for further calculationsThe incoming energy rate to LCPV module
119876in is given as
119876in =
119876119892120591 (8)
where 120591 represents transmission coefficient of front glass ofLCPV module
The output energy rate of LCPV module 119876out is calcu-
lated using the following expression [15]
119876out =
119876el + 119876th = 119881OC119868SC +
119876th (9)
where 119876el represents electrical output energy rate and
119876threpresents thermal output energy rate respectively Theenergy efficiency of LCPV system can be defined as theratio of output energy rate to the input energy rate Adetailed calculation of LCPV modulersquos electrical power con-version efficiency starting with terminal equation is given inSection 23
Similar expression for output exergy rate of LCPV systemis given as [15]
119864119909out =
119864119909el + 119864119909th +
119864119909des (10)
where 119864119909des =
119864119909desel + 119864119909desopt +
119864119909desΔ119879sun +
119864119909desΔ119879mod
which includes electrical exergy destruction rate (
119864119909desel)caused by series and shunt resistance losses [15] opticalexergy destruction rate (
119864119909desopt) caused by optical losses inLCPV module surface [17 18] thermal exergy destructionrate (
119864119909desΔ119879sun) caused by temperature difference between
LCPV module surface and the sun surface temperature [17ndash20] and thermal exergy destruction rate (
119864119909desΔ119879mod) caused
by temperature variation of LCPV module with respect toreference environmental state [19 20] The electrical exergydestruction rate is given as [15]
119864119909desel = 119881OC119868SC minus 119881mp119868mp (11)
In case of LCPVT systems thermal losses become thermalgain which is not in the scope of this paper (which deals withonly electrical energy and exergy analysis of LCPV system)Under this scenario in (10) the term representing exergydestruction rate is insignificant compared with electricalexergy rate (
119864119909el) and thermal exergy rate (
119864119909th) so the
effective expression for output exergy rate is given as [15]
119864119909out =
119864119909el plusmn 119864119909th
= 119881mp119868mp minus 119880119892119860 (119879119862 minus 119879amb) (1 minus119879amb119879119862
)
(12)
where the first term represents electrical exergy rate (119881mpand 119868mp being a voltage and current resp at maximumpower point of LCPV module) and the second term repre-sents thermal exergy rate due to the temperature differencebetween cell temperature and ambient temperature Thenegative sign with the second term in (12) corresponds tothe lost thermal exergy which would have been a gain incase of LCPVT system with a positive sign The inputexergy includes solar radiation intensity exergy which can beestimated by maximum efficiency ratio 120595 given by Petalarsquostheorem [16]
120595 = 1 +
1
3
(
119879amb119879sun
)
4
minus
4
3
119879amb119879sun
(13)
The input exergy rate to the PLPTC is found as [16]
119864119909in = 119866119887119860120595 (14)
The exergy efficiency of LCPV system is defined as ratio ofoutput exergy rate to the input exergy rate of the system [15]
120578ex =
119864119909out
119864119909in
=
119881mp119868mp minus 119880119892119860 (119879119862 minus 119879amb) (1 minus 119879amb119879119862)
1198661198871198601 + (13) (119879amb119879sun)4minus (43) (119879amb119879sun)
(15)
23 Model for Electrical Energy Analysis When a solar PVmodule is exposed to solar radiation it shows nonlinearcurrent-voltage characteristics The output current-voltagecharacteristic of solar PV module is mainly influenced bythe solar insolation and cell temperature There exist manymathematical models used for computer simulation whichdescribe the effect of solar insolation and cell temperatureon output current-voltage characteristics of solar PV module[21ndash23]
A crystalline silicon wafer-based solar photovoltaic (PV)cell of size 125mm times 125mm typically produces around25W at a voltage of 560mV These cells are connected inseries andor parallel configuration on a module to producerequired power The equivalent circuit for solar PV modulehaving 119873119875 numbers of cells arranged in parallel and 119873119878
number of cells arranged in series is shown in Figure 2The terminal equation for current and voltage of the
solar PV array is mentioned as follows as described by otherresearchers [25ndash28]
119868 = 119873119875119868PH minus 119873119875119868119878 [exp(119902 (119881119873119878 + 119868119877119878119873119875)
119896119861119879119862119860
) minus 1]
minus
(119873119875119881119873119878 + 119868119877119878)
119877SH
(16)
Ideally a solar PV module offers a low series resistance andhigh shunt resistance for higher solar energy conversion Insolar PV modules the PV cells are generally connected inseries in order to obtain adequate working voltage The solar
4 International Journal of Photoenergy
+
minus
RS
NS
NP
RSHNS
NP
NS
NP
NPIPH
I
Figure 2 The general model for solar PV module
PVmodules can be arranged in series-parallel combination tomake an array which produces desired power The current-voltage characteristic of such array is described by (16)Generally for the solar PVmodule 119868PH ≫ 119868119878 in (16) the smalldiode and ground-leakage currents can be ignored underzero-terminal voltage Therefore the short-circuit current isapproximately equal to the photocurrent The expression for119868PH is given by
119868PH = [119868SC + 119870119868 (119879119862 minus 119879Ref)] 120582 (17)
where 120582 = 120588mirror times CR times 119866119887 in Wm2 120588mirror representsreflection coefficient of mirrors
The photocurrent (119868PH) mainly depends on the solarinsolation and cellrsquos working temperature The saturationcurrent of a solar cell varies with the cell temperature whichis described by
119868119878 = 119868RS(119879119862
119879Ref)
3
exp[119902119864119892 (1119879Ref minus 1119879119862)
119896119861119860
] (18)
Reverse saturation current of the cell at reference temperaturedepends on the open-circuit voltage (119881OC) and can beapproximately obtained by following equation as given byTsai et al [29]
119868RS =119868SC
[exp (119902119881OC119873119878119896119861119860119879119862) minus 1]
(19)
The maximum power output of LCPV module is related tothe 119868SC and 119881OC by following
119875MAX = FF times 119881OC times 119868SC (20)
The values of 119868SC 119881OC and FF can be determined from the119868-119881 characteristics obtained by (16) The electrical powerconversion efficiency (120578) of LCPV module can be calculatedby the ratio of maximum output power generated by LCPVmodule to the input power carried by solar radiation (ie 120578 =
119875MAX120582)A solar PV module mainly consists of three types of
resistance series resistance (119877119878) shunt resistance (119877SH) anddynamic resistance (119903119889) The series resistance 119877119878 can be
determined by various illumination conditions such as darkconstant illumination and varying illumination and theyyield different results [30] The output impedance of solarPV module that is dynamic resistance is usually composedof the series resistance and shunt resistance In this paperdynamic resistance of LCPV module is quantified by usingdirect estimation method reported by Wang et al [31] Theequivalent circuit for solar PV module is shown in Figure 2
In order to estimate the dynamic resistance which isdefined as the negative reciprocal of 119889119868119889119881 (16) is differenti-ated with respect to 119881 that is
119889119868
119889119881
= minus
119873119875
119873119878119877SHminus
119889119868
119889119881
sdot
119877119878
119877SH
minus
119873119875119868119878119902
119896119879119862119860
[
1
119873119878
+
119889119868
119889119881
sdot
119877119878
119873119875
]
times exp [119902
119896119879119862119860
sdot (
119881
119873119878
+
119868119877119878
119873119875
)]
(21)
For the open-circuit condition and short-circuit conditions ofLCPVmodule the following two expressions are given usingthe slope of one 119868-119881 characteristics at the points (119881OC 0) and(0 119868SC) by
1198771199040 = minus(
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
)
minus1
(22)
119877sh0 = minus(
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
)
minus1
(23)
respectively When the load is disconnected from the LCPVmodule and the output current (119868) is equal to zero (21) canbe expressed by
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
= minus
119873119875
119873119878119877SHminus
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
sdot
119877119878
119877SH
minus
119873119875119868119878119902
119896119879119862119860
[
1
119873119878
+
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
sdot
119877119878
119873119875
]
times exp [119902
119896119879119862119860
sdot
119881
119873119878
]
(24)
Equation (24) is further simplified to
minus
1
119873119875119868119878
119896119879119862119860
119902
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
exp [minus119902
119896119879119862119860
sdot
119881OC119873119878
]
cong
1
119873119878
+
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
sdot
119877119878
119873119875
(25)
Therefore series resistance 119877119878 is expressed by
119877119878 =1198771199040119873119875
119873119878
minus
119896119879119862119860
119902119868119878
exp [minus119902
119896119879119862119860
sdot
119881OC119873119878
] (26)
International Journal of Photoenergy 5
Table 1 Simulation parameters for desired CR in developed LCPV system
Number ofmirrors Width119882 (m) Rim angle (0119903) Acceptance angle (120579119888) Length 119871 (m) Effective 119860119886 (m
2) CR Solar radiation (Wm2)
2 mirrors 027 1351∘ 317∘ 030 0054 185 12254 mirrors 045 2502∘ 307∘ 030 0108 356 22546 mirrors 062 3378∘ 294∘ 030 0159 472 32348 mirrors 079 4198∘ 280∘ 030 0211 517 3822
For short-circuit condition the output voltage of LCPVmodule is zero so (21) is reduced to
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
= minus
119873119875
119873119878119877SHminus
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
sdot
119877119878
119877SH
minus
119873119875119868119878119902
119896119879119862119860
[
1
119873119878
+
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
sdot
119877119878
119873119875
]
times exp [119902
119896119879119862119860
sdot (
119868SC119877119878119873119875
)]
(27)
Equation (27) can be further simplified as
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
= minus
119873119875
119873119878119877SHminus
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
sdot
119877119878
119877SH (28)
Therefore the shunt resistance can be expressed by
119877SH = minus
119873119878
119873119875
(
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
)
minus1
119877SH =
119873119878
119873119875
119877sh0
(29)
By analysis of (21) we conclude that the dynamic resistance ofLCPVmodule is dependent on the solar irradiance and solarPV module temperature
24 Statistical Analysis To compare the theoretical andobtained experimental results the correlation coefficient(119903) and root-mean square percent deviation (119890) have beenevaluated by using the following expressions [32]
119903 =
119873sum119883119894119884119894 minus (sum119883119894sum119884119894)
radic119873sum1198832119894minus (sum119883119894)
2radic119873sum119884
2119894minus (sum119884119894)
2
119890 =radic(sum 119890119894)
2
119873
(30)
where 119890119894 = [(119883119894 minus 119884119894)119883119894] times 100 The variables 119883119894 and 119884119894
represent theoretical and experimental data respectivelyThelinear coefficient of correlation (119903) which ranges betweenminus1 and 1 measures strength and the direction of a linearrelationship between two variables that is 119883119894 and 119884119894 The 119903value close to 1 indicates that two variables are in a strongpositive linear correlation
Figure 3 The constructed model of concentrator photovoltaic(CPV) system
3 LCPV Development and Validation of theProposed Model
31 System Development A MATLABSimulink computercode is developed using the mathematical model discussedin Section 2 to simulate LCPV system Table 1 shows theparameters used for calculating CR of the developed PLPTCThe CR depends on the effective aperture area which isgoverned by the number of mirrors used as reflectors FromTable 1 it is clear that by changing the number of mirrorsfrom 2 to 8 the geometric CR changes from sim2 to 8 Sun
A piecewise linear parabolic LCPV system is developed asshown in Figure 3 by using the modeling parameters listed inTable 1 The effective aperture area available using 8 mirrorsis 0211m2 and the effective receiver area is 0027m2 whichgives the geometric concentration ratio of sim8 The receiver ismade of a solar PV module fabricated by a string of sixteencommercially available silicon cell pieces (material mono-crystalline silicon size 14mm times 64mm efficiency sim14)The reason behind the selection of this specific size of thecells is to solve the current handling problem of the solarcells under concentration A typical solar cell of size 125mmtimes 125mm producing 25W at a voltage of 560mV wouldhave a current handling capability of around 45 A This cellwhen used under 10 Sun concentration may produce 45Acurrent by assuming a linear relationship between the currentincrement and CR But if the size of the cell is reduced to110th normal size then the current generated under 10 Sunconcentration would be less than or equal to 45 A thenit will be easily handled without damaging the solar cellcontacts The incident solar radiation is reflected by PLPTCand concentrated on the focal plane havingwidth of 064mm
6 International Journal of Photoenergy
Table 2 The parameters used for simulation under 1 Sun
Parametersunits 119877119878 (Ω) 119864119892 (eV) 119873119878 119873119875 119860 119879119862 (K) 119879ref (K) 119896119861 (JK) 119870119868 119902 (C) 119868SC (A) 119868RS (A) 119881OC (V)
For 1 Sun 0071 112 16 1 15 298 298 138 times 10
minus23065 times 10
minus31602 times 10
minus19 0259 086 times 10
minus12 986
Table 3 The value of 119877 119862 and corresponding 120591 obtained fromthe measured impedance spectra under different bias voltage con-ditions
Appliedvoltage(V)
Resistance inequivalent circuit
119877 (kΩ)
Capacitance inequivalent circuit
119862 (nF)
Timeconstant 120591
(ms)minus05 70 49 343minus02 55 514 2830 45 362 16302 37 351 13005 28 321 090
An active cooling mechanism is employed by flowing waterbehind the encapsulated solar PV module which is shown inFigure 3 By employing this mechanismmodule temperaturecould be lowered down to 45∘C A light dependent resistor(LDR) based one axis tracking system is developed for Suntracking with a provision of manual tracking on second axiswith an accuracy of plusmn3∘ as shown in Figure 3
32 Theory Validation and Characterization of LCPVModuleThe module characterization was done under standard testconditions (STC) by 119868-119881 characteristics impedance spec-troscopy (IS) and capacitance-voltage (CV) measurementand detailed parameters are given in Tables 2 and 3 Theconcentrated light is received by the solar PV module whichis placed at the focal plane of the PLPTC To simulate theelectrical power generated from this PV module the inputparameters are series resistance energy band gap number ofcells connected in series number of strings connected parallelto each other cell temperature ambient temperature short-circuit current ofmodule open-circuit voltage of themoduleand so on These input parameters are listed in Table 2
In this LCPV system a solar PV module manufacturedat WAAREE Energies Pvt Ltd module production line isused The open-circuit voltage and short-circuit current ofthis module aremeasured as119881OC = 986V and 119868SC = 0259Arespectively under AM15 spectrum at 29814 KThe current-voltage output characteristics of generalized solar PVmoduleunder AM15 solar spectrum are shown in Figure 4 In thesimulation short-circuit current open-circuit voltage seriesresistance and cell temperature measured under standardtest conditions (STC) by manufacturer are taken as inputparameters The current-voltage characteristic generatedfrom simulation programmatches well with the experimentalcurrent-voltage characteristic
Looking at the current-voltage curve it can be identifiedthat the photovoltaic module is a constant current source atlower values of voltage with current equal to the short-circuitcurrent (119868SC) With the further increase in voltage values the
0 2 4 6 8 100
005
01
015
02
025
03
Voltage (V)
Curr
ent (
A)
TheoreticalExperimental
e = 025 r = 0999
Figure 4 Current-voltage characteristics of the designed solar PVmodule under 1 Sun AM15 at 29814 K
current starts decreasing exponentially at certain point Thevalue of current becomes zero at open-circuit voltage (119881OC)The point where themodule operates at the highest efficiencyis called maximum power point (119875MAX)
For impedance measurements an ac signal having fre-quency in the range from 1 Hz to 01MHz with amplitudeof 5mV is used The impedance spectra were plotted in acomplex plane (ie 1198851015840 versus 119885
10158401015840 also known as Nyquistor ColendashCole plot [33]) which can provide information onany system that is composed of combination of interfacialand bulk process The measurements were carried out onthe developed LCPVmodule under forward and reverse bias(+05 V to minus05 V) conditions in the dark Figure 5 shows theimpedance spectrum of the LCPVmodule under reverse biasconditions (from 0 to minus05 V) The radius of the semicircleincreases with the increase in bias voltage as compared tozero bias demonstrating the bias dependence of resistanceand capacitance [33] The increase in the radius of semicircleduring reverse bias is observed due to expansion of depletionregion of the solar cell which increases the resistance offeredby the cell
Figure 6 shows the impedance spectrum under the for-ward bias conditions (from0 to 05V)where in contrast to thereverse bias opposite behavior is observed Here the radiusof the semicircle decreases with increasing positive bias fromits maximum value at zero bias The decrease in the radius ofsemicircle during forward bias is observed due to shrinking
International Journal of Photoenergy 7
0 2 4 6 8
times104
times104
0
05
1
15
2
25
3
35
Bias = 0VBias = minus02VBias = minus05V
Z998400 (Ohm)
Z998400998400
(Ohm
)
Figure 5 Impedance spectra of LCPV module under reverse biasconditions
times104
times104
0
05
1
15
2
25
Z998400 (Ohm)
Z998400998400
(Ohm
)
Bias = 0V
0 1 2 3 4 5
Bias = 02VBias = 05V
Figure 6 Impedance spectra of LCPV module under forward biasconditions
of depletion region of the solar cell which decreases theresistance offered by the cell
The ac equivalent circuit of the n+-p-p+structure underconsideration is shown in Figure 7 which incorporates thecapacitive effect owing to the excess minority carriers (119862119889commonly known as the diffusion capacitance) in parallelwith the depletion layer capacitance 119862119905 (Figure 7) Resistiveeffects arising from the minority carrier recombination areshown as the diffusion resistance (119877119889) in parallel with a shunt
RS
C = (Cd + Ct)
R = (RSH Rd)
Figure 7 The ac equivalent circuit of LCPV module to explainobserved impedance spectra
(119877SH) resistance and a series resistance 119877119878 connected in thecircuit [33]
Under forward bias condition due to the accumulationof minority carriers in the bulk the magnitude of thediffusion capacitance is large compared to the depletionregion capacitance [34] The ac impedance of the circuit isgiven by
119885 (120596) = 119885
1015840(120596) minus 119895119885
10158401015840(120596) (31)
where 119885
1015840 and 119885
10158401015840 are the magnitudes of the real andimaginary parts of impedance and a minus sign arises dueto capacitive reactance involved in the circuit On analyzingthe circuit 1198851015840 and 119885
10158401015840 can be written as
119885
1015840(120596) = 119877119904 +
119877
1 + (120596119877119862)
2
119885
10158401015840(120596) =
120596119862119877
2
1 + (120596119877119862)
2
(32)
For the case of very low 119877119878 when 119885
1015840 and 119885
10158401015840 are plotted ina complex plane by varying the frequency (120596) a semicircleof radius 1198772 with its center at (1198772 0) is obtained Furtherbecause of the semicircular geometry the maximum valueof 11988510158401015840 arises when 120596119898119877119862 = 1 where 120596119898 is the frequencyat which 119885
10158401015840 becomes maximum Thus we have that 119862 =
1120596119898119877 and the presence of 119877119878 shifts the semicircle byits value on the 119909-axis The analysis of the impedancediagram on the complex plane therefore gives values ofall the three parameters that is 119877 119862 and 119877119878 used in theequivalent circuit The product of resistance and capacitance(119877119862) represents the time constant (120591) The value of 119877 119862and corresponding 120591 obtained from themeasured impedancespectra under different bias voltage conditions is listed inTable 3These values are in good agreement with the existingliterature for silicon solar cells [33 35]
Capacitance-voltage (119862-119881) measurement is an importanttool to understand the transient behavior of a semiconductordevice Generally capacitance is measured in the reversedbias (Mott-Schottky) condition to determine barrier poten-tial and effective doping concentration Capacitance-voltagecharacterization is done for the developed LCPV module asshown in Figure 8
8 International Journal of Photoenergy
minus08 minus06 minus04 minus02 0 02 04 06 08Voltage (V)
times1014
0
05
1
15
2
25
3
1C
2(1F2)
Figure 8 The capacitance-voltage characterization of LCPV mod-ule
The dependence of barrier potential and doping concen-tration on the depletion region capacitance per unit area isgiven by [30]
1
1198622=
2
1199021198701205760119873
(119881bi minus 119881 minus
2119896119861119879
119902
)
119889 (1119862
2)
119889119881
= minus
2
1199021198701205760119873
(33)
where 119902 is the electron charge 119870 is dielectric constant ofsilicon 1205760 is the permittivity of free space 119881bi is barrierpotential 119896119861 is Boltzmannrsquos constant119879 is equal to 29814 K119873is doping concentration and 119881 represents applied potential
The slope and its intersection on the abscissa in theMott-Schottky plot shown in Figure 8 for the LCPV module givesthe doping concentration (119873) and barrier potential (119881bi)respectivelyThe119873 value is found as 779 times 1016 cmminus3 and thevalue of119881bi minus2119896119879119902 is equal to 056 eV which corresponds to119881bi = 061 eV The calculated values are in good agreementwith the reported values for commercially available siliconsolar cells [36 37]
4 LCPV Experiment under ATC
The experiments were carried out in the campus of Schoolof Solar Energy located in Gandhinagar India (Lat 2322∘Long 7268E) in the month of December (Year 2012) Themodule temperature was measured with the digital ther-mometer having an accuracy of plusmn01∘C during experimentswind speed was measured by anemometer as 085ms withan accuracy of plusmn5 Solar radiation and ambient temperaturewere recorded at the weather station located in the universitycampus The following parameters were measured duringexperiments ambient temperature solar radiation LCPVmodule and ambient temperature load current load voltageshort-circuit current and open-circuit voltage During theexperiments the module temperature was varied in the
range of 300ndash350K by controlling the flow rate of waterbehind the LCPV module Since the aim of this paper is toextract maximum electrical output from LCPV systems thethermodynamic analysis of flowingwater is avoided hereThecurrent-voltage measurements of an LCPV system are takenby Agilent SMU 6632B and by using multimeters and loadrheostat The sensitivity of the current-voltage measurementinstrument is given as plusmn3 The developed LCPV system isstudied by varying the number of reflecting mirrors arrangedin PLPTC
5 Result and Discussion
51 Exergy and Energy Analysis The effect of the lightconcentration and module temperature on the input exergyrate electrical exergy output rate and thermal exergy outputrate of LCPV module is estimated from the proposed modelin Section 2 It is found that with the increase in CR the inputexergy rate increases which results in increased amount ofenergy available to do useful work by the system The datalisted in Table 4 shows that the exergy efficiency decreaseswith the increase in the input exergy rate This decrease ismainly due to the increase in cell temperature which resultsin electrical exergy destruction with a rate of ldquo119881OC119868SC minus
119881mp119868mprdquo [38] Further the increase in the cell temperatureaffects 119881OC with a negative temperature coefficient as shownin the Figure 9 Figure 9 shows that 119881OC decreases from848V to 824V with increase in input exergy rate from3081W to 9612W when the cell temperature changesfrom 321 K to 3325 K The influence of the cell temperatureon exergy efficiency is clearly observed (Table 4) whichdecreases with the increase in the cell temperature Similareffect is observed by other researchers [15 38] Since the celltemperature changes with the increase in the input exergyrate it is imperative to design the LCPV system based on thisinformation so that useful exergy can bemaximized For thispurpose it is very important to track maximum power pointwhich depends on dynamic resistance of LCPV system
The proposed model in Section 2 is used to performenergy analysis of the LCPV module having 16 cells con-nected in series The static parameters (119868SC 119881OC 119875MAX and119877119878) of the LCPV module are measured in ATC conditionsas well as calculated by the proposed theoretical model Themeasured and simulated current-voltage characteristics ofLCPVmodule is shown in Figure 9 with varying input energyrate and corresponding temperature
It can be seen from Figure 9 that there is good agreementbetween the experimental and theoretical current-voltagecharacteristics which include 119868SC 119881OC 119875MAX 119877119878 FF 119903119889and efficiency The mean square of percentage deviation (119890)
is in the range of 274ndash843 and the linear coefficient ofcorrelation (119903) is in the range of 0995ndash0999
The measured values of solar irradiation 119868SC 119881OC 119875MAX119877119878 temperature FF 119903119889 and efficiency are listed in Table 5Generally the output current of the solar PV modulesincreases with the increase in input energy rate (ie solarirradiance received at focal point of PLPTC) With increasein the solar irradiance the higher number of photons strikes
International Journal of Photoenergy 9
Table 4 Exergy analysis of LCPV system
Solar irradiation(Wm2)
Cell temperature 119879119862 (K) Input exergy rate (W)Output exergy rate (W)
Exergy efficiency 120578ex ()Electricalexergy rate (W)
Thermal exergyrate (W)
1225 321 3081 2 043 5102254 328 5668 355 070 5033234 331 8133 491 083 5013822 3325 9612 554 091 482
Table 5 Parameter estimated from 119868-119881 curves plotted under various CR
Solarirradiation(Wm2)
Celltemperature
119879119862 (K)
Short-circuitcurrent 119868SC
(A)
Seriesresistance 119877119878
(Ω)
Dynamicresistance 119903119889
(Ω)
Open-circuitvoltage 119881OC
(V)
Maximumpower 119875MAX
(W)
Fill factor FF()
Energyefficiency 120578
()1000 298 025 112 1799 986 191 7458 7071225 321 033 120 1923 848 207 7397 6262254 328 063 129 2073 839 372 7037 6113234 331 091 139 2227 831 500 6700 5733822 3325 107 155 2484 824 584 6623 566
0 2 4 6 8 10Voltage (V)
Curr
ent (
A)
0
02
04
06
08
1
12
Simulation (2 mirrors)Experimental (2 mirrors)Simulation (4 mirrors)Experimental (4 mirrors)
Simulation (6 mirrors)Experimental (6 mirrors)Simulation (8 mirrors)Experimental (8 mirrors)
Figure 9 Simulated and experimental 119868-119881 characteristics of LCPVsystem under ATC
the solar PVmodule which results in enhanced electron-holepair production and higher photocurrent [39] The valuesof the dynamic resistance at MPP are computed using thevalues of 119868PH 119868SC and 119877119878 The dynamic resistance of LCPVmodule is calculated in an effective manner using (21) andis listed in Table 5 Approximate error between experimentaland theoretical dynamic resistance of the LCPV module isfound as sim13ndash21 which shows the uncertainty is wellwithin the practically acceptable limits
The plot shown in Figure 9 and extracted data listed inTable 5 describe the dependence of FF and efficiency of LCPV
module on the change in input energy rate and moduletemperature From the observed results it can be concludedthat the FF and efficiency of LCPV module decrease as theinput energy rate increasesThe decrease in FF and efficiencyof solar PV module with the increasing energy rate is highlydependent on the increase in electrical exergy destructionof LCPV module due to the increase in input energy rateand temperature As a result of increased input energy ratedynamic resistance offers greater resistive power losses inLCPV module and thus reduces its performance by reducingthe FF and efficiency The increase in the dynamic resistanceand reduction in the FF of LCPV module are foremostparameters for the decrease in the electrical energy efficiency
The effects of the cell temperature (119879119862) on 119868-119881 curveof LCPV module is estimated from the proposed model asshown in Figure 10 As the device temperature increasessmall increase in short-circuit current is observed how-ever the open-circuit voltage rapidly decreases due to theexponential dependence of the saturation current on thetemperature as given by (18) [39] In the actual experimentssimilar effect of temperature on open-circuit voltage (119881OC) isobserved and it is found that the 119881OC decreases from 986 to824V with temperature coefficient of voltage asymp minus0021 VKunder ATC as shown in Figure 9
A decrease in the 119875MAX with the increase in 119879119862 isobserved because with the increase in temperature the bandgap of the intrinsic semiconductor shrinks The increasedtemperature causes reduction in open-circuit voltage (119881OC)and the increase in the photocurrent for a given irradiancebecause of high injection of electrons from valance band toconduction band of semiconductor material [39]
52 Economical Analysis of LCPV System Net Present Value(NPV) method allows analyzing the economic aspects of anyengineering system and is used for the economic analysis of
10 International Journal of Photoenergy
Table 6 Cost of various components of LCPV system (asymp1 kWP) to find initial investment cost (numbers provided here are in accordancewith the current market price)lowast
Components Module BOSBattery Charge controller Support structure Tracker Cabling
Cost (in US$) 206 800 48 320 590 120Total initial investment cost (in US$) 2084
lowastThe price is based on market survey which may vary depending on specific location or company
Table 7 Economical analysis of LCPV system (having a lifetime of 25 years [24])
Period (year) 0 1 2 3 4 5 6 7 8Initial investment cost minus2084
Benefitslowastlowast 29043 29043 29043 29043 29043 29043 29043 29043O and M costlowastlowastlowast minus218 minus230 minus243 minus257 minus272 minus288 minus304 minus321
Discount rate 001 001 001 001 001 001 001 001 001Net cash flow 28825 28813 287995 28786 28771 28755 28739 28721119886 099 099 098 097 096 095 094 093 092Discounted net cash flow 28539 28245 27953 27662 27374 27089 26805 26524NPV minus17986 minus15162 minus12366 minus960 minus68626 minus41537 minus14732 11792lowastlowastBenefits are based on the tariff policy of Gujarat Electricity Regulatory Commission released for projects commissioned in 2012 [24]lowastlowastlowastEscalation in operating cost is taken as 572 annually [24]
300K325K
350K375K
0 2 4 6 8 100
005
01
015
02
025
03
Voltage (V)
Curr
ent (
A)
Figure 10 Variation of current-voltage characteristics with the celltemperature 119879119862
developed LCPV system of 1 kWP As the system presented inthis paper is very small for economic analysis the calculationsare done for 1 kWP system NPV method allows accountingfor the present value of annual capital expenditures andsavings during the lifetime of the system Net present value(NPV) includes sum of all the current values (costs are shownas negative and net savings are shown as positive) Foracceptance of any engineering project the positive NPV is
desiredThe formulas for calculatingNPVand correspondingfactor are given as [16]
NPV =
119899
sum
119894=1
(119861 minus 119862)119894
119886 =
1
(1 + 119894)
119901
(34)
where ldquo119886rdquo represents net present value factor ldquo119861rdquo representsgain ldquo119901rdquo represents the period and ldquo119894rdquo represents discountrate in the equation given previously
The initial investment cost is required in order to calculateNPV which includes module cost and balance of systems(BOS) cost The components of BOS include battery storagecharge controllers support structure tracking system andtransmission cables Cost of all these components is listedin Table 6 Using the initial investment cost and the formulaoutlined in (34) the NPV is calculated (Table 7) Operationandmaintenance (O andM) cost is taken as 075 of the totalinvestment cost with escalation in operating cost as 572 perannum [24] The feasibility of this project is demonstrated bya positive value of NPV obtained within 8 years
6 Conclusions
A theoretical model is used to perform electrical energy andexergy analyses of low-concentration photovoltaic (LCPV)system working under actual test conditions (ATC) Theexergy efficiency of LCPV system is in the range from51 to 482 with increasing rate of input exergy ratefrom 3081W to 9612W when concentration ratio changes
International Journal of Photoenergy 11
from 185 to 517 Sun Short-circuit current shows increasingtrend with increasing input exergy rate of asymp0011 AW Powerconversion efficiency decreases from 707 to 566 and open-circuit voltage decreases from986 to 824Vwith temperaturecoefficient of voltage asymp minus0021 VK under ATC The resultsconfirm that the commercially available silicon solar PVmodule performs satisfactorily under low concentration
Nomenclature
CR Concentration ratio119882 Width of the profile119863 Depth of the profile0119903 Rim angle120579119888 Acceptance angle119865 Focus point120588mirror Reflectivity of mirrors119877min Half width of the solar panel119871 Parabolic trough length120572 Absorption coefficient119860119886 Aperture area119896119861 Boltzmannrsquos constant (138 times 10minus23)119868PH Light generated current119868119878 Cell saturation or dark current119902 Electron charge (16 times 10minus19 C)119860 Ideality factor119880rad Radiative heat loss coefficient119880con Convective heat loss coefficient119879119862 Working temperature of solar cell (Kelvin)119877SH Shunt resistance119877119878 Series resistance119873119878 Series number of cells in a PV module119873119875 Parallel number of modules for a PV array119868SC Cellrsquos short-circuit current at 29814 K and
1 kWm2119870119868 Cellrsquos short-circuit current temperature
coefficient119879Ref Cellrsquos reference temperature120582 Solar insolation in kWm2119868RS Cellrsquos reverse saturation current at a
reference temperature and solar radiation119864119892 Band gap energy of the semiconductor119868mp Current at maximum power point119881mp Voltage at maximum power point
Acknowledgments
The authors acknowledge the financial support providedby Gujarat Energy Development Agency (GEDA) todevelop CPV system by Grant no GEDAECRECMarch-201039174 Authors also acknowledge WAAREE EnergiesPvt Ltd India for providing encapsulated crystallinesilicon solar PV modules for this study
References
[1] G Sala D Pachon I Anton and Test Test Rating andSpecification of PV Concentrator Components and Systems
(C-Rating Project) Book1 Classification of PV ConcentratorsUniversidad Politecnica de Madrid Madrid Spain 2002httpwwwies-defupmesiesCRATINGDocumentshtm
[2] M Yamaguchi andA Luque ldquoHigh efficiency and high concen-tration in photovoltaicsrdquo IEEE Transactions on Electron Devicesvol 46 no 10 pp 2139ndash2144 1999
[3] M A Green and A Ho-Baillie ldquoForty three per cent compositesplit-spectrum concentrator solar cell efficiencyrdquo Progress inPhotovoltaics vol 18 no 1 pp 42ndash47 2010
[4] H Cotal C Fetzer J Boisvert et al ldquoIII-V multijunction solarcells for concentrating photovoltaicsrdquo Energy and Environmen-tal Science vol 2 no 2 pp 174ndash192 2009
[5] G Sala I Anton J Monedero et al ldquoThe euclides-thermieconcentrator power plant in continuous operationrdquo in Proceed-ings of the 17th European Photovoltaic Solar Energy Conference(EUPVSEC rsquo01) pp 488ndash491 Munich Germany 2001
[6] V Garboushian S Yoon G Turner A Gunn and D FairldquoNovel high-concentration PV technology for cost competitiveutility bulk power generationrdquo in Proceedings of the 24th IEEEPhotovoltaic Specialists Conference Part 2 (of 2) pp 1060ndash1063December 1994
[7] M Castro I Anton and G Sala ldquoPilot production of concen-trator silicon solar cells approaching industrializationrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1697ndash17052008
[8] A Zahedi ldquoReview of modelling details in relation to low-concentration solar concentrating photovoltaicrdquoRenewable andSustainable Energy Reviews vol 15 no 3 pp 1609ndash1614 2011
[9] M Li X Ji G Li S Wei Y Li and F Shi ldquoPerformancestudy of solar cell arrays based on a trough concentratingphotovoltaicthermal systemrdquoApplied Energy vol 88 no 9 pp3218ndash3227 2011
[10] M A Schuetz K A Shell S A Brown G S Reinbolt RH French and R J Davis ldquoDesign and construction of a sim
7times low-concentration photovoltaic system based on compoundparabolic concentratorsrdquo IEEE Journal of Photovoltaics vol 2no 3 pp 382ndash386 2012
[11] H G Riveros and A I Oliva ldquoGraphical analysis of sunconcentrating collectorsrdquo Solar Energy vol 36 no 4 pp 313ndash322 1986
[12] O A Jaramillo J A Del Rıo and G Huelsz ldquoThermal study ofoptical fibres transmitting concentrated solar energyrdquo Journal ofPhysics D vol 32 no 9 pp 1000ndash1005 1999
[13] O A Jaramillo G Huelsz and J A Del Rıo ldquoA theoretical andexperimental thermal study of SiO2 optical fibres transmittingconcentrated radiative energyrdquo Journal of Physics D vol 35 no2 pp 95ndash102 2002
[14] C Kandilli and K Ulgen ldquoReview and modelling the systemsof transmission concentrated solar energy via optical fibresrdquoRenewable and Sustainable Energy Reviews vol 13 no 1 pp 67ndash84 2009
[15] A S Joshi I Dincer and B V Reddy ldquoThermodynamicassessment of photovoltaic systemsrdquo Solar Energy vol 83 no8 pp 1139ndash1149 2009
[16] C Kandilli ldquoPerformance analysis of novel concentrating solarphotovoltaic combined systemrdquo Energy Conversion and Man-agement vol 67 pp 186ndash196 2013
[17] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part I the concept of net exergyflow and the modeling of solar air heatersrdquo Solar Energy vol 41no 2 pp 127ndash132 1988
12 International Journal of Photoenergy
[18] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part 2 results of optimizationand analysis of sensibility to variations of operating conditionsrdquoSolar Energy vol 41 no 4 pp 309ndash317 1988
[19] S Farahat F Sarhaddi and H Ajam ldquoExergetic optimization offlat plate solar collectorsrdquo Renewable Energy vol 34 no 4 pp1169ndash1174 2009
[20] H Ajam S Farahat and F Sarhaddi ldquoExergetic optimizationof solar air heaters and comparison with energy analysisrdquoInternational Journal of Thermodynamics vol 8 no 4 pp 183ndash190 2005
[21] M J Kerr and A Cuevas ldquoGeneralized analysis of the illumi-nation intensity versus open-circuit voltage of solar cellsrdquo SolarEnergy vol 76 no 1ndash3 pp 263ndash267 2004
[22] E Radziemska and E Klugmann ldquoThermally affected parame-ters of the current-voltage characteristics of silicon photocellrdquoEnergy Conversion and Management vol 43 no 14 pp 1889ndash1900 2002
[23] E E van Dyk B J Scott E L Meyer and A W R LeitchldquoTemperature dependence of performance of crystalline siliconphotovoltaic modulesrdquo South African Journal of Science vol 96no 4 pp 198ndash200 2000
[24] httpwwwgercinorgrenewablepdfSolar20Tariff20Order20120of202012pdf 2013
[25] M Veerachary T Senjyu and K Uezato ldquoVoltage-basedmaximum power point tracking control of PV systemrdquo IEEETransactions on Aerospace and Electronic Systems vol 38 no1 pp 262ndash270 2002
[26] M Veerachary and K S Shinoy ldquoV2-based power tracking fornonlinear PV sourcesrdquo IEE Proceedings-Electric Power Applica-tions vol 152 no 5 pp 1263ndash1270 2005
[27] I S Kim and M J Youn ldquoVariable-structure observer for solararray current estimation in a photovoltaic power-generationsystemrdquo IEE Proceedings-Electric Power Applications vol 152no 4 pp 953ndash959 2005
[28] I S Kim M B Kim and M J Youn ldquoNew maximum powerpoint tracker using sliding-mode observer for estimation ofsolar array current in the grid-connected photovoltaic systemrdquoIEEE Transactions on Industrial Electronics vol 53 no 4 pp1027ndash1035 2006
[29] H L Tsai C S Tu and Y J Su ldquoDevelopment of generalizedphotovoltaic model using MATLABSIMULINKrdquo in Proceed-ings of theWorld Congress on Engineering and Computer ScienceSan Francisco NC USA October 2008
[30] J CThongpron K Kirtikara and C Jivacate ldquoAmethod for thedetermination of dynamic resistance of photovoltaic modulesunder illuminationrdquo Solar Energy Materials and Solar Cells vol90 no 18-19 pp 3078ndash3084 2006
[31] J C Wang J C Shieh Y L Su et al ldquoA novel method for thedetermination of dynamic resistance for photovoltaicmodulesrdquoEnergy vol 36 no 10 pp 5968ndash5974 2011
[32] S Dubey G S Sandhu andG N Tiwari ldquoAnalytical expressionfor electrical efficiency of PVT hybrid air collectorrdquo AppliedEnergy vol 86 no 5 pp 697ndash705 2009
[33] S Kumar P K Singh G S Chilana and S R Dhariwal ldquoGen-eration and recombination lifetime measurement in siliconwafers using impedance spectroscopyrdquo Semiconductor Scienceand Technology vol 24 no 9 Article ID 095001 pp 1ndash8 2009
[34] J Millman and C C Halkias Integrated Electronics McGraw-Hill New York NY USA 1972
[35] S Kumar P K Singh and G S Chilana ldquoStudy of siliconsolar cell at different intensities of illumination andwavelengthsusing impedance spectroscopyrdquo Solar Energy Materials andSolar Cells vol 93 no 10 pp 1881ndash1884 2009
[36] S Kumar V Sareen N Batra and P K Singh ldquoStudy of C-Vcharacteristics in thin n+-p-p+ silicon solar cells and inducedjunction n-p-p+ cell structuresrdquo Solar Energy Materials andSolar Cells vol 94 no 9 pp 1469ndash1472 2010
[37] I Mora-Sero G Garcia-Belmonte P P Boix M A Vazquezand J Bisquert ldquoImpedance spectroscopy characterisation ofhighly efficient silicon solar cells under different light illumina-tion intensitiesrdquo Energy and Environmental Science vol 2 no 6pp 678ndash686 2009
[38] F Sarhaddi S Farahat H Ajam andA Behzadmehr ldquoExergeticoptimization of a solar photovoltaic arrayrdquo Journal of Thermo-dynamics vol 2009 Article ID 313561 11 pages 2009
[39] S M Sze Physics of Semiconductor Devices Wiley New YorkNY USA 2nd edition 1981
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
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Carbohydrate Chemistry
International Journal of
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Journal of
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
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Analytical Methods in Chemistry
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Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Quantum Chemistry
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CatalystsJournal of
International Journal of Photoenergy 3
at front glass of LCPV module undergoes radiative andconvective losses which can be expressed in terms of heat losscoefficient 119880119892 (measured in terms of WK) [16]
119880119892 = 119880con + 119880rad (6)
After considering these heat losses the energy rate on thefront glass of LCPV module
119876119892 can be expressed as
119876119892 =
119876119891 minus 119880119892 (119879119892 minus 119879amb) (7)
Since the thickness of the glass is very small the conductionheat loss coefficient could be ignored for further calculationsThe incoming energy rate to LCPV module
119876in is given as
119876in =
119876119892120591 (8)
where 120591 represents transmission coefficient of front glass ofLCPV module
The output energy rate of LCPV module 119876out is calcu-
lated using the following expression [15]
119876out =
119876el + 119876th = 119881OC119868SC +
119876th (9)
where 119876el represents electrical output energy rate and
119876threpresents thermal output energy rate respectively Theenergy efficiency of LCPV system can be defined as theratio of output energy rate to the input energy rate Adetailed calculation of LCPV modulersquos electrical power con-version efficiency starting with terminal equation is given inSection 23
Similar expression for output exergy rate of LCPV systemis given as [15]
119864119909out =
119864119909el + 119864119909th +
119864119909des (10)
where 119864119909des =
119864119909desel + 119864119909desopt +
119864119909desΔ119879sun +
119864119909desΔ119879mod
which includes electrical exergy destruction rate (
119864119909desel)caused by series and shunt resistance losses [15] opticalexergy destruction rate (
119864119909desopt) caused by optical losses inLCPV module surface [17 18] thermal exergy destructionrate (
119864119909desΔ119879sun) caused by temperature difference between
LCPV module surface and the sun surface temperature [17ndash20] and thermal exergy destruction rate (
119864119909desΔ119879mod) caused
by temperature variation of LCPV module with respect toreference environmental state [19 20] The electrical exergydestruction rate is given as [15]
119864119909desel = 119881OC119868SC minus 119881mp119868mp (11)
In case of LCPVT systems thermal losses become thermalgain which is not in the scope of this paper (which deals withonly electrical energy and exergy analysis of LCPV system)Under this scenario in (10) the term representing exergydestruction rate is insignificant compared with electricalexergy rate (
119864119909el) and thermal exergy rate (
119864119909th) so the
effective expression for output exergy rate is given as [15]
119864119909out =
119864119909el plusmn 119864119909th
= 119881mp119868mp minus 119880119892119860 (119879119862 minus 119879amb) (1 minus119879amb119879119862
)
(12)
where the first term represents electrical exergy rate (119881mpand 119868mp being a voltage and current resp at maximumpower point of LCPV module) and the second term repre-sents thermal exergy rate due to the temperature differencebetween cell temperature and ambient temperature Thenegative sign with the second term in (12) corresponds tothe lost thermal exergy which would have been a gain incase of LCPVT system with a positive sign The inputexergy includes solar radiation intensity exergy which can beestimated by maximum efficiency ratio 120595 given by Petalarsquostheorem [16]
120595 = 1 +
1
3
(
119879amb119879sun
)
4
minus
4
3
119879amb119879sun
(13)
The input exergy rate to the PLPTC is found as [16]
119864119909in = 119866119887119860120595 (14)
The exergy efficiency of LCPV system is defined as ratio ofoutput exergy rate to the input exergy rate of the system [15]
120578ex =
119864119909out
119864119909in
=
119881mp119868mp minus 119880119892119860 (119879119862 minus 119879amb) (1 minus 119879amb119879119862)
1198661198871198601 + (13) (119879amb119879sun)4minus (43) (119879amb119879sun)
(15)
23 Model for Electrical Energy Analysis When a solar PVmodule is exposed to solar radiation it shows nonlinearcurrent-voltage characteristics The output current-voltagecharacteristic of solar PV module is mainly influenced bythe solar insolation and cell temperature There exist manymathematical models used for computer simulation whichdescribe the effect of solar insolation and cell temperatureon output current-voltage characteristics of solar PV module[21ndash23]
A crystalline silicon wafer-based solar photovoltaic (PV)cell of size 125mm times 125mm typically produces around25W at a voltage of 560mV These cells are connected inseries andor parallel configuration on a module to producerequired power The equivalent circuit for solar PV modulehaving 119873119875 numbers of cells arranged in parallel and 119873119878
number of cells arranged in series is shown in Figure 2The terminal equation for current and voltage of the
solar PV array is mentioned as follows as described by otherresearchers [25ndash28]
119868 = 119873119875119868PH minus 119873119875119868119878 [exp(119902 (119881119873119878 + 119868119877119878119873119875)
119896119861119879119862119860
) minus 1]
minus
(119873119875119881119873119878 + 119868119877119878)
119877SH
(16)
Ideally a solar PV module offers a low series resistance andhigh shunt resistance for higher solar energy conversion Insolar PV modules the PV cells are generally connected inseries in order to obtain adequate working voltage The solar
4 International Journal of Photoenergy
+
minus
RS
NS
NP
RSHNS
NP
NS
NP
NPIPH
I
Figure 2 The general model for solar PV module
PVmodules can be arranged in series-parallel combination tomake an array which produces desired power The current-voltage characteristic of such array is described by (16)Generally for the solar PVmodule 119868PH ≫ 119868119878 in (16) the smalldiode and ground-leakage currents can be ignored underzero-terminal voltage Therefore the short-circuit current isapproximately equal to the photocurrent The expression for119868PH is given by
119868PH = [119868SC + 119870119868 (119879119862 minus 119879Ref)] 120582 (17)
where 120582 = 120588mirror times CR times 119866119887 in Wm2 120588mirror representsreflection coefficient of mirrors
The photocurrent (119868PH) mainly depends on the solarinsolation and cellrsquos working temperature The saturationcurrent of a solar cell varies with the cell temperature whichis described by
119868119878 = 119868RS(119879119862
119879Ref)
3
exp[119902119864119892 (1119879Ref minus 1119879119862)
119896119861119860
] (18)
Reverse saturation current of the cell at reference temperaturedepends on the open-circuit voltage (119881OC) and can beapproximately obtained by following equation as given byTsai et al [29]
119868RS =119868SC
[exp (119902119881OC119873119878119896119861119860119879119862) minus 1]
(19)
The maximum power output of LCPV module is related tothe 119868SC and 119881OC by following
119875MAX = FF times 119881OC times 119868SC (20)
The values of 119868SC 119881OC and FF can be determined from the119868-119881 characteristics obtained by (16) The electrical powerconversion efficiency (120578) of LCPV module can be calculatedby the ratio of maximum output power generated by LCPVmodule to the input power carried by solar radiation (ie 120578 =
119875MAX120582)A solar PV module mainly consists of three types of
resistance series resistance (119877119878) shunt resistance (119877SH) anddynamic resistance (119903119889) The series resistance 119877119878 can be
determined by various illumination conditions such as darkconstant illumination and varying illumination and theyyield different results [30] The output impedance of solarPV module that is dynamic resistance is usually composedof the series resistance and shunt resistance In this paperdynamic resistance of LCPV module is quantified by usingdirect estimation method reported by Wang et al [31] Theequivalent circuit for solar PV module is shown in Figure 2
In order to estimate the dynamic resistance which isdefined as the negative reciprocal of 119889119868119889119881 (16) is differenti-ated with respect to 119881 that is
119889119868
119889119881
= minus
119873119875
119873119878119877SHminus
119889119868
119889119881
sdot
119877119878
119877SH
minus
119873119875119868119878119902
119896119879119862119860
[
1
119873119878
+
119889119868
119889119881
sdot
119877119878
119873119875
]
times exp [119902
119896119879119862119860
sdot (
119881
119873119878
+
119868119877119878
119873119875
)]
(21)
For the open-circuit condition and short-circuit conditions ofLCPVmodule the following two expressions are given usingthe slope of one 119868-119881 characteristics at the points (119881OC 0) and(0 119868SC) by
1198771199040 = minus(
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
)
minus1
(22)
119877sh0 = minus(
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
)
minus1
(23)
respectively When the load is disconnected from the LCPVmodule and the output current (119868) is equal to zero (21) canbe expressed by
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
= minus
119873119875
119873119878119877SHminus
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
sdot
119877119878
119877SH
minus
119873119875119868119878119902
119896119879119862119860
[
1
119873119878
+
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
sdot
119877119878
119873119875
]
times exp [119902
119896119879119862119860
sdot
119881
119873119878
]
(24)
Equation (24) is further simplified to
minus
1
119873119875119868119878
119896119879119862119860
119902
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
exp [minus119902
119896119879119862119860
sdot
119881OC119873119878
]
cong
1
119873119878
+
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
sdot
119877119878
119873119875
(25)
Therefore series resistance 119877119878 is expressed by
119877119878 =1198771199040119873119875
119873119878
minus
119896119879119862119860
119902119868119878
exp [minus119902
119896119879119862119860
sdot
119881OC119873119878
] (26)
International Journal of Photoenergy 5
Table 1 Simulation parameters for desired CR in developed LCPV system
Number ofmirrors Width119882 (m) Rim angle (0119903) Acceptance angle (120579119888) Length 119871 (m) Effective 119860119886 (m
2) CR Solar radiation (Wm2)
2 mirrors 027 1351∘ 317∘ 030 0054 185 12254 mirrors 045 2502∘ 307∘ 030 0108 356 22546 mirrors 062 3378∘ 294∘ 030 0159 472 32348 mirrors 079 4198∘ 280∘ 030 0211 517 3822
For short-circuit condition the output voltage of LCPVmodule is zero so (21) is reduced to
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
= minus
119873119875
119873119878119877SHminus
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
sdot
119877119878
119877SH
minus
119873119875119868119878119902
119896119879119862119860
[
1
119873119878
+
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
sdot
119877119878
119873119875
]
times exp [119902
119896119879119862119860
sdot (
119868SC119877119878119873119875
)]
(27)
Equation (27) can be further simplified as
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
= minus
119873119875
119873119878119877SHminus
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
sdot
119877119878
119877SH (28)
Therefore the shunt resistance can be expressed by
119877SH = minus
119873119878
119873119875
(
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
)
minus1
119877SH =
119873119878
119873119875
119877sh0
(29)
By analysis of (21) we conclude that the dynamic resistance ofLCPVmodule is dependent on the solar irradiance and solarPV module temperature
24 Statistical Analysis To compare the theoretical andobtained experimental results the correlation coefficient(119903) and root-mean square percent deviation (119890) have beenevaluated by using the following expressions [32]
119903 =
119873sum119883119894119884119894 minus (sum119883119894sum119884119894)
radic119873sum1198832119894minus (sum119883119894)
2radic119873sum119884
2119894minus (sum119884119894)
2
119890 =radic(sum 119890119894)
2
119873
(30)
where 119890119894 = [(119883119894 minus 119884119894)119883119894] times 100 The variables 119883119894 and 119884119894
represent theoretical and experimental data respectivelyThelinear coefficient of correlation (119903) which ranges betweenminus1 and 1 measures strength and the direction of a linearrelationship between two variables that is 119883119894 and 119884119894 The 119903value close to 1 indicates that two variables are in a strongpositive linear correlation
Figure 3 The constructed model of concentrator photovoltaic(CPV) system
3 LCPV Development and Validation of theProposed Model
31 System Development A MATLABSimulink computercode is developed using the mathematical model discussedin Section 2 to simulate LCPV system Table 1 shows theparameters used for calculating CR of the developed PLPTCThe CR depends on the effective aperture area which isgoverned by the number of mirrors used as reflectors FromTable 1 it is clear that by changing the number of mirrorsfrom 2 to 8 the geometric CR changes from sim2 to 8 Sun
A piecewise linear parabolic LCPV system is developed asshown in Figure 3 by using the modeling parameters listed inTable 1 The effective aperture area available using 8 mirrorsis 0211m2 and the effective receiver area is 0027m2 whichgives the geometric concentration ratio of sim8 The receiver ismade of a solar PV module fabricated by a string of sixteencommercially available silicon cell pieces (material mono-crystalline silicon size 14mm times 64mm efficiency sim14)The reason behind the selection of this specific size of thecells is to solve the current handling problem of the solarcells under concentration A typical solar cell of size 125mmtimes 125mm producing 25W at a voltage of 560mV wouldhave a current handling capability of around 45 A This cellwhen used under 10 Sun concentration may produce 45Acurrent by assuming a linear relationship between the currentincrement and CR But if the size of the cell is reduced to110th normal size then the current generated under 10 Sunconcentration would be less than or equal to 45 A thenit will be easily handled without damaging the solar cellcontacts The incident solar radiation is reflected by PLPTCand concentrated on the focal plane havingwidth of 064mm
6 International Journal of Photoenergy
Table 2 The parameters used for simulation under 1 Sun
Parametersunits 119877119878 (Ω) 119864119892 (eV) 119873119878 119873119875 119860 119879119862 (K) 119879ref (K) 119896119861 (JK) 119870119868 119902 (C) 119868SC (A) 119868RS (A) 119881OC (V)
For 1 Sun 0071 112 16 1 15 298 298 138 times 10
minus23065 times 10
minus31602 times 10
minus19 0259 086 times 10
minus12 986
Table 3 The value of 119877 119862 and corresponding 120591 obtained fromthe measured impedance spectra under different bias voltage con-ditions
Appliedvoltage(V)
Resistance inequivalent circuit
119877 (kΩ)
Capacitance inequivalent circuit
119862 (nF)
Timeconstant 120591
(ms)minus05 70 49 343minus02 55 514 2830 45 362 16302 37 351 13005 28 321 090
An active cooling mechanism is employed by flowing waterbehind the encapsulated solar PV module which is shown inFigure 3 By employing this mechanismmodule temperaturecould be lowered down to 45∘C A light dependent resistor(LDR) based one axis tracking system is developed for Suntracking with a provision of manual tracking on second axiswith an accuracy of plusmn3∘ as shown in Figure 3
32 Theory Validation and Characterization of LCPVModuleThe module characterization was done under standard testconditions (STC) by 119868-119881 characteristics impedance spec-troscopy (IS) and capacitance-voltage (CV) measurementand detailed parameters are given in Tables 2 and 3 Theconcentrated light is received by the solar PV module whichis placed at the focal plane of the PLPTC To simulate theelectrical power generated from this PV module the inputparameters are series resistance energy band gap number ofcells connected in series number of strings connected parallelto each other cell temperature ambient temperature short-circuit current ofmodule open-circuit voltage of themoduleand so on These input parameters are listed in Table 2
In this LCPV system a solar PV module manufacturedat WAAREE Energies Pvt Ltd module production line isused The open-circuit voltage and short-circuit current ofthis module aremeasured as119881OC = 986V and 119868SC = 0259Arespectively under AM15 spectrum at 29814 KThe current-voltage output characteristics of generalized solar PVmoduleunder AM15 solar spectrum are shown in Figure 4 In thesimulation short-circuit current open-circuit voltage seriesresistance and cell temperature measured under standardtest conditions (STC) by manufacturer are taken as inputparameters The current-voltage characteristic generatedfrom simulation programmatches well with the experimentalcurrent-voltage characteristic
Looking at the current-voltage curve it can be identifiedthat the photovoltaic module is a constant current source atlower values of voltage with current equal to the short-circuitcurrent (119868SC) With the further increase in voltage values the
0 2 4 6 8 100
005
01
015
02
025
03
Voltage (V)
Curr
ent (
A)
TheoreticalExperimental
e = 025 r = 0999
Figure 4 Current-voltage characteristics of the designed solar PVmodule under 1 Sun AM15 at 29814 K
current starts decreasing exponentially at certain point Thevalue of current becomes zero at open-circuit voltage (119881OC)The point where themodule operates at the highest efficiencyis called maximum power point (119875MAX)
For impedance measurements an ac signal having fre-quency in the range from 1 Hz to 01MHz with amplitudeof 5mV is used The impedance spectra were plotted in acomplex plane (ie 1198851015840 versus 119885
10158401015840 also known as Nyquistor ColendashCole plot [33]) which can provide information onany system that is composed of combination of interfacialand bulk process The measurements were carried out onthe developed LCPVmodule under forward and reverse bias(+05 V to minus05 V) conditions in the dark Figure 5 shows theimpedance spectrum of the LCPVmodule under reverse biasconditions (from 0 to minus05 V) The radius of the semicircleincreases with the increase in bias voltage as compared tozero bias demonstrating the bias dependence of resistanceand capacitance [33] The increase in the radius of semicircleduring reverse bias is observed due to expansion of depletionregion of the solar cell which increases the resistance offeredby the cell
Figure 6 shows the impedance spectrum under the for-ward bias conditions (from0 to 05V)where in contrast to thereverse bias opposite behavior is observed Here the radiusof the semicircle decreases with increasing positive bias fromits maximum value at zero bias The decrease in the radius ofsemicircle during forward bias is observed due to shrinking
International Journal of Photoenergy 7
0 2 4 6 8
times104
times104
0
05
1
15
2
25
3
35
Bias = 0VBias = minus02VBias = minus05V
Z998400 (Ohm)
Z998400998400
(Ohm
)
Figure 5 Impedance spectra of LCPV module under reverse biasconditions
times104
times104
0
05
1
15
2
25
Z998400 (Ohm)
Z998400998400
(Ohm
)
Bias = 0V
0 1 2 3 4 5
Bias = 02VBias = 05V
Figure 6 Impedance spectra of LCPV module under forward biasconditions
of depletion region of the solar cell which decreases theresistance offered by the cell
The ac equivalent circuit of the n+-p-p+structure underconsideration is shown in Figure 7 which incorporates thecapacitive effect owing to the excess minority carriers (119862119889commonly known as the diffusion capacitance) in parallelwith the depletion layer capacitance 119862119905 (Figure 7) Resistiveeffects arising from the minority carrier recombination areshown as the diffusion resistance (119877119889) in parallel with a shunt
RS
C = (Cd + Ct)
R = (RSH Rd)
Figure 7 The ac equivalent circuit of LCPV module to explainobserved impedance spectra
(119877SH) resistance and a series resistance 119877119878 connected in thecircuit [33]
Under forward bias condition due to the accumulationof minority carriers in the bulk the magnitude of thediffusion capacitance is large compared to the depletionregion capacitance [34] The ac impedance of the circuit isgiven by
119885 (120596) = 119885
1015840(120596) minus 119895119885
10158401015840(120596) (31)
where 119885
1015840 and 119885
10158401015840 are the magnitudes of the real andimaginary parts of impedance and a minus sign arises dueto capacitive reactance involved in the circuit On analyzingthe circuit 1198851015840 and 119885
10158401015840 can be written as
119885
1015840(120596) = 119877119904 +
119877
1 + (120596119877119862)
2
119885
10158401015840(120596) =
120596119862119877
2
1 + (120596119877119862)
2
(32)
For the case of very low 119877119878 when 119885
1015840 and 119885
10158401015840 are plotted ina complex plane by varying the frequency (120596) a semicircleof radius 1198772 with its center at (1198772 0) is obtained Furtherbecause of the semicircular geometry the maximum valueof 11988510158401015840 arises when 120596119898119877119862 = 1 where 120596119898 is the frequencyat which 119885
10158401015840 becomes maximum Thus we have that 119862 =
1120596119898119877 and the presence of 119877119878 shifts the semicircle byits value on the 119909-axis The analysis of the impedancediagram on the complex plane therefore gives values ofall the three parameters that is 119877 119862 and 119877119878 used in theequivalent circuit The product of resistance and capacitance(119877119862) represents the time constant (120591) The value of 119877 119862and corresponding 120591 obtained from themeasured impedancespectra under different bias voltage conditions is listed inTable 3These values are in good agreement with the existingliterature for silicon solar cells [33 35]
Capacitance-voltage (119862-119881) measurement is an importanttool to understand the transient behavior of a semiconductordevice Generally capacitance is measured in the reversedbias (Mott-Schottky) condition to determine barrier poten-tial and effective doping concentration Capacitance-voltagecharacterization is done for the developed LCPV module asshown in Figure 8
8 International Journal of Photoenergy
minus08 minus06 minus04 minus02 0 02 04 06 08Voltage (V)
times1014
0
05
1
15
2
25
3
1C
2(1F2)
Figure 8 The capacitance-voltage characterization of LCPV mod-ule
The dependence of barrier potential and doping concen-tration on the depletion region capacitance per unit area isgiven by [30]
1
1198622=
2
1199021198701205760119873
(119881bi minus 119881 minus
2119896119861119879
119902
)
119889 (1119862
2)
119889119881
= minus
2
1199021198701205760119873
(33)
where 119902 is the electron charge 119870 is dielectric constant ofsilicon 1205760 is the permittivity of free space 119881bi is barrierpotential 119896119861 is Boltzmannrsquos constant119879 is equal to 29814 K119873is doping concentration and 119881 represents applied potential
The slope and its intersection on the abscissa in theMott-Schottky plot shown in Figure 8 for the LCPV module givesthe doping concentration (119873) and barrier potential (119881bi)respectivelyThe119873 value is found as 779 times 1016 cmminus3 and thevalue of119881bi minus2119896119879119902 is equal to 056 eV which corresponds to119881bi = 061 eV The calculated values are in good agreementwith the reported values for commercially available siliconsolar cells [36 37]
4 LCPV Experiment under ATC
The experiments were carried out in the campus of Schoolof Solar Energy located in Gandhinagar India (Lat 2322∘Long 7268E) in the month of December (Year 2012) Themodule temperature was measured with the digital ther-mometer having an accuracy of plusmn01∘C during experimentswind speed was measured by anemometer as 085ms withan accuracy of plusmn5 Solar radiation and ambient temperaturewere recorded at the weather station located in the universitycampus The following parameters were measured duringexperiments ambient temperature solar radiation LCPVmodule and ambient temperature load current load voltageshort-circuit current and open-circuit voltage During theexperiments the module temperature was varied in the
range of 300ndash350K by controlling the flow rate of waterbehind the LCPV module Since the aim of this paper is toextract maximum electrical output from LCPV systems thethermodynamic analysis of flowingwater is avoided hereThecurrent-voltage measurements of an LCPV system are takenby Agilent SMU 6632B and by using multimeters and loadrheostat The sensitivity of the current-voltage measurementinstrument is given as plusmn3 The developed LCPV system isstudied by varying the number of reflecting mirrors arrangedin PLPTC
5 Result and Discussion
51 Exergy and Energy Analysis The effect of the lightconcentration and module temperature on the input exergyrate electrical exergy output rate and thermal exergy outputrate of LCPV module is estimated from the proposed modelin Section 2 It is found that with the increase in CR the inputexergy rate increases which results in increased amount ofenergy available to do useful work by the system The datalisted in Table 4 shows that the exergy efficiency decreaseswith the increase in the input exergy rate This decrease ismainly due to the increase in cell temperature which resultsin electrical exergy destruction with a rate of ldquo119881OC119868SC minus
119881mp119868mprdquo [38] Further the increase in the cell temperatureaffects 119881OC with a negative temperature coefficient as shownin the Figure 9 Figure 9 shows that 119881OC decreases from848V to 824V with increase in input exergy rate from3081W to 9612W when the cell temperature changesfrom 321 K to 3325 K The influence of the cell temperatureon exergy efficiency is clearly observed (Table 4) whichdecreases with the increase in the cell temperature Similareffect is observed by other researchers [15 38] Since the celltemperature changes with the increase in the input exergyrate it is imperative to design the LCPV system based on thisinformation so that useful exergy can bemaximized For thispurpose it is very important to track maximum power pointwhich depends on dynamic resistance of LCPV system
The proposed model in Section 2 is used to performenergy analysis of the LCPV module having 16 cells con-nected in series The static parameters (119868SC 119881OC 119875MAX and119877119878) of the LCPV module are measured in ATC conditionsas well as calculated by the proposed theoretical model Themeasured and simulated current-voltage characteristics ofLCPVmodule is shown in Figure 9 with varying input energyrate and corresponding temperature
It can be seen from Figure 9 that there is good agreementbetween the experimental and theoretical current-voltagecharacteristics which include 119868SC 119881OC 119875MAX 119877119878 FF 119903119889and efficiency The mean square of percentage deviation (119890)
is in the range of 274ndash843 and the linear coefficient ofcorrelation (119903) is in the range of 0995ndash0999
The measured values of solar irradiation 119868SC 119881OC 119875MAX119877119878 temperature FF 119903119889 and efficiency are listed in Table 5Generally the output current of the solar PV modulesincreases with the increase in input energy rate (ie solarirradiance received at focal point of PLPTC) With increasein the solar irradiance the higher number of photons strikes
International Journal of Photoenergy 9
Table 4 Exergy analysis of LCPV system
Solar irradiation(Wm2)
Cell temperature 119879119862 (K) Input exergy rate (W)Output exergy rate (W)
Exergy efficiency 120578ex ()Electricalexergy rate (W)
Thermal exergyrate (W)
1225 321 3081 2 043 5102254 328 5668 355 070 5033234 331 8133 491 083 5013822 3325 9612 554 091 482
Table 5 Parameter estimated from 119868-119881 curves plotted under various CR
Solarirradiation(Wm2)
Celltemperature
119879119862 (K)
Short-circuitcurrent 119868SC
(A)
Seriesresistance 119877119878
(Ω)
Dynamicresistance 119903119889
(Ω)
Open-circuitvoltage 119881OC
(V)
Maximumpower 119875MAX
(W)
Fill factor FF()
Energyefficiency 120578
()1000 298 025 112 1799 986 191 7458 7071225 321 033 120 1923 848 207 7397 6262254 328 063 129 2073 839 372 7037 6113234 331 091 139 2227 831 500 6700 5733822 3325 107 155 2484 824 584 6623 566
0 2 4 6 8 10Voltage (V)
Curr
ent (
A)
0
02
04
06
08
1
12
Simulation (2 mirrors)Experimental (2 mirrors)Simulation (4 mirrors)Experimental (4 mirrors)
Simulation (6 mirrors)Experimental (6 mirrors)Simulation (8 mirrors)Experimental (8 mirrors)
Figure 9 Simulated and experimental 119868-119881 characteristics of LCPVsystem under ATC
the solar PVmodule which results in enhanced electron-holepair production and higher photocurrent [39] The valuesof the dynamic resistance at MPP are computed using thevalues of 119868PH 119868SC and 119877119878 The dynamic resistance of LCPVmodule is calculated in an effective manner using (21) andis listed in Table 5 Approximate error between experimentaland theoretical dynamic resistance of the LCPV module isfound as sim13ndash21 which shows the uncertainty is wellwithin the practically acceptable limits
The plot shown in Figure 9 and extracted data listed inTable 5 describe the dependence of FF and efficiency of LCPV
module on the change in input energy rate and moduletemperature From the observed results it can be concludedthat the FF and efficiency of LCPV module decrease as theinput energy rate increasesThe decrease in FF and efficiencyof solar PV module with the increasing energy rate is highlydependent on the increase in electrical exergy destructionof LCPV module due to the increase in input energy rateand temperature As a result of increased input energy ratedynamic resistance offers greater resistive power losses inLCPV module and thus reduces its performance by reducingthe FF and efficiency The increase in the dynamic resistanceand reduction in the FF of LCPV module are foremostparameters for the decrease in the electrical energy efficiency
The effects of the cell temperature (119879119862) on 119868-119881 curveof LCPV module is estimated from the proposed model asshown in Figure 10 As the device temperature increasessmall increase in short-circuit current is observed how-ever the open-circuit voltage rapidly decreases due to theexponential dependence of the saturation current on thetemperature as given by (18) [39] In the actual experimentssimilar effect of temperature on open-circuit voltage (119881OC) isobserved and it is found that the 119881OC decreases from 986 to824V with temperature coefficient of voltage asymp minus0021 VKunder ATC as shown in Figure 9
A decrease in the 119875MAX with the increase in 119879119862 isobserved because with the increase in temperature the bandgap of the intrinsic semiconductor shrinks The increasedtemperature causes reduction in open-circuit voltage (119881OC)and the increase in the photocurrent for a given irradiancebecause of high injection of electrons from valance band toconduction band of semiconductor material [39]
52 Economical Analysis of LCPV System Net Present Value(NPV) method allows analyzing the economic aspects of anyengineering system and is used for the economic analysis of
10 International Journal of Photoenergy
Table 6 Cost of various components of LCPV system (asymp1 kWP) to find initial investment cost (numbers provided here are in accordancewith the current market price)lowast
Components Module BOSBattery Charge controller Support structure Tracker Cabling
Cost (in US$) 206 800 48 320 590 120Total initial investment cost (in US$) 2084
lowastThe price is based on market survey which may vary depending on specific location or company
Table 7 Economical analysis of LCPV system (having a lifetime of 25 years [24])
Period (year) 0 1 2 3 4 5 6 7 8Initial investment cost minus2084
Benefitslowastlowast 29043 29043 29043 29043 29043 29043 29043 29043O and M costlowastlowastlowast minus218 minus230 minus243 minus257 minus272 minus288 minus304 minus321
Discount rate 001 001 001 001 001 001 001 001 001Net cash flow 28825 28813 287995 28786 28771 28755 28739 28721119886 099 099 098 097 096 095 094 093 092Discounted net cash flow 28539 28245 27953 27662 27374 27089 26805 26524NPV minus17986 minus15162 minus12366 minus960 minus68626 minus41537 minus14732 11792lowastlowastBenefits are based on the tariff policy of Gujarat Electricity Regulatory Commission released for projects commissioned in 2012 [24]lowastlowastlowastEscalation in operating cost is taken as 572 annually [24]
300K325K
350K375K
0 2 4 6 8 100
005
01
015
02
025
03
Voltage (V)
Curr
ent (
A)
Figure 10 Variation of current-voltage characteristics with the celltemperature 119879119862
developed LCPV system of 1 kWP As the system presented inthis paper is very small for economic analysis the calculationsare done for 1 kWP system NPV method allows accountingfor the present value of annual capital expenditures andsavings during the lifetime of the system Net present value(NPV) includes sum of all the current values (costs are shownas negative and net savings are shown as positive) Foracceptance of any engineering project the positive NPV is
desiredThe formulas for calculatingNPVand correspondingfactor are given as [16]
NPV =
119899
sum
119894=1
(119861 minus 119862)119894
119886 =
1
(1 + 119894)
119901
(34)
where ldquo119886rdquo represents net present value factor ldquo119861rdquo representsgain ldquo119901rdquo represents the period and ldquo119894rdquo represents discountrate in the equation given previously
The initial investment cost is required in order to calculateNPV which includes module cost and balance of systems(BOS) cost The components of BOS include battery storagecharge controllers support structure tracking system andtransmission cables Cost of all these components is listedin Table 6 Using the initial investment cost and the formulaoutlined in (34) the NPV is calculated (Table 7) Operationandmaintenance (O andM) cost is taken as 075 of the totalinvestment cost with escalation in operating cost as 572 perannum [24] The feasibility of this project is demonstrated bya positive value of NPV obtained within 8 years
6 Conclusions
A theoretical model is used to perform electrical energy andexergy analyses of low-concentration photovoltaic (LCPV)system working under actual test conditions (ATC) Theexergy efficiency of LCPV system is in the range from51 to 482 with increasing rate of input exergy ratefrom 3081W to 9612W when concentration ratio changes
International Journal of Photoenergy 11
from 185 to 517 Sun Short-circuit current shows increasingtrend with increasing input exergy rate of asymp0011 AW Powerconversion efficiency decreases from 707 to 566 and open-circuit voltage decreases from986 to 824Vwith temperaturecoefficient of voltage asymp minus0021 VK under ATC The resultsconfirm that the commercially available silicon solar PVmodule performs satisfactorily under low concentration
Nomenclature
CR Concentration ratio119882 Width of the profile119863 Depth of the profile0119903 Rim angle120579119888 Acceptance angle119865 Focus point120588mirror Reflectivity of mirrors119877min Half width of the solar panel119871 Parabolic trough length120572 Absorption coefficient119860119886 Aperture area119896119861 Boltzmannrsquos constant (138 times 10minus23)119868PH Light generated current119868119878 Cell saturation or dark current119902 Electron charge (16 times 10minus19 C)119860 Ideality factor119880rad Radiative heat loss coefficient119880con Convective heat loss coefficient119879119862 Working temperature of solar cell (Kelvin)119877SH Shunt resistance119877119878 Series resistance119873119878 Series number of cells in a PV module119873119875 Parallel number of modules for a PV array119868SC Cellrsquos short-circuit current at 29814 K and
1 kWm2119870119868 Cellrsquos short-circuit current temperature
coefficient119879Ref Cellrsquos reference temperature120582 Solar insolation in kWm2119868RS Cellrsquos reverse saturation current at a
reference temperature and solar radiation119864119892 Band gap energy of the semiconductor119868mp Current at maximum power point119881mp Voltage at maximum power point
Acknowledgments
The authors acknowledge the financial support providedby Gujarat Energy Development Agency (GEDA) todevelop CPV system by Grant no GEDAECRECMarch-201039174 Authors also acknowledge WAAREE EnergiesPvt Ltd India for providing encapsulated crystallinesilicon solar PV modules for this study
References
[1] G Sala D Pachon I Anton and Test Test Rating andSpecification of PV Concentrator Components and Systems
(C-Rating Project) Book1 Classification of PV ConcentratorsUniversidad Politecnica de Madrid Madrid Spain 2002httpwwwies-defupmesiesCRATINGDocumentshtm
[2] M Yamaguchi andA Luque ldquoHigh efficiency and high concen-tration in photovoltaicsrdquo IEEE Transactions on Electron Devicesvol 46 no 10 pp 2139ndash2144 1999
[3] M A Green and A Ho-Baillie ldquoForty three per cent compositesplit-spectrum concentrator solar cell efficiencyrdquo Progress inPhotovoltaics vol 18 no 1 pp 42ndash47 2010
[4] H Cotal C Fetzer J Boisvert et al ldquoIII-V multijunction solarcells for concentrating photovoltaicsrdquo Energy and Environmen-tal Science vol 2 no 2 pp 174ndash192 2009
[5] G Sala I Anton J Monedero et al ldquoThe euclides-thermieconcentrator power plant in continuous operationrdquo in Proceed-ings of the 17th European Photovoltaic Solar Energy Conference(EUPVSEC rsquo01) pp 488ndash491 Munich Germany 2001
[6] V Garboushian S Yoon G Turner A Gunn and D FairldquoNovel high-concentration PV technology for cost competitiveutility bulk power generationrdquo in Proceedings of the 24th IEEEPhotovoltaic Specialists Conference Part 2 (of 2) pp 1060ndash1063December 1994
[7] M Castro I Anton and G Sala ldquoPilot production of concen-trator silicon solar cells approaching industrializationrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1697ndash17052008
[8] A Zahedi ldquoReview of modelling details in relation to low-concentration solar concentrating photovoltaicrdquoRenewable andSustainable Energy Reviews vol 15 no 3 pp 1609ndash1614 2011
[9] M Li X Ji G Li S Wei Y Li and F Shi ldquoPerformancestudy of solar cell arrays based on a trough concentratingphotovoltaicthermal systemrdquoApplied Energy vol 88 no 9 pp3218ndash3227 2011
[10] M A Schuetz K A Shell S A Brown G S Reinbolt RH French and R J Davis ldquoDesign and construction of a sim
7times low-concentration photovoltaic system based on compoundparabolic concentratorsrdquo IEEE Journal of Photovoltaics vol 2no 3 pp 382ndash386 2012
[11] H G Riveros and A I Oliva ldquoGraphical analysis of sunconcentrating collectorsrdquo Solar Energy vol 36 no 4 pp 313ndash322 1986
[12] O A Jaramillo J A Del Rıo and G Huelsz ldquoThermal study ofoptical fibres transmitting concentrated solar energyrdquo Journal ofPhysics D vol 32 no 9 pp 1000ndash1005 1999
[13] O A Jaramillo G Huelsz and J A Del Rıo ldquoA theoretical andexperimental thermal study of SiO2 optical fibres transmittingconcentrated radiative energyrdquo Journal of Physics D vol 35 no2 pp 95ndash102 2002
[14] C Kandilli and K Ulgen ldquoReview and modelling the systemsof transmission concentrated solar energy via optical fibresrdquoRenewable and Sustainable Energy Reviews vol 13 no 1 pp 67ndash84 2009
[15] A S Joshi I Dincer and B V Reddy ldquoThermodynamicassessment of photovoltaic systemsrdquo Solar Energy vol 83 no8 pp 1139ndash1149 2009
[16] C Kandilli ldquoPerformance analysis of novel concentrating solarphotovoltaic combined systemrdquo Energy Conversion and Man-agement vol 67 pp 186ndash196 2013
[17] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part I the concept of net exergyflow and the modeling of solar air heatersrdquo Solar Energy vol 41no 2 pp 127ndash132 1988
12 International Journal of Photoenergy
[18] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part 2 results of optimizationand analysis of sensibility to variations of operating conditionsrdquoSolar Energy vol 41 no 4 pp 309ndash317 1988
[19] S Farahat F Sarhaddi and H Ajam ldquoExergetic optimization offlat plate solar collectorsrdquo Renewable Energy vol 34 no 4 pp1169ndash1174 2009
[20] H Ajam S Farahat and F Sarhaddi ldquoExergetic optimizationof solar air heaters and comparison with energy analysisrdquoInternational Journal of Thermodynamics vol 8 no 4 pp 183ndash190 2005
[21] M J Kerr and A Cuevas ldquoGeneralized analysis of the illumi-nation intensity versus open-circuit voltage of solar cellsrdquo SolarEnergy vol 76 no 1ndash3 pp 263ndash267 2004
[22] E Radziemska and E Klugmann ldquoThermally affected parame-ters of the current-voltage characteristics of silicon photocellrdquoEnergy Conversion and Management vol 43 no 14 pp 1889ndash1900 2002
[23] E E van Dyk B J Scott E L Meyer and A W R LeitchldquoTemperature dependence of performance of crystalline siliconphotovoltaic modulesrdquo South African Journal of Science vol 96no 4 pp 198ndash200 2000
[24] httpwwwgercinorgrenewablepdfSolar20Tariff20Order20120of202012pdf 2013
[25] M Veerachary T Senjyu and K Uezato ldquoVoltage-basedmaximum power point tracking control of PV systemrdquo IEEETransactions on Aerospace and Electronic Systems vol 38 no1 pp 262ndash270 2002
[26] M Veerachary and K S Shinoy ldquoV2-based power tracking fornonlinear PV sourcesrdquo IEE Proceedings-Electric Power Applica-tions vol 152 no 5 pp 1263ndash1270 2005
[27] I S Kim and M J Youn ldquoVariable-structure observer for solararray current estimation in a photovoltaic power-generationsystemrdquo IEE Proceedings-Electric Power Applications vol 152no 4 pp 953ndash959 2005
[28] I S Kim M B Kim and M J Youn ldquoNew maximum powerpoint tracker using sliding-mode observer for estimation ofsolar array current in the grid-connected photovoltaic systemrdquoIEEE Transactions on Industrial Electronics vol 53 no 4 pp1027ndash1035 2006
[29] H L Tsai C S Tu and Y J Su ldquoDevelopment of generalizedphotovoltaic model using MATLABSIMULINKrdquo in Proceed-ings of theWorld Congress on Engineering and Computer ScienceSan Francisco NC USA October 2008
[30] J CThongpron K Kirtikara and C Jivacate ldquoAmethod for thedetermination of dynamic resistance of photovoltaic modulesunder illuminationrdquo Solar Energy Materials and Solar Cells vol90 no 18-19 pp 3078ndash3084 2006
[31] J C Wang J C Shieh Y L Su et al ldquoA novel method for thedetermination of dynamic resistance for photovoltaicmodulesrdquoEnergy vol 36 no 10 pp 5968ndash5974 2011
[32] S Dubey G S Sandhu andG N Tiwari ldquoAnalytical expressionfor electrical efficiency of PVT hybrid air collectorrdquo AppliedEnergy vol 86 no 5 pp 697ndash705 2009
[33] S Kumar P K Singh G S Chilana and S R Dhariwal ldquoGen-eration and recombination lifetime measurement in siliconwafers using impedance spectroscopyrdquo Semiconductor Scienceand Technology vol 24 no 9 Article ID 095001 pp 1ndash8 2009
[34] J Millman and C C Halkias Integrated Electronics McGraw-Hill New York NY USA 1972
[35] S Kumar P K Singh and G S Chilana ldquoStudy of siliconsolar cell at different intensities of illumination andwavelengthsusing impedance spectroscopyrdquo Solar Energy Materials andSolar Cells vol 93 no 10 pp 1881ndash1884 2009
[36] S Kumar V Sareen N Batra and P K Singh ldquoStudy of C-Vcharacteristics in thin n+-p-p+ silicon solar cells and inducedjunction n-p-p+ cell structuresrdquo Solar Energy Materials andSolar Cells vol 94 no 9 pp 1469ndash1472 2010
[37] I Mora-Sero G Garcia-Belmonte P P Boix M A Vazquezand J Bisquert ldquoImpedance spectroscopy characterisation ofhighly efficient silicon solar cells under different light illumina-tion intensitiesrdquo Energy and Environmental Science vol 2 no 6pp 678ndash686 2009
[38] F Sarhaddi S Farahat H Ajam andA Behzadmehr ldquoExergeticoptimization of a solar photovoltaic arrayrdquo Journal of Thermo-dynamics vol 2009 Article ID 313561 11 pages 2009
[39] S M Sze Physics of Semiconductor Devices Wiley New YorkNY USA 2nd edition 1981
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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CatalystsJournal of
4 International Journal of Photoenergy
+
minus
RS
NS
NP
RSHNS
NP
NS
NP
NPIPH
I
Figure 2 The general model for solar PV module
PVmodules can be arranged in series-parallel combination tomake an array which produces desired power The current-voltage characteristic of such array is described by (16)Generally for the solar PVmodule 119868PH ≫ 119868119878 in (16) the smalldiode and ground-leakage currents can be ignored underzero-terminal voltage Therefore the short-circuit current isapproximately equal to the photocurrent The expression for119868PH is given by
119868PH = [119868SC + 119870119868 (119879119862 minus 119879Ref)] 120582 (17)
where 120582 = 120588mirror times CR times 119866119887 in Wm2 120588mirror representsreflection coefficient of mirrors
The photocurrent (119868PH) mainly depends on the solarinsolation and cellrsquos working temperature The saturationcurrent of a solar cell varies with the cell temperature whichis described by
119868119878 = 119868RS(119879119862
119879Ref)
3
exp[119902119864119892 (1119879Ref minus 1119879119862)
119896119861119860
] (18)
Reverse saturation current of the cell at reference temperaturedepends on the open-circuit voltage (119881OC) and can beapproximately obtained by following equation as given byTsai et al [29]
119868RS =119868SC
[exp (119902119881OC119873119878119896119861119860119879119862) minus 1]
(19)
The maximum power output of LCPV module is related tothe 119868SC and 119881OC by following
119875MAX = FF times 119881OC times 119868SC (20)
The values of 119868SC 119881OC and FF can be determined from the119868-119881 characteristics obtained by (16) The electrical powerconversion efficiency (120578) of LCPV module can be calculatedby the ratio of maximum output power generated by LCPVmodule to the input power carried by solar radiation (ie 120578 =
119875MAX120582)A solar PV module mainly consists of three types of
resistance series resistance (119877119878) shunt resistance (119877SH) anddynamic resistance (119903119889) The series resistance 119877119878 can be
determined by various illumination conditions such as darkconstant illumination and varying illumination and theyyield different results [30] The output impedance of solarPV module that is dynamic resistance is usually composedof the series resistance and shunt resistance In this paperdynamic resistance of LCPV module is quantified by usingdirect estimation method reported by Wang et al [31] Theequivalent circuit for solar PV module is shown in Figure 2
In order to estimate the dynamic resistance which isdefined as the negative reciprocal of 119889119868119889119881 (16) is differenti-ated with respect to 119881 that is
119889119868
119889119881
= minus
119873119875
119873119878119877SHminus
119889119868
119889119881
sdot
119877119878
119877SH
minus
119873119875119868119878119902
119896119879119862119860
[
1
119873119878
+
119889119868
119889119881
sdot
119877119878
119873119875
]
times exp [119902
119896119879119862119860
sdot (
119881
119873119878
+
119868119877119878
119873119875
)]
(21)
For the open-circuit condition and short-circuit conditions ofLCPVmodule the following two expressions are given usingthe slope of one 119868-119881 characteristics at the points (119881OC 0) and(0 119868SC) by
1198771199040 = minus(
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
)
minus1
(22)
119877sh0 = minus(
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
)
minus1
(23)
respectively When the load is disconnected from the LCPVmodule and the output current (119868) is equal to zero (21) canbe expressed by
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
= minus
119873119875
119873119878119877SHminus
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
sdot
119877119878
119877SH
minus
119873119875119868119878119902
119896119879119862119860
[
1
119873119878
+
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
sdot
119877119878
119873119875
]
times exp [119902
119896119879119862119860
sdot
119881
119873119878
]
(24)
Equation (24) is further simplified to
minus
1
119873119875119868119878
119896119879119862119860
119902
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
exp [minus119902
119896119879119862119860
sdot
119881OC119873119878
]
cong
1
119873119878
+
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119881=119881OC
sdot
119877119878
119873119875
(25)
Therefore series resistance 119877119878 is expressed by
119877119878 =1198771199040119873119875
119873119878
minus
119896119879119862119860
119902119868119878
exp [minus119902
119896119879119862119860
sdot
119881OC119873119878
] (26)
International Journal of Photoenergy 5
Table 1 Simulation parameters for desired CR in developed LCPV system
Number ofmirrors Width119882 (m) Rim angle (0119903) Acceptance angle (120579119888) Length 119871 (m) Effective 119860119886 (m
2) CR Solar radiation (Wm2)
2 mirrors 027 1351∘ 317∘ 030 0054 185 12254 mirrors 045 2502∘ 307∘ 030 0108 356 22546 mirrors 062 3378∘ 294∘ 030 0159 472 32348 mirrors 079 4198∘ 280∘ 030 0211 517 3822
For short-circuit condition the output voltage of LCPVmodule is zero so (21) is reduced to
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
= minus
119873119875
119873119878119877SHminus
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
sdot
119877119878
119877SH
minus
119873119875119868119878119902
119896119879119862119860
[
1
119873119878
+
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
sdot
119877119878
119873119875
]
times exp [119902
119896119879119862119860
sdot (
119868SC119877119878119873119875
)]
(27)
Equation (27) can be further simplified as
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
= minus
119873119875
119873119878119877SHminus
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
sdot
119877119878
119877SH (28)
Therefore the shunt resistance can be expressed by
119877SH = minus
119873119878
119873119875
(
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
)
minus1
119877SH =
119873119878
119873119875
119877sh0
(29)
By analysis of (21) we conclude that the dynamic resistance ofLCPVmodule is dependent on the solar irradiance and solarPV module temperature
24 Statistical Analysis To compare the theoretical andobtained experimental results the correlation coefficient(119903) and root-mean square percent deviation (119890) have beenevaluated by using the following expressions [32]
119903 =
119873sum119883119894119884119894 minus (sum119883119894sum119884119894)
radic119873sum1198832119894minus (sum119883119894)
2radic119873sum119884
2119894minus (sum119884119894)
2
119890 =radic(sum 119890119894)
2
119873
(30)
where 119890119894 = [(119883119894 minus 119884119894)119883119894] times 100 The variables 119883119894 and 119884119894
represent theoretical and experimental data respectivelyThelinear coefficient of correlation (119903) which ranges betweenminus1 and 1 measures strength and the direction of a linearrelationship between two variables that is 119883119894 and 119884119894 The 119903value close to 1 indicates that two variables are in a strongpositive linear correlation
Figure 3 The constructed model of concentrator photovoltaic(CPV) system
3 LCPV Development and Validation of theProposed Model
31 System Development A MATLABSimulink computercode is developed using the mathematical model discussedin Section 2 to simulate LCPV system Table 1 shows theparameters used for calculating CR of the developed PLPTCThe CR depends on the effective aperture area which isgoverned by the number of mirrors used as reflectors FromTable 1 it is clear that by changing the number of mirrorsfrom 2 to 8 the geometric CR changes from sim2 to 8 Sun
A piecewise linear parabolic LCPV system is developed asshown in Figure 3 by using the modeling parameters listed inTable 1 The effective aperture area available using 8 mirrorsis 0211m2 and the effective receiver area is 0027m2 whichgives the geometric concentration ratio of sim8 The receiver ismade of a solar PV module fabricated by a string of sixteencommercially available silicon cell pieces (material mono-crystalline silicon size 14mm times 64mm efficiency sim14)The reason behind the selection of this specific size of thecells is to solve the current handling problem of the solarcells under concentration A typical solar cell of size 125mmtimes 125mm producing 25W at a voltage of 560mV wouldhave a current handling capability of around 45 A This cellwhen used under 10 Sun concentration may produce 45Acurrent by assuming a linear relationship between the currentincrement and CR But if the size of the cell is reduced to110th normal size then the current generated under 10 Sunconcentration would be less than or equal to 45 A thenit will be easily handled without damaging the solar cellcontacts The incident solar radiation is reflected by PLPTCand concentrated on the focal plane havingwidth of 064mm
6 International Journal of Photoenergy
Table 2 The parameters used for simulation under 1 Sun
Parametersunits 119877119878 (Ω) 119864119892 (eV) 119873119878 119873119875 119860 119879119862 (K) 119879ref (K) 119896119861 (JK) 119870119868 119902 (C) 119868SC (A) 119868RS (A) 119881OC (V)
For 1 Sun 0071 112 16 1 15 298 298 138 times 10
minus23065 times 10
minus31602 times 10
minus19 0259 086 times 10
minus12 986
Table 3 The value of 119877 119862 and corresponding 120591 obtained fromthe measured impedance spectra under different bias voltage con-ditions
Appliedvoltage(V)
Resistance inequivalent circuit
119877 (kΩ)
Capacitance inequivalent circuit
119862 (nF)
Timeconstant 120591
(ms)minus05 70 49 343minus02 55 514 2830 45 362 16302 37 351 13005 28 321 090
An active cooling mechanism is employed by flowing waterbehind the encapsulated solar PV module which is shown inFigure 3 By employing this mechanismmodule temperaturecould be lowered down to 45∘C A light dependent resistor(LDR) based one axis tracking system is developed for Suntracking with a provision of manual tracking on second axiswith an accuracy of plusmn3∘ as shown in Figure 3
32 Theory Validation and Characterization of LCPVModuleThe module characterization was done under standard testconditions (STC) by 119868-119881 characteristics impedance spec-troscopy (IS) and capacitance-voltage (CV) measurementand detailed parameters are given in Tables 2 and 3 Theconcentrated light is received by the solar PV module whichis placed at the focal plane of the PLPTC To simulate theelectrical power generated from this PV module the inputparameters are series resistance energy band gap number ofcells connected in series number of strings connected parallelto each other cell temperature ambient temperature short-circuit current ofmodule open-circuit voltage of themoduleand so on These input parameters are listed in Table 2
In this LCPV system a solar PV module manufacturedat WAAREE Energies Pvt Ltd module production line isused The open-circuit voltage and short-circuit current ofthis module aremeasured as119881OC = 986V and 119868SC = 0259Arespectively under AM15 spectrum at 29814 KThe current-voltage output characteristics of generalized solar PVmoduleunder AM15 solar spectrum are shown in Figure 4 In thesimulation short-circuit current open-circuit voltage seriesresistance and cell temperature measured under standardtest conditions (STC) by manufacturer are taken as inputparameters The current-voltage characteristic generatedfrom simulation programmatches well with the experimentalcurrent-voltage characteristic
Looking at the current-voltage curve it can be identifiedthat the photovoltaic module is a constant current source atlower values of voltage with current equal to the short-circuitcurrent (119868SC) With the further increase in voltage values the
0 2 4 6 8 100
005
01
015
02
025
03
Voltage (V)
Curr
ent (
A)
TheoreticalExperimental
e = 025 r = 0999
Figure 4 Current-voltage characteristics of the designed solar PVmodule under 1 Sun AM15 at 29814 K
current starts decreasing exponentially at certain point Thevalue of current becomes zero at open-circuit voltage (119881OC)The point where themodule operates at the highest efficiencyis called maximum power point (119875MAX)
For impedance measurements an ac signal having fre-quency in the range from 1 Hz to 01MHz with amplitudeof 5mV is used The impedance spectra were plotted in acomplex plane (ie 1198851015840 versus 119885
10158401015840 also known as Nyquistor ColendashCole plot [33]) which can provide information onany system that is composed of combination of interfacialand bulk process The measurements were carried out onthe developed LCPVmodule under forward and reverse bias(+05 V to minus05 V) conditions in the dark Figure 5 shows theimpedance spectrum of the LCPVmodule under reverse biasconditions (from 0 to minus05 V) The radius of the semicircleincreases with the increase in bias voltage as compared tozero bias demonstrating the bias dependence of resistanceand capacitance [33] The increase in the radius of semicircleduring reverse bias is observed due to expansion of depletionregion of the solar cell which increases the resistance offeredby the cell
Figure 6 shows the impedance spectrum under the for-ward bias conditions (from0 to 05V)where in contrast to thereverse bias opposite behavior is observed Here the radiusof the semicircle decreases with increasing positive bias fromits maximum value at zero bias The decrease in the radius ofsemicircle during forward bias is observed due to shrinking
International Journal of Photoenergy 7
0 2 4 6 8
times104
times104
0
05
1
15
2
25
3
35
Bias = 0VBias = minus02VBias = minus05V
Z998400 (Ohm)
Z998400998400
(Ohm
)
Figure 5 Impedance spectra of LCPV module under reverse biasconditions
times104
times104
0
05
1
15
2
25
Z998400 (Ohm)
Z998400998400
(Ohm
)
Bias = 0V
0 1 2 3 4 5
Bias = 02VBias = 05V
Figure 6 Impedance spectra of LCPV module under forward biasconditions
of depletion region of the solar cell which decreases theresistance offered by the cell
The ac equivalent circuit of the n+-p-p+structure underconsideration is shown in Figure 7 which incorporates thecapacitive effect owing to the excess minority carriers (119862119889commonly known as the diffusion capacitance) in parallelwith the depletion layer capacitance 119862119905 (Figure 7) Resistiveeffects arising from the minority carrier recombination areshown as the diffusion resistance (119877119889) in parallel with a shunt
RS
C = (Cd + Ct)
R = (RSH Rd)
Figure 7 The ac equivalent circuit of LCPV module to explainobserved impedance spectra
(119877SH) resistance and a series resistance 119877119878 connected in thecircuit [33]
Under forward bias condition due to the accumulationof minority carriers in the bulk the magnitude of thediffusion capacitance is large compared to the depletionregion capacitance [34] The ac impedance of the circuit isgiven by
119885 (120596) = 119885
1015840(120596) minus 119895119885
10158401015840(120596) (31)
where 119885
1015840 and 119885
10158401015840 are the magnitudes of the real andimaginary parts of impedance and a minus sign arises dueto capacitive reactance involved in the circuit On analyzingthe circuit 1198851015840 and 119885
10158401015840 can be written as
119885
1015840(120596) = 119877119904 +
119877
1 + (120596119877119862)
2
119885
10158401015840(120596) =
120596119862119877
2
1 + (120596119877119862)
2
(32)
For the case of very low 119877119878 when 119885
1015840 and 119885
10158401015840 are plotted ina complex plane by varying the frequency (120596) a semicircleof radius 1198772 with its center at (1198772 0) is obtained Furtherbecause of the semicircular geometry the maximum valueof 11988510158401015840 arises when 120596119898119877119862 = 1 where 120596119898 is the frequencyat which 119885
10158401015840 becomes maximum Thus we have that 119862 =
1120596119898119877 and the presence of 119877119878 shifts the semicircle byits value on the 119909-axis The analysis of the impedancediagram on the complex plane therefore gives values ofall the three parameters that is 119877 119862 and 119877119878 used in theequivalent circuit The product of resistance and capacitance(119877119862) represents the time constant (120591) The value of 119877 119862and corresponding 120591 obtained from themeasured impedancespectra under different bias voltage conditions is listed inTable 3These values are in good agreement with the existingliterature for silicon solar cells [33 35]
Capacitance-voltage (119862-119881) measurement is an importanttool to understand the transient behavior of a semiconductordevice Generally capacitance is measured in the reversedbias (Mott-Schottky) condition to determine barrier poten-tial and effective doping concentration Capacitance-voltagecharacterization is done for the developed LCPV module asshown in Figure 8
8 International Journal of Photoenergy
minus08 minus06 minus04 minus02 0 02 04 06 08Voltage (V)
times1014
0
05
1
15
2
25
3
1C
2(1F2)
Figure 8 The capacitance-voltage characterization of LCPV mod-ule
The dependence of barrier potential and doping concen-tration on the depletion region capacitance per unit area isgiven by [30]
1
1198622=
2
1199021198701205760119873
(119881bi minus 119881 minus
2119896119861119879
119902
)
119889 (1119862
2)
119889119881
= minus
2
1199021198701205760119873
(33)
where 119902 is the electron charge 119870 is dielectric constant ofsilicon 1205760 is the permittivity of free space 119881bi is barrierpotential 119896119861 is Boltzmannrsquos constant119879 is equal to 29814 K119873is doping concentration and 119881 represents applied potential
The slope and its intersection on the abscissa in theMott-Schottky plot shown in Figure 8 for the LCPV module givesthe doping concentration (119873) and barrier potential (119881bi)respectivelyThe119873 value is found as 779 times 1016 cmminus3 and thevalue of119881bi minus2119896119879119902 is equal to 056 eV which corresponds to119881bi = 061 eV The calculated values are in good agreementwith the reported values for commercially available siliconsolar cells [36 37]
4 LCPV Experiment under ATC
The experiments were carried out in the campus of Schoolof Solar Energy located in Gandhinagar India (Lat 2322∘Long 7268E) in the month of December (Year 2012) Themodule temperature was measured with the digital ther-mometer having an accuracy of plusmn01∘C during experimentswind speed was measured by anemometer as 085ms withan accuracy of plusmn5 Solar radiation and ambient temperaturewere recorded at the weather station located in the universitycampus The following parameters were measured duringexperiments ambient temperature solar radiation LCPVmodule and ambient temperature load current load voltageshort-circuit current and open-circuit voltage During theexperiments the module temperature was varied in the
range of 300ndash350K by controlling the flow rate of waterbehind the LCPV module Since the aim of this paper is toextract maximum electrical output from LCPV systems thethermodynamic analysis of flowingwater is avoided hereThecurrent-voltage measurements of an LCPV system are takenby Agilent SMU 6632B and by using multimeters and loadrheostat The sensitivity of the current-voltage measurementinstrument is given as plusmn3 The developed LCPV system isstudied by varying the number of reflecting mirrors arrangedin PLPTC
5 Result and Discussion
51 Exergy and Energy Analysis The effect of the lightconcentration and module temperature on the input exergyrate electrical exergy output rate and thermal exergy outputrate of LCPV module is estimated from the proposed modelin Section 2 It is found that with the increase in CR the inputexergy rate increases which results in increased amount ofenergy available to do useful work by the system The datalisted in Table 4 shows that the exergy efficiency decreaseswith the increase in the input exergy rate This decrease ismainly due to the increase in cell temperature which resultsin electrical exergy destruction with a rate of ldquo119881OC119868SC minus
119881mp119868mprdquo [38] Further the increase in the cell temperatureaffects 119881OC with a negative temperature coefficient as shownin the Figure 9 Figure 9 shows that 119881OC decreases from848V to 824V with increase in input exergy rate from3081W to 9612W when the cell temperature changesfrom 321 K to 3325 K The influence of the cell temperatureon exergy efficiency is clearly observed (Table 4) whichdecreases with the increase in the cell temperature Similareffect is observed by other researchers [15 38] Since the celltemperature changes with the increase in the input exergyrate it is imperative to design the LCPV system based on thisinformation so that useful exergy can bemaximized For thispurpose it is very important to track maximum power pointwhich depends on dynamic resistance of LCPV system
The proposed model in Section 2 is used to performenergy analysis of the LCPV module having 16 cells con-nected in series The static parameters (119868SC 119881OC 119875MAX and119877119878) of the LCPV module are measured in ATC conditionsas well as calculated by the proposed theoretical model Themeasured and simulated current-voltage characteristics ofLCPVmodule is shown in Figure 9 with varying input energyrate and corresponding temperature
It can be seen from Figure 9 that there is good agreementbetween the experimental and theoretical current-voltagecharacteristics which include 119868SC 119881OC 119875MAX 119877119878 FF 119903119889and efficiency The mean square of percentage deviation (119890)
is in the range of 274ndash843 and the linear coefficient ofcorrelation (119903) is in the range of 0995ndash0999
The measured values of solar irradiation 119868SC 119881OC 119875MAX119877119878 temperature FF 119903119889 and efficiency are listed in Table 5Generally the output current of the solar PV modulesincreases with the increase in input energy rate (ie solarirradiance received at focal point of PLPTC) With increasein the solar irradiance the higher number of photons strikes
International Journal of Photoenergy 9
Table 4 Exergy analysis of LCPV system
Solar irradiation(Wm2)
Cell temperature 119879119862 (K) Input exergy rate (W)Output exergy rate (W)
Exergy efficiency 120578ex ()Electricalexergy rate (W)
Thermal exergyrate (W)
1225 321 3081 2 043 5102254 328 5668 355 070 5033234 331 8133 491 083 5013822 3325 9612 554 091 482
Table 5 Parameter estimated from 119868-119881 curves plotted under various CR
Solarirradiation(Wm2)
Celltemperature
119879119862 (K)
Short-circuitcurrent 119868SC
(A)
Seriesresistance 119877119878
(Ω)
Dynamicresistance 119903119889
(Ω)
Open-circuitvoltage 119881OC
(V)
Maximumpower 119875MAX
(W)
Fill factor FF()
Energyefficiency 120578
()1000 298 025 112 1799 986 191 7458 7071225 321 033 120 1923 848 207 7397 6262254 328 063 129 2073 839 372 7037 6113234 331 091 139 2227 831 500 6700 5733822 3325 107 155 2484 824 584 6623 566
0 2 4 6 8 10Voltage (V)
Curr
ent (
A)
0
02
04
06
08
1
12
Simulation (2 mirrors)Experimental (2 mirrors)Simulation (4 mirrors)Experimental (4 mirrors)
Simulation (6 mirrors)Experimental (6 mirrors)Simulation (8 mirrors)Experimental (8 mirrors)
Figure 9 Simulated and experimental 119868-119881 characteristics of LCPVsystem under ATC
the solar PVmodule which results in enhanced electron-holepair production and higher photocurrent [39] The valuesof the dynamic resistance at MPP are computed using thevalues of 119868PH 119868SC and 119877119878 The dynamic resistance of LCPVmodule is calculated in an effective manner using (21) andis listed in Table 5 Approximate error between experimentaland theoretical dynamic resistance of the LCPV module isfound as sim13ndash21 which shows the uncertainty is wellwithin the practically acceptable limits
The plot shown in Figure 9 and extracted data listed inTable 5 describe the dependence of FF and efficiency of LCPV
module on the change in input energy rate and moduletemperature From the observed results it can be concludedthat the FF and efficiency of LCPV module decrease as theinput energy rate increasesThe decrease in FF and efficiencyof solar PV module with the increasing energy rate is highlydependent on the increase in electrical exergy destructionof LCPV module due to the increase in input energy rateand temperature As a result of increased input energy ratedynamic resistance offers greater resistive power losses inLCPV module and thus reduces its performance by reducingthe FF and efficiency The increase in the dynamic resistanceand reduction in the FF of LCPV module are foremostparameters for the decrease in the electrical energy efficiency
The effects of the cell temperature (119879119862) on 119868-119881 curveof LCPV module is estimated from the proposed model asshown in Figure 10 As the device temperature increasessmall increase in short-circuit current is observed how-ever the open-circuit voltage rapidly decreases due to theexponential dependence of the saturation current on thetemperature as given by (18) [39] In the actual experimentssimilar effect of temperature on open-circuit voltage (119881OC) isobserved and it is found that the 119881OC decreases from 986 to824V with temperature coefficient of voltage asymp minus0021 VKunder ATC as shown in Figure 9
A decrease in the 119875MAX with the increase in 119879119862 isobserved because with the increase in temperature the bandgap of the intrinsic semiconductor shrinks The increasedtemperature causes reduction in open-circuit voltage (119881OC)and the increase in the photocurrent for a given irradiancebecause of high injection of electrons from valance band toconduction band of semiconductor material [39]
52 Economical Analysis of LCPV System Net Present Value(NPV) method allows analyzing the economic aspects of anyengineering system and is used for the economic analysis of
10 International Journal of Photoenergy
Table 6 Cost of various components of LCPV system (asymp1 kWP) to find initial investment cost (numbers provided here are in accordancewith the current market price)lowast
Components Module BOSBattery Charge controller Support structure Tracker Cabling
Cost (in US$) 206 800 48 320 590 120Total initial investment cost (in US$) 2084
lowastThe price is based on market survey which may vary depending on specific location or company
Table 7 Economical analysis of LCPV system (having a lifetime of 25 years [24])
Period (year) 0 1 2 3 4 5 6 7 8Initial investment cost minus2084
Benefitslowastlowast 29043 29043 29043 29043 29043 29043 29043 29043O and M costlowastlowastlowast minus218 minus230 minus243 minus257 minus272 minus288 minus304 minus321
Discount rate 001 001 001 001 001 001 001 001 001Net cash flow 28825 28813 287995 28786 28771 28755 28739 28721119886 099 099 098 097 096 095 094 093 092Discounted net cash flow 28539 28245 27953 27662 27374 27089 26805 26524NPV minus17986 minus15162 minus12366 minus960 minus68626 minus41537 minus14732 11792lowastlowastBenefits are based on the tariff policy of Gujarat Electricity Regulatory Commission released for projects commissioned in 2012 [24]lowastlowastlowastEscalation in operating cost is taken as 572 annually [24]
300K325K
350K375K
0 2 4 6 8 100
005
01
015
02
025
03
Voltage (V)
Curr
ent (
A)
Figure 10 Variation of current-voltage characteristics with the celltemperature 119879119862
developed LCPV system of 1 kWP As the system presented inthis paper is very small for economic analysis the calculationsare done for 1 kWP system NPV method allows accountingfor the present value of annual capital expenditures andsavings during the lifetime of the system Net present value(NPV) includes sum of all the current values (costs are shownas negative and net savings are shown as positive) Foracceptance of any engineering project the positive NPV is
desiredThe formulas for calculatingNPVand correspondingfactor are given as [16]
NPV =
119899
sum
119894=1
(119861 minus 119862)119894
119886 =
1
(1 + 119894)
119901
(34)
where ldquo119886rdquo represents net present value factor ldquo119861rdquo representsgain ldquo119901rdquo represents the period and ldquo119894rdquo represents discountrate in the equation given previously
The initial investment cost is required in order to calculateNPV which includes module cost and balance of systems(BOS) cost The components of BOS include battery storagecharge controllers support structure tracking system andtransmission cables Cost of all these components is listedin Table 6 Using the initial investment cost and the formulaoutlined in (34) the NPV is calculated (Table 7) Operationandmaintenance (O andM) cost is taken as 075 of the totalinvestment cost with escalation in operating cost as 572 perannum [24] The feasibility of this project is demonstrated bya positive value of NPV obtained within 8 years
6 Conclusions
A theoretical model is used to perform electrical energy andexergy analyses of low-concentration photovoltaic (LCPV)system working under actual test conditions (ATC) Theexergy efficiency of LCPV system is in the range from51 to 482 with increasing rate of input exergy ratefrom 3081W to 9612W when concentration ratio changes
International Journal of Photoenergy 11
from 185 to 517 Sun Short-circuit current shows increasingtrend with increasing input exergy rate of asymp0011 AW Powerconversion efficiency decreases from 707 to 566 and open-circuit voltage decreases from986 to 824Vwith temperaturecoefficient of voltage asymp minus0021 VK under ATC The resultsconfirm that the commercially available silicon solar PVmodule performs satisfactorily under low concentration
Nomenclature
CR Concentration ratio119882 Width of the profile119863 Depth of the profile0119903 Rim angle120579119888 Acceptance angle119865 Focus point120588mirror Reflectivity of mirrors119877min Half width of the solar panel119871 Parabolic trough length120572 Absorption coefficient119860119886 Aperture area119896119861 Boltzmannrsquos constant (138 times 10minus23)119868PH Light generated current119868119878 Cell saturation or dark current119902 Electron charge (16 times 10minus19 C)119860 Ideality factor119880rad Radiative heat loss coefficient119880con Convective heat loss coefficient119879119862 Working temperature of solar cell (Kelvin)119877SH Shunt resistance119877119878 Series resistance119873119878 Series number of cells in a PV module119873119875 Parallel number of modules for a PV array119868SC Cellrsquos short-circuit current at 29814 K and
1 kWm2119870119868 Cellrsquos short-circuit current temperature
coefficient119879Ref Cellrsquos reference temperature120582 Solar insolation in kWm2119868RS Cellrsquos reverse saturation current at a
reference temperature and solar radiation119864119892 Band gap energy of the semiconductor119868mp Current at maximum power point119881mp Voltage at maximum power point
Acknowledgments
The authors acknowledge the financial support providedby Gujarat Energy Development Agency (GEDA) todevelop CPV system by Grant no GEDAECRECMarch-201039174 Authors also acknowledge WAAREE EnergiesPvt Ltd India for providing encapsulated crystallinesilicon solar PV modules for this study
References
[1] G Sala D Pachon I Anton and Test Test Rating andSpecification of PV Concentrator Components and Systems
(C-Rating Project) Book1 Classification of PV ConcentratorsUniversidad Politecnica de Madrid Madrid Spain 2002httpwwwies-defupmesiesCRATINGDocumentshtm
[2] M Yamaguchi andA Luque ldquoHigh efficiency and high concen-tration in photovoltaicsrdquo IEEE Transactions on Electron Devicesvol 46 no 10 pp 2139ndash2144 1999
[3] M A Green and A Ho-Baillie ldquoForty three per cent compositesplit-spectrum concentrator solar cell efficiencyrdquo Progress inPhotovoltaics vol 18 no 1 pp 42ndash47 2010
[4] H Cotal C Fetzer J Boisvert et al ldquoIII-V multijunction solarcells for concentrating photovoltaicsrdquo Energy and Environmen-tal Science vol 2 no 2 pp 174ndash192 2009
[5] G Sala I Anton J Monedero et al ldquoThe euclides-thermieconcentrator power plant in continuous operationrdquo in Proceed-ings of the 17th European Photovoltaic Solar Energy Conference(EUPVSEC rsquo01) pp 488ndash491 Munich Germany 2001
[6] V Garboushian S Yoon G Turner A Gunn and D FairldquoNovel high-concentration PV technology for cost competitiveutility bulk power generationrdquo in Proceedings of the 24th IEEEPhotovoltaic Specialists Conference Part 2 (of 2) pp 1060ndash1063December 1994
[7] M Castro I Anton and G Sala ldquoPilot production of concen-trator silicon solar cells approaching industrializationrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1697ndash17052008
[8] A Zahedi ldquoReview of modelling details in relation to low-concentration solar concentrating photovoltaicrdquoRenewable andSustainable Energy Reviews vol 15 no 3 pp 1609ndash1614 2011
[9] M Li X Ji G Li S Wei Y Li and F Shi ldquoPerformancestudy of solar cell arrays based on a trough concentratingphotovoltaicthermal systemrdquoApplied Energy vol 88 no 9 pp3218ndash3227 2011
[10] M A Schuetz K A Shell S A Brown G S Reinbolt RH French and R J Davis ldquoDesign and construction of a sim
7times low-concentration photovoltaic system based on compoundparabolic concentratorsrdquo IEEE Journal of Photovoltaics vol 2no 3 pp 382ndash386 2012
[11] H G Riveros and A I Oliva ldquoGraphical analysis of sunconcentrating collectorsrdquo Solar Energy vol 36 no 4 pp 313ndash322 1986
[12] O A Jaramillo J A Del Rıo and G Huelsz ldquoThermal study ofoptical fibres transmitting concentrated solar energyrdquo Journal ofPhysics D vol 32 no 9 pp 1000ndash1005 1999
[13] O A Jaramillo G Huelsz and J A Del Rıo ldquoA theoretical andexperimental thermal study of SiO2 optical fibres transmittingconcentrated radiative energyrdquo Journal of Physics D vol 35 no2 pp 95ndash102 2002
[14] C Kandilli and K Ulgen ldquoReview and modelling the systemsof transmission concentrated solar energy via optical fibresrdquoRenewable and Sustainable Energy Reviews vol 13 no 1 pp 67ndash84 2009
[15] A S Joshi I Dincer and B V Reddy ldquoThermodynamicassessment of photovoltaic systemsrdquo Solar Energy vol 83 no8 pp 1139ndash1149 2009
[16] C Kandilli ldquoPerformance analysis of novel concentrating solarphotovoltaic combined systemrdquo Energy Conversion and Man-agement vol 67 pp 186ndash196 2013
[17] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part I the concept of net exergyflow and the modeling of solar air heatersrdquo Solar Energy vol 41no 2 pp 127ndash132 1988
12 International Journal of Photoenergy
[18] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part 2 results of optimizationand analysis of sensibility to variations of operating conditionsrdquoSolar Energy vol 41 no 4 pp 309ndash317 1988
[19] S Farahat F Sarhaddi and H Ajam ldquoExergetic optimization offlat plate solar collectorsrdquo Renewable Energy vol 34 no 4 pp1169ndash1174 2009
[20] H Ajam S Farahat and F Sarhaddi ldquoExergetic optimizationof solar air heaters and comparison with energy analysisrdquoInternational Journal of Thermodynamics vol 8 no 4 pp 183ndash190 2005
[21] M J Kerr and A Cuevas ldquoGeneralized analysis of the illumi-nation intensity versus open-circuit voltage of solar cellsrdquo SolarEnergy vol 76 no 1ndash3 pp 263ndash267 2004
[22] E Radziemska and E Klugmann ldquoThermally affected parame-ters of the current-voltage characteristics of silicon photocellrdquoEnergy Conversion and Management vol 43 no 14 pp 1889ndash1900 2002
[23] E E van Dyk B J Scott E L Meyer and A W R LeitchldquoTemperature dependence of performance of crystalline siliconphotovoltaic modulesrdquo South African Journal of Science vol 96no 4 pp 198ndash200 2000
[24] httpwwwgercinorgrenewablepdfSolar20Tariff20Order20120of202012pdf 2013
[25] M Veerachary T Senjyu and K Uezato ldquoVoltage-basedmaximum power point tracking control of PV systemrdquo IEEETransactions on Aerospace and Electronic Systems vol 38 no1 pp 262ndash270 2002
[26] M Veerachary and K S Shinoy ldquoV2-based power tracking fornonlinear PV sourcesrdquo IEE Proceedings-Electric Power Applica-tions vol 152 no 5 pp 1263ndash1270 2005
[27] I S Kim and M J Youn ldquoVariable-structure observer for solararray current estimation in a photovoltaic power-generationsystemrdquo IEE Proceedings-Electric Power Applications vol 152no 4 pp 953ndash959 2005
[28] I S Kim M B Kim and M J Youn ldquoNew maximum powerpoint tracker using sliding-mode observer for estimation ofsolar array current in the grid-connected photovoltaic systemrdquoIEEE Transactions on Industrial Electronics vol 53 no 4 pp1027ndash1035 2006
[29] H L Tsai C S Tu and Y J Su ldquoDevelopment of generalizedphotovoltaic model using MATLABSIMULINKrdquo in Proceed-ings of theWorld Congress on Engineering and Computer ScienceSan Francisco NC USA October 2008
[30] J CThongpron K Kirtikara and C Jivacate ldquoAmethod for thedetermination of dynamic resistance of photovoltaic modulesunder illuminationrdquo Solar Energy Materials and Solar Cells vol90 no 18-19 pp 3078ndash3084 2006
[31] J C Wang J C Shieh Y L Su et al ldquoA novel method for thedetermination of dynamic resistance for photovoltaicmodulesrdquoEnergy vol 36 no 10 pp 5968ndash5974 2011
[32] S Dubey G S Sandhu andG N Tiwari ldquoAnalytical expressionfor electrical efficiency of PVT hybrid air collectorrdquo AppliedEnergy vol 86 no 5 pp 697ndash705 2009
[33] S Kumar P K Singh G S Chilana and S R Dhariwal ldquoGen-eration and recombination lifetime measurement in siliconwafers using impedance spectroscopyrdquo Semiconductor Scienceand Technology vol 24 no 9 Article ID 095001 pp 1ndash8 2009
[34] J Millman and C C Halkias Integrated Electronics McGraw-Hill New York NY USA 1972
[35] S Kumar P K Singh and G S Chilana ldquoStudy of siliconsolar cell at different intensities of illumination andwavelengthsusing impedance spectroscopyrdquo Solar Energy Materials andSolar Cells vol 93 no 10 pp 1881ndash1884 2009
[36] S Kumar V Sareen N Batra and P K Singh ldquoStudy of C-Vcharacteristics in thin n+-p-p+ silicon solar cells and inducedjunction n-p-p+ cell structuresrdquo Solar Energy Materials andSolar Cells vol 94 no 9 pp 1469ndash1472 2010
[37] I Mora-Sero G Garcia-Belmonte P P Boix M A Vazquezand J Bisquert ldquoImpedance spectroscopy characterisation ofhighly efficient silicon solar cells under different light illumina-tion intensitiesrdquo Energy and Environmental Science vol 2 no 6pp 678ndash686 2009
[38] F Sarhaddi S Farahat H Ajam andA Behzadmehr ldquoExergeticoptimization of a solar photovoltaic arrayrdquo Journal of Thermo-dynamics vol 2009 Article ID 313561 11 pages 2009
[39] S M Sze Physics of Semiconductor Devices Wiley New YorkNY USA 2nd edition 1981
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
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Analytical Methods in Chemistry
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Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
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Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
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CatalystsJournal of
International Journal of Photoenergy 5
Table 1 Simulation parameters for desired CR in developed LCPV system
Number ofmirrors Width119882 (m) Rim angle (0119903) Acceptance angle (120579119888) Length 119871 (m) Effective 119860119886 (m
2) CR Solar radiation (Wm2)
2 mirrors 027 1351∘ 317∘ 030 0054 185 12254 mirrors 045 2502∘ 307∘ 030 0108 356 22546 mirrors 062 3378∘ 294∘ 030 0159 472 32348 mirrors 079 4198∘ 280∘ 030 0211 517 3822
For short-circuit condition the output voltage of LCPVmodule is zero so (21) is reduced to
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
= minus
119873119875
119873119878119877SHminus
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
sdot
119877119878
119877SH
minus
119873119875119868119878119902
119896119879119862119860
[
1
119873119878
+
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
sdot
119877119878
119873119875
]
times exp [119902
119896119879119862119860
sdot (
119868SC119877119878119873119875
)]
(27)
Equation (27) can be further simplified as
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
= minus
119873119875
119873119878119877SHminus
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
sdot
119877119878
119877SH (28)
Therefore the shunt resistance can be expressed by
119877SH = minus
119873119878
119873119875
(
119889119868
119889119881
10038161003816100381610038161003816100381610038161003816119868=119868SC
)
minus1
119877SH =
119873119878
119873119875
119877sh0
(29)
By analysis of (21) we conclude that the dynamic resistance ofLCPVmodule is dependent on the solar irradiance and solarPV module temperature
24 Statistical Analysis To compare the theoretical andobtained experimental results the correlation coefficient(119903) and root-mean square percent deviation (119890) have beenevaluated by using the following expressions [32]
119903 =
119873sum119883119894119884119894 minus (sum119883119894sum119884119894)
radic119873sum1198832119894minus (sum119883119894)
2radic119873sum119884
2119894minus (sum119884119894)
2
119890 =radic(sum 119890119894)
2
119873
(30)
where 119890119894 = [(119883119894 minus 119884119894)119883119894] times 100 The variables 119883119894 and 119884119894
represent theoretical and experimental data respectivelyThelinear coefficient of correlation (119903) which ranges betweenminus1 and 1 measures strength and the direction of a linearrelationship between two variables that is 119883119894 and 119884119894 The 119903value close to 1 indicates that two variables are in a strongpositive linear correlation
Figure 3 The constructed model of concentrator photovoltaic(CPV) system
3 LCPV Development and Validation of theProposed Model
31 System Development A MATLABSimulink computercode is developed using the mathematical model discussedin Section 2 to simulate LCPV system Table 1 shows theparameters used for calculating CR of the developed PLPTCThe CR depends on the effective aperture area which isgoverned by the number of mirrors used as reflectors FromTable 1 it is clear that by changing the number of mirrorsfrom 2 to 8 the geometric CR changes from sim2 to 8 Sun
A piecewise linear parabolic LCPV system is developed asshown in Figure 3 by using the modeling parameters listed inTable 1 The effective aperture area available using 8 mirrorsis 0211m2 and the effective receiver area is 0027m2 whichgives the geometric concentration ratio of sim8 The receiver ismade of a solar PV module fabricated by a string of sixteencommercially available silicon cell pieces (material mono-crystalline silicon size 14mm times 64mm efficiency sim14)The reason behind the selection of this specific size of thecells is to solve the current handling problem of the solarcells under concentration A typical solar cell of size 125mmtimes 125mm producing 25W at a voltage of 560mV wouldhave a current handling capability of around 45 A This cellwhen used under 10 Sun concentration may produce 45Acurrent by assuming a linear relationship between the currentincrement and CR But if the size of the cell is reduced to110th normal size then the current generated under 10 Sunconcentration would be less than or equal to 45 A thenit will be easily handled without damaging the solar cellcontacts The incident solar radiation is reflected by PLPTCand concentrated on the focal plane havingwidth of 064mm
6 International Journal of Photoenergy
Table 2 The parameters used for simulation under 1 Sun
Parametersunits 119877119878 (Ω) 119864119892 (eV) 119873119878 119873119875 119860 119879119862 (K) 119879ref (K) 119896119861 (JK) 119870119868 119902 (C) 119868SC (A) 119868RS (A) 119881OC (V)
For 1 Sun 0071 112 16 1 15 298 298 138 times 10
minus23065 times 10
minus31602 times 10
minus19 0259 086 times 10
minus12 986
Table 3 The value of 119877 119862 and corresponding 120591 obtained fromthe measured impedance spectra under different bias voltage con-ditions
Appliedvoltage(V)
Resistance inequivalent circuit
119877 (kΩ)
Capacitance inequivalent circuit
119862 (nF)
Timeconstant 120591
(ms)minus05 70 49 343minus02 55 514 2830 45 362 16302 37 351 13005 28 321 090
An active cooling mechanism is employed by flowing waterbehind the encapsulated solar PV module which is shown inFigure 3 By employing this mechanismmodule temperaturecould be lowered down to 45∘C A light dependent resistor(LDR) based one axis tracking system is developed for Suntracking with a provision of manual tracking on second axiswith an accuracy of plusmn3∘ as shown in Figure 3
32 Theory Validation and Characterization of LCPVModuleThe module characterization was done under standard testconditions (STC) by 119868-119881 characteristics impedance spec-troscopy (IS) and capacitance-voltage (CV) measurementand detailed parameters are given in Tables 2 and 3 Theconcentrated light is received by the solar PV module whichis placed at the focal plane of the PLPTC To simulate theelectrical power generated from this PV module the inputparameters are series resistance energy band gap number ofcells connected in series number of strings connected parallelto each other cell temperature ambient temperature short-circuit current ofmodule open-circuit voltage of themoduleand so on These input parameters are listed in Table 2
In this LCPV system a solar PV module manufacturedat WAAREE Energies Pvt Ltd module production line isused The open-circuit voltage and short-circuit current ofthis module aremeasured as119881OC = 986V and 119868SC = 0259Arespectively under AM15 spectrum at 29814 KThe current-voltage output characteristics of generalized solar PVmoduleunder AM15 solar spectrum are shown in Figure 4 In thesimulation short-circuit current open-circuit voltage seriesresistance and cell temperature measured under standardtest conditions (STC) by manufacturer are taken as inputparameters The current-voltage characteristic generatedfrom simulation programmatches well with the experimentalcurrent-voltage characteristic
Looking at the current-voltage curve it can be identifiedthat the photovoltaic module is a constant current source atlower values of voltage with current equal to the short-circuitcurrent (119868SC) With the further increase in voltage values the
0 2 4 6 8 100
005
01
015
02
025
03
Voltage (V)
Curr
ent (
A)
TheoreticalExperimental
e = 025 r = 0999
Figure 4 Current-voltage characteristics of the designed solar PVmodule under 1 Sun AM15 at 29814 K
current starts decreasing exponentially at certain point Thevalue of current becomes zero at open-circuit voltage (119881OC)The point where themodule operates at the highest efficiencyis called maximum power point (119875MAX)
For impedance measurements an ac signal having fre-quency in the range from 1 Hz to 01MHz with amplitudeof 5mV is used The impedance spectra were plotted in acomplex plane (ie 1198851015840 versus 119885
10158401015840 also known as Nyquistor ColendashCole plot [33]) which can provide information onany system that is composed of combination of interfacialand bulk process The measurements were carried out onthe developed LCPVmodule under forward and reverse bias(+05 V to minus05 V) conditions in the dark Figure 5 shows theimpedance spectrum of the LCPVmodule under reverse biasconditions (from 0 to minus05 V) The radius of the semicircleincreases with the increase in bias voltage as compared tozero bias demonstrating the bias dependence of resistanceand capacitance [33] The increase in the radius of semicircleduring reverse bias is observed due to expansion of depletionregion of the solar cell which increases the resistance offeredby the cell
Figure 6 shows the impedance spectrum under the for-ward bias conditions (from0 to 05V)where in contrast to thereverse bias opposite behavior is observed Here the radiusof the semicircle decreases with increasing positive bias fromits maximum value at zero bias The decrease in the radius ofsemicircle during forward bias is observed due to shrinking
International Journal of Photoenergy 7
0 2 4 6 8
times104
times104
0
05
1
15
2
25
3
35
Bias = 0VBias = minus02VBias = minus05V
Z998400 (Ohm)
Z998400998400
(Ohm
)
Figure 5 Impedance spectra of LCPV module under reverse biasconditions
times104
times104
0
05
1
15
2
25
Z998400 (Ohm)
Z998400998400
(Ohm
)
Bias = 0V
0 1 2 3 4 5
Bias = 02VBias = 05V
Figure 6 Impedance spectra of LCPV module under forward biasconditions
of depletion region of the solar cell which decreases theresistance offered by the cell
The ac equivalent circuit of the n+-p-p+structure underconsideration is shown in Figure 7 which incorporates thecapacitive effect owing to the excess minority carriers (119862119889commonly known as the diffusion capacitance) in parallelwith the depletion layer capacitance 119862119905 (Figure 7) Resistiveeffects arising from the minority carrier recombination areshown as the diffusion resistance (119877119889) in parallel with a shunt
RS
C = (Cd + Ct)
R = (RSH Rd)
Figure 7 The ac equivalent circuit of LCPV module to explainobserved impedance spectra
(119877SH) resistance and a series resistance 119877119878 connected in thecircuit [33]
Under forward bias condition due to the accumulationof minority carriers in the bulk the magnitude of thediffusion capacitance is large compared to the depletionregion capacitance [34] The ac impedance of the circuit isgiven by
119885 (120596) = 119885
1015840(120596) minus 119895119885
10158401015840(120596) (31)
where 119885
1015840 and 119885
10158401015840 are the magnitudes of the real andimaginary parts of impedance and a minus sign arises dueto capacitive reactance involved in the circuit On analyzingthe circuit 1198851015840 and 119885
10158401015840 can be written as
119885
1015840(120596) = 119877119904 +
119877
1 + (120596119877119862)
2
119885
10158401015840(120596) =
120596119862119877
2
1 + (120596119877119862)
2
(32)
For the case of very low 119877119878 when 119885
1015840 and 119885
10158401015840 are plotted ina complex plane by varying the frequency (120596) a semicircleof radius 1198772 with its center at (1198772 0) is obtained Furtherbecause of the semicircular geometry the maximum valueof 11988510158401015840 arises when 120596119898119877119862 = 1 where 120596119898 is the frequencyat which 119885
10158401015840 becomes maximum Thus we have that 119862 =
1120596119898119877 and the presence of 119877119878 shifts the semicircle byits value on the 119909-axis The analysis of the impedancediagram on the complex plane therefore gives values ofall the three parameters that is 119877 119862 and 119877119878 used in theequivalent circuit The product of resistance and capacitance(119877119862) represents the time constant (120591) The value of 119877 119862and corresponding 120591 obtained from themeasured impedancespectra under different bias voltage conditions is listed inTable 3These values are in good agreement with the existingliterature for silicon solar cells [33 35]
Capacitance-voltage (119862-119881) measurement is an importanttool to understand the transient behavior of a semiconductordevice Generally capacitance is measured in the reversedbias (Mott-Schottky) condition to determine barrier poten-tial and effective doping concentration Capacitance-voltagecharacterization is done for the developed LCPV module asshown in Figure 8
8 International Journal of Photoenergy
minus08 minus06 minus04 minus02 0 02 04 06 08Voltage (V)
times1014
0
05
1
15
2
25
3
1C
2(1F2)
Figure 8 The capacitance-voltage characterization of LCPV mod-ule
The dependence of barrier potential and doping concen-tration on the depletion region capacitance per unit area isgiven by [30]
1
1198622=
2
1199021198701205760119873
(119881bi minus 119881 minus
2119896119861119879
119902
)
119889 (1119862
2)
119889119881
= minus
2
1199021198701205760119873
(33)
where 119902 is the electron charge 119870 is dielectric constant ofsilicon 1205760 is the permittivity of free space 119881bi is barrierpotential 119896119861 is Boltzmannrsquos constant119879 is equal to 29814 K119873is doping concentration and 119881 represents applied potential
The slope and its intersection on the abscissa in theMott-Schottky plot shown in Figure 8 for the LCPV module givesthe doping concentration (119873) and barrier potential (119881bi)respectivelyThe119873 value is found as 779 times 1016 cmminus3 and thevalue of119881bi minus2119896119879119902 is equal to 056 eV which corresponds to119881bi = 061 eV The calculated values are in good agreementwith the reported values for commercially available siliconsolar cells [36 37]
4 LCPV Experiment under ATC
The experiments were carried out in the campus of Schoolof Solar Energy located in Gandhinagar India (Lat 2322∘Long 7268E) in the month of December (Year 2012) Themodule temperature was measured with the digital ther-mometer having an accuracy of plusmn01∘C during experimentswind speed was measured by anemometer as 085ms withan accuracy of plusmn5 Solar radiation and ambient temperaturewere recorded at the weather station located in the universitycampus The following parameters were measured duringexperiments ambient temperature solar radiation LCPVmodule and ambient temperature load current load voltageshort-circuit current and open-circuit voltage During theexperiments the module temperature was varied in the
range of 300ndash350K by controlling the flow rate of waterbehind the LCPV module Since the aim of this paper is toextract maximum electrical output from LCPV systems thethermodynamic analysis of flowingwater is avoided hereThecurrent-voltage measurements of an LCPV system are takenby Agilent SMU 6632B and by using multimeters and loadrheostat The sensitivity of the current-voltage measurementinstrument is given as plusmn3 The developed LCPV system isstudied by varying the number of reflecting mirrors arrangedin PLPTC
5 Result and Discussion
51 Exergy and Energy Analysis The effect of the lightconcentration and module temperature on the input exergyrate electrical exergy output rate and thermal exergy outputrate of LCPV module is estimated from the proposed modelin Section 2 It is found that with the increase in CR the inputexergy rate increases which results in increased amount ofenergy available to do useful work by the system The datalisted in Table 4 shows that the exergy efficiency decreaseswith the increase in the input exergy rate This decrease ismainly due to the increase in cell temperature which resultsin electrical exergy destruction with a rate of ldquo119881OC119868SC minus
119881mp119868mprdquo [38] Further the increase in the cell temperatureaffects 119881OC with a negative temperature coefficient as shownin the Figure 9 Figure 9 shows that 119881OC decreases from848V to 824V with increase in input exergy rate from3081W to 9612W when the cell temperature changesfrom 321 K to 3325 K The influence of the cell temperatureon exergy efficiency is clearly observed (Table 4) whichdecreases with the increase in the cell temperature Similareffect is observed by other researchers [15 38] Since the celltemperature changes with the increase in the input exergyrate it is imperative to design the LCPV system based on thisinformation so that useful exergy can bemaximized For thispurpose it is very important to track maximum power pointwhich depends on dynamic resistance of LCPV system
The proposed model in Section 2 is used to performenergy analysis of the LCPV module having 16 cells con-nected in series The static parameters (119868SC 119881OC 119875MAX and119877119878) of the LCPV module are measured in ATC conditionsas well as calculated by the proposed theoretical model Themeasured and simulated current-voltage characteristics ofLCPVmodule is shown in Figure 9 with varying input energyrate and corresponding temperature
It can be seen from Figure 9 that there is good agreementbetween the experimental and theoretical current-voltagecharacteristics which include 119868SC 119881OC 119875MAX 119877119878 FF 119903119889and efficiency The mean square of percentage deviation (119890)
is in the range of 274ndash843 and the linear coefficient ofcorrelation (119903) is in the range of 0995ndash0999
The measured values of solar irradiation 119868SC 119881OC 119875MAX119877119878 temperature FF 119903119889 and efficiency are listed in Table 5Generally the output current of the solar PV modulesincreases with the increase in input energy rate (ie solarirradiance received at focal point of PLPTC) With increasein the solar irradiance the higher number of photons strikes
International Journal of Photoenergy 9
Table 4 Exergy analysis of LCPV system
Solar irradiation(Wm2)
Cell temperature 119879119862 (K) Input exergy rate (W)Output exergy rate (W)
Exergy efficiency 120578ex ()Electricalexergy rate (W)
Thermal exergyrate (W)
1225 321 3081 2 043 5102254 328 5668 355 070 5033234 331 8133 491 083 5013822 3325 9612 554 091 482
Table 5 Parameter estimated from 119868-119881 curves plotted under various CR
Solarirradiation(Wm2)
Celltemperature
119879119862 (K)
Short-circuitcurrent 119868SC
(A)
Seriesresistance 119877119878
(Ω)
Dynamicresistance 119903119889
(Ω)
Open-circuitvoltage 119881OC
(V)
Maximumpower 119875MAX
(W)
Fill factor FF()
Energyefficiency 120578
()1000 298 025 112 1799 986 191 7458 7071225 321 033 120 1923 848 207 7397 6262254 328 063 129 2073 839 372 7037 6113234 331 091 139 2227 831 500 6700 5733822 3325 107 155 2484 824 584 6623 566
0 2 4 6 8 10Voltage (V)
Curr
ent (
A)
0
02
04
06
08
1
12
Simulation (2 mirrors)Experimental (2 mirrors)Simulation (4 mirrors)Experimental (4 mirrors)
Simulation (6 mirrors)Experimental (6 mirrors)Simulation (8 mirrors)Experimental (8 mirrors)
Figure 9 Simulated and experimental 119868-119881 characteristics of LCPVsystem under ATC
the solar PVmodule which results in enhanced electron-holepair production and higher photocurrent [39] The valuesof the dynamic resistance at MPP are computed using thevalues of 119868PH 119868SC and 119877119878 The dynamic resistance of LCPVmodule is calculated in an effective manner using (21) andis listed in Table 5 Approximate error between experimentaland theoretical dynamic resistance of the LCPV module isfound as sim13ndash21 which shows the uncertainty is wellwithin the practically acceptable limits
The plot shown in Figure 9 and extracted data listed inTable 5 describe the dependence of FF and efficiency of LCPV
module on the change in input energy rate and moduletemperature From the observed results it can be concludedthat the FF and efficiency of LCPV module decrease as theinput energy rate increasesThe decrease in FF and efficiencyof solar PV module with the increasing energy rate is highlydependent on the increase in electrical exergy destructionof LCPV module due to the increase in input energy rateand temperature As a result of increased input energy ratedynamic resistance offers greater resistive power losses inLCPV module and thus reduces its performance by reducingthe FF and efficiency The increase in the dynamic resistanceand reduction in the FF of LCPV module are foremostparameters for the decrease in the electrical energy efficiency
The effects of the cell temperature (119879119862) on 119868-119881 curveof LCPV module is estimated from the proposed model asshown in Figure 10 As the device temperature increasessmall increase in short-circuit current is observed how-ever the open-circuit voltage rapidly decreases due to theexponential dependence of the saturation current on thetemperature as given by (18) [39] In the actual experimentssimilar effect of temperature on open-circuit voltage (119881OC) isobserved and it is found that the 119881OC decreases from 986 to824V with temperature coefficient of voltage asymp minus0021 VKunder ATC as shown in Figure 9
A decrease in the 119875MAX with the increase in 119879119862 isobserved because with the increase in temperature the bandgap of the intrinsic semiconductor shrinks The increasedtemperature causes reduction in open-circuit voltage (119881OC)and the increase in the photocurrent for a given irradiancebecause of high injection of electrons from valance band toconduction band of semiconductor material [39]
52 Economical Analysis of LCPV System Net Present Value(NPV) method allows analyzing the economic aspects of anyengineering system and is used for the economic analysis of
10 International Journal of Photoenergy
Table 6 Cost of various components of LCPV system (asymp1 kWP) to find initial investment cost (numbers provided here are in accordancewith the current market price)lowast
Components Module BOSBattery Charge controller Support structure Tracker Cabling
Cost (in US$) 206 800 48 320 590 120Total initial investment cost (in US$) 2084
lowastThe price is based on market survey which may vary depending on specific location or company
Table 7 Economical analysis of LCPV system (having a lifetime of 25 years [24])
Period (year) 0 1 2 3 4 5 6 7 8Initial investment cost minus2084
Benefitslowastlowast 29043 29043 29043 29043 29043 29043 29043 29043O and M costlowastlowastlowast minus218 minus230 minus243 minus257 minus272 minus288 minus304 minus321
Discount rate 001 001 001 001 001 001 001 001 001Net cash flow 28825 28813 287995 28786 28771 28755 28739 28721119886 099 099 098 097 096 095 094 093 092Discounted net cash flow 28539 28245 27953 27662 27374 27089 26805 26524NPV minus17986 minus15162 minus12366 minus960 minus68626 minus41537 minus14732 11792lowastlowastBenefits are based on the tariff policy of Gujarat Electricity Regulatory Commission released for projects commissioned in 2012 [24]lowastlowastlowastEscalation in operating cost is taken as 572 annually [24]
300K325K
350K375K
0 2 4 6 8 100
005
01
015
02
025
03
Voltage (V)
Curr
ent (
A)
Figure 10 Variation of current-voltage characteristics with the celltemperature 119879119862
developed LCPV system of 1 kWP As the system presented inthis paper is very small for economic analysis the calculationsare done for 1 kWP system NPV method allows accountingfor the present value of annual capital expenditures andsavings during the lifetime of the system Net present value(NPV) includes sum of all the current values (costs are shownas negative and net savings are shown as positive) Foracceptance of any engineering project the positive NPV is
desiredThe formulas for calculatingNPVand correspondingfactor are given as [16]
NPV =
119899
sum
119894=1
(119861 minus 119862)119894
119886 =
1
(1 + 119894)
119901
(34)
where ldquo119886rdquo represents net present value factor ldquo119861rdquo representsgain ldquo119901rdquo represents the period and ldquo119894rdquo represents discountrate in the equation given previously
The initial investment cost is required in order to calculateNPV which includes module cost and balance of systems(BOS) cost The components of BOS include battery storagecharge controllers support structure tracking system andtransmission cables Cost of all these components is listedin Table 6 Using the initial investment cost and the formulaoutlined in (34) the NPV is calculated (Table 7) Operationandmaintenance (O andM) cost is taken as 075 of the totalinvestment cost with escalation in operating cost as 572 perannum [24] The feasibility of this project is demonstrated bya positive value of NPV obtained within 8 years
6 Conclusions
A theoretical model is used to perform electrical energy andexergy analyses of low-concentration photovoltaic (LCPV)system working under actual test conditions (ATC) Theexergy efficiency of LCPV system is in the range from51 to 482 with increasing rate of input exergy ratefrom 3081W to 9612W when concentration ratio changes
International Journal of Photoenergy 11
from 185 to 517 Sun Short-circuit current shows increasingtrend with increasing input exergy rate of asymp0011 AW Powerconversion efficiency decreases from 707 to 566 and open-circuit voltage decreases from986 to 824Vwith temperaturecoefficient of voltage asymp minus0021 VK under ATC The resultsconfirm that the commercially available silicon solar PVmodule performs satisfactorily under low concentration
Nomenclature
CR Concentration ratio119882 Width of the profile119863 Depth of the profile0119903 Rim angle120579119888 Acceptance angle119865 Focus point120588mirror Reflectivity of mirrors119877min Half width of the solar panel119871 Parabolic trough length120572 Absorption coefficient119860119886 Aperture area119896119861 Boltzmannrsquos constant (138 times 10minus23)119868PH Light generated current119868119878 Cell saturation or dark current119902 Electron charge (16 times 10minus19 C)119860 Ideality factor119880rad Radiative heat loss coefficient119880con Convective heat loss coefficient119879119862 Working temperature of solar cell (Kelvin)119877SH Shunt resistance119877119878 Series resistance119873119878 Series number of cells in a PV module119873119875 Parallel number of modules for a PV array119868SC Cellrsquos short-circuit current at 29814 K and
1 kWm2119870119868 Cellrsquos short-circuit current temperature
coefficient119879Ref Cellrsquos reference temperature120582 Solar insolation in kWm2119868RS Cellrsquos reverse saturation current at a
reference temperature and solar radiation119864119892 Band gap energy of the semiconductor119868mp Current at maximum power point119881mp Voltage at maximum power point
Acknowledgments
The authors acknowledge the financial support providedby Gujarat Energy Development Agency (GEDA) todevelop CPV system by Grant no GEDAECRECMarch-201039174 Authors also acknowledge WAAREE EnergiesPvt Ltd India for providing encapsulated crystallinesilicon solar PV modules for this study
References
[1] G Sala D Pachon I Anton and Test Test Rating andSpecification of PV Concentrator Components and Systems
(C-Rating Project) Book1 Classification of PV ConcentratorsUniversidad Politecnica de Madrid Madrid Spain 2002httpwwwies-defupmesiesCRATINGDocumentshtm
[2] M Yamaguchi andA Luque ldquoHigh efficiency and high concen-tration in photovoltaicsrdquo IEEE Transactions on Electron Devicesvol 46 no 10 pp 2139ndash2144 1999
[3] M A Green and A Ho-Baillie ldquoForty three per cent compositesplit-spectrum concentrator solar cell efficiencyrdquo Progress inPhotovoltaics vol 18 no 1 pp 42ndash47 2010
[4] H Cotal C Fetzer J Boisvert et al ldquoIII-V multijunction solarcells for concentrating photovoltaicsrdquo Energy and Environmen-tal Science vol 2 no 2 pp 174ndash192 2009
[5] G Sala I Anton J Monedero et al ldquoThe euclides-thermieconcentrator power plant in continuous operationrdquo in Proceed-ings of the 17th European Photovoltaic Solar Energy Conference(EUPVSEC rsquo01) pp 488ndash491 Munich Germany 2001
[6] V Garboushian S Yoon G Turner A Gunn and D FairldquoNovel high-concentration PV technology for cost competitiveutility bulk power generationrdquo in Proceedings of the 24th IEEEPhotovoltaic Specialists Conference Part 2 (of 2) pp 1060ndash1063December 1994
[7] M Castro I Anton and G Sala ldquoPilot production of concen-trator silicon solar cells approaching industrializationrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1697ndash17052008
[8] A Zahedi ldquoReview of modelling details in relation to low-concentration solar concentrating photovoltaicrdquoRenewable andSustainable Energy Reviews vol 15 no 3 pp 1609ndash1614 2011
[9] M Li X Ji G Li S Wei Y Li and F Shi ldquoPerformancestudy of solar cell arrays based on a trough concentratingphotovoltaicthermal systemrdquoApplied Energy vol 88 no 9 pp3218ndash3227 2011
[10] M A Schuetz K A Shell S A Brown G S Reinbolt RH French and R J Davis ldquoDesign and construction of a sim
7times low-concentration photovoltaic system based on compoundparabolic concentratorsrdquo IEEE Journal of Photovoltaics vol 2no 3 pp 382ndash386 2012
[11] H G Riveros and A I Oliva ldquoGraphical analysis of sunconcentrating collectorsrdquo Solar Energy vol 36 no 4 pp 313ndash322 1986
[12] O A Jaramillo J A Del Rıo and G Huelsz ldquoThermal study ofoptical fibres transmitting concentrated solar energyrdquo Journal ofPhysics D vol 32 no 9 pp 1000ndash1005 1999
[13] O A Jaramillo G Huelsz and J A Del Rıo ldquoA theoretical andexperimental thermal study of SiO2 optical fibres transmittingconcentrated radiative energyrdquo Journal of Physics D vol 35 no2 pp 95ndash102 2002
[14] C Kandilli and K Ulgen ldquoReview and modelling the systemsof transmission concentrated solar energy via optical fibresrdquoRenewable and Sustainable Energy Reviews vol 13 no 1 pp 67ndash84 2009
[15] A S Joshi I Dincer and B V Reddy ldquoThermodynamicassessment of photovoltaic systemsrdquo Solar Energy vol 83 no8 pp 1139ndash1149 2009
[16] C Kandilli ldquoPerformance analysis of novel concentrating solarphotovoltaic combined systemrdquo Energy Conversion and Man-agement vol 67 pp 186ndash196 2013
[17] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part I the concept of net exergyflow and the modeling of solar air heatersrdquo Solar Energy vol 41no 2 pp 127ndash132 1988
12 International Journal of Photoenergy
[18] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part 2 results of optimizationand analysis of sensibility to variations of operating conditionsrdquoSolar Energy vol 41 no 4 pp 309ndash317 1988
[19] S Farahat F Sarhaddi and H Ajam ldquoExergetic optimization offlat plate solar collectorsrdquo Renewable Energy vol 34 no 4 pp1169ndash1174 2009
[20] H Ajam S Farahat and F Sarhaddi ldquoExergetic optimizationof solar air heaters and comparison with energy analysisrdquoInternational Journal of Thermodynamics vol 8 no 4 pp 183ndash190 2005
[21] M J Kerr and A Cuevas ldquoGeneralized analysis of the illumi-nation intensity versus open-circuit voltage of solar cellsrdquo SolarEnergy vol 76 no 1ndash3 pp 263ndash267 2004
[22] E Radziemska and E Klugmann ldquoThermally affected parame-ters of the current-voltage characteristics of silicon photocellrdquoEnergy Conversion and Management vol 43 no 14 pp 1889ndash1900 2002
[23] E E van Dyk B J Scott E L Meyer and A W R LeitchldquoTemperature dependence of performance of crystalline siliconphotovoltaic modulesrdquo South African Journal of Science vol 96no 4 pp 198ndash200 2000
[24] httpwwwgercinorgrenewablepdfSolar20Tariff20Order20120of202012pdf 2013
[25] M Veerachary T Senjyu and K Uezato ldquoVoltage-basedmaximum power point tracking control of PV systemrdquo IEEETransactions on Aerospace and Electronic Systems vol 38 no1 pp 262ndash270 2002
[26] M Veerachary and K S Shinoy ldquoV2-based power tracking fornonlinear PV sourcesrdquo IEE Proceedings-Electric Power Applica-tions vol 152 no 5 pp 1263ndash1270 2005
[27] I S Kim and M J Youn ldquoVariable-structure observer for solararray current estimation in a photovoltaic power-generationsystemrdquo IEE Proceedings-Electric Power Applications vol 152no 4 pp 953ndash959 2005
[28] I S Kim M B Kim and M J Youn ldquoNew maximum powerpoint tracker using sliding-mode observer for estimation ofsolar array current in the grid-connected photovoltaic systemrdquoIEEE Transactions on Industrial Electronics vol 53 no 4 pp1027ndash1035 2006
[29] H L Tsai C S Tu and Y J Su ldquoDevelopment of generalizedphotovoltaic model using MATLABSIMULINKrdquo in Proceed-ings of theWorld Congress on Engineering and Computer ScienceSan Francisco NC USA October 2008
[30] J CThongpron K Kirtikara and C Jivacate ldquoAmethod for thedetermination of dynamic resistance of photovoltaic modulesunder illuminationrdquo Solar Energy Materials and Solar Cells vol90 no 18-19 pp 3078ndash3084 2006
[31] J C Wang J C Shieh Y L Su et al ldquoA novel method for thedetermination of dynamic resistance for photovoltaicmodulesrdquoEnergy vol 36 no 10 pp 5968ndash5974 2011
[32] S Dubey G S Sandhu andG N Tiwari ldquoAnalytical expressionfor electrical efficiency of PVT hybrid air collectorrdquo AppliedEnergy vol 86 no 5 pp 697ndash705 2009
[33] S Kumar P K Singh G S Chilana and S R Dhariwal ldquoGen-eration and recombination lifetime measurement in siliconwafers using impedance spectroscopyrdquo Semiconductor Scienceand Technology vol 24 no 9 Article ID 095001 pp 1ndash8 2009
[34] J Millman and C C Halkias Integrated Electronics McGraw-Hill New York NY USA 1972
[35] S Kumar P K Singh and G S Chilana ldquoStudy of siliconsolar cell at different intensities of illumination andwavelengthsusing impedance spectroscopyrdquo Solar Energy Materials andSolar Cells vol 93 no 10 pp 1881ndash1884 2009
[36] S Kumar V Sareen N Batra and P K Singh ldquoStudy of C-Vcharacteristics in thin n+-p-p+ silicon solar cells and inducedjunction n-p-p+ cell structuresrdquo Solar Energy Materials andSolar Cells vol 94 no 9 pp 1469ndash1472 2010
[37] I Mora-Sero G Garcia-Belmonte P P Boix M A Vazquezand J Bisquert ldquoImpedance spectroscopy characterisation ofhighly efficient silicon solar cells under different light illumina-tion intensitiesrdquo Energy and Environmental Science vol 2 no 6pp 678ndash686 2009
[38] F Sarhaddi S Farahat H Ajam andA Behzadmehr ldquoExergeticoptimization of a solar photovoltaic arrayrdquo Journal of Thermo-dynamics vol 2009 Article ID 313561 11 pages 2009
[39] S M Sze Physics of Semiconductor Devices Wiley New YorkNY USA 2nd edition 1981
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
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International Journal ofPhotoenergy
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Carbohydrate Chemistry
International Journal of
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Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
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Analytical Methods in Chemistry
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Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Quantum Chemistry
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Organic Chemistry International
ElectrochemistryInternational Journal of
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CatalystsJournal of
6 International Journal of Photoenergy
Table 2 The parameters used for simulation under 1 Sun
Parametersunits 119877119878 (Ω) 119864119892 (eV) 119873119878 119873119875 119860 119879119862 (K) 119879ref (K) 119896119861 (JK) 119870119868 119902 (C) 119868SC (A) 119868RS (A) 119881OC (V)
For 1 Sun 0071 112 16 1 15 298 298 138 times 10
minus23065 times 10
minus31602 times 10
minus19 0259 086 times 10
minus12 986
Table 3 The value of 119877 119862 and corresponding 120591 obtained fromthe measured impedance spectra under different bias voltage con-ditions
Appliedvoltage(V)
Resistance inequivalent circuit
119877 (kΩ)
Capacitance inequivalent circuit
119862 (nF)
Timeconstant 120591
(ms)minus05 70 49 343minus02 55 514 2830 45 362 16302 37 351 13005 28 321 090
An active cooling mechanism is employed by flowing waterbehind the encapsulated solar PV module which is shown inFigure 3 By employing this mechanismmodule temperaturecould be lowered down to 45∘C A light dependent resistor(LDR) based one axis tracking system is developed for Suntracking with a provision of manual tracking on second axiswith an accuracy of plusmn3∘ as shown in Figure 3
32 Theory Validation and Characterization of LCPVModuleThe module characterization was done under standard testconditions (STC) by 119868-119881 characteristics impedance spec-troscopy (IS) and capacitance-voltage (CV) measurementand detailed parameters are given in Tables 2 and 3 Theconcentrated light is received by the solar PV module whichis placed at the focal plane of the PLPTC To simulate theelectrical power generated from this PV module the inputparameters are series resistance energy band gap number ofcells connected in series number of strings connected parallelto each other cell temperature ambient temperature short-circuit current ofmodule open-circuit voltage of themoduleand so on These input parameters are listed in Table 2
In this LCPV system a solar PV module manufacturedat WAAREE Energies Pvt Ltd module production line isused The open-circuit voltage and short-circuit current ofthis module aremeasured as119881OC = 986V and 119868SC = 0259Arespectively under AM15 spectrum at 29814 KThe current-voltage output characteristics of generalized solar PVmoduleunder AM15 solar spectrum are shown in Figure 4 In thesimulation short-circuit current open-circuit voltage seriesresistance and cell temperature measured under standardtest conditions (STC) by manufacturer are taken as inputparameters The current-voltage characteristic generatedfrom simulation programmatches well with the experimentalcurrent-voltage characteristic
Looking at the current-voltage curve it can be identifiedthat the photovoltaic module is a constant current source atlower values of voltage with current equal to the short-circuitcurrent (119868SC) With the further increase in voltage values the
0 2 4 6 8 100
005
01
015
02
025
03
Voltage (V)
Curr
ent (
A)
TheoreticalExperimental
e = 025 r = 0999
Figure 4 Current-voltage characteristics of the designed solar PVmodule under 1 Sun AM15 at 29814 K
current starts decreasing exponentially at certain point Thevalue of current becomes zero at open-circuit voltage (119881OC)The point where themodule operates at the highest efficiencyis called maximum power point (119875MAX)
For impedance measurements an ac signal having fre-quency in the range from 1 Hz to 01MHz with amplitudeof 5mV is used The impedance spectra were plotted in acomplex plane (ie 1198851015840 versus 119885
10158401015840 also known as Nyquistor ColendashCole plot [33]) which can provide information onany system that is composed of combination of interfacialand bulk process The measurements were carried out onthe developed LCPVmodule under forward and reverse bias(+05 V to minus05 V) conditions in the dark Figure 5 shows theimpedance spectrum of the LCPVmodule under reverse biasconditions (from 0 to minus05 V) The radius of the semicircleincreases with the increase in bias voltage as compared tozero bias demonstrating the bias dependence of resistanceand capacitance [33] The increase in the radius of semicircleduring reverse bias is observed due to expansion of depletionregion of the solar cell which increases the resistance offeredby the cell
Figure 6 shows the impedance spectrum under the for-ward bias conditions (from0 to 05V)where in contrast to thereverse bias opposite behavior is observed Here the radiusof the semicircle decreases with increasing positive bias fromits maximum value at zero bias The decrease in the radius ofsemicircle during forward bias is observed due to shrinking
International Journal of Photoenergy 7
0 2 4 6 8
times104
times104
0
05
1
15
2
25
3
35
Bias = 0VBias = minus02VBias = minus05V
Z998400 (Ohm)
Z998400998400
(Ohm
)
Figure 5 Impedance spectra of LCPV module under reverse biasconditions
times104
times104
0
05
1
15
2
25
Z998400 (Ohm)
Z998400998400
(Ohm
)
Bias = 0V
0 1 2 3 4 5
Bias = 02VBias = 05V
Figure 6 Impedance spectra of LCPV module under forward biasconditions
of depletion region of the solar cell which decreases theresistance offered by the cell
The ac equivalent circuit of the n+-p-p+structure underconsideration is shown in Figure 7 which incorporates thecapacitive effect owing to the excess minority carriers (119862119889commonly known as the diffusion capacitance) in parallelwith the depletion layer capacitance 119862119905 (Figure 7) Resistiveeffects arising from the minority carrier recombination areshown as the diffusion resistance (119877119889) in parallel with a shunt
RS
C = (Cd + Ct)
R = (RSH Rd)
Figure 7 The ac equivalent circuit of LCPV module to explainobserved impedance spectra
(119877SH) resistance and a series resistance 119877119878 connected in thecircuit [33]
Under forward bias condition due to the accumulationof minority carriers in the bulk the magnitude of thediffusion capacitance is large compared to the depletionregion capacitance [34] The ac impedance of the circuit isgiven by
119885 (120596) = 119885
1015840(120596) minus 119895119885
10158401015840(120596) (31)
where 119885
1015840 and 119885
10158401015840 are the magnitudes of the real andimaginary parts of impedance and a minus sign arises dueto capacitive reactance involved in the circuit On analyzingthe circuit 1198851015840 and 119885
10158401015840 can be written as
119885
1015840(120596) = 119877119904 +
119877
1 + (120596119877119862)
2
119885
10158401015840(120596) =
120596119862119877
2
1 + (120596119877119862)
2
(32)
For the case of very low 119877119878 when 119885
1015840 and 119885
10158401015840 are plotted ina complex plane by varying the frequency (120596) a semicircleof radius 1198772 with its center at (1198772 0) is obtained Furtherbecause of the semicircular geometry the maximum valueof 11988510158401015840 arises when 120596119898119877119862 = 1 where 120596119898 is the frequencyat which 119885
10158401015840 becomes maximum Thus we have that 119862 =
1120596119898119877 and the presence of 119877119878 shifts the semicircle byits value on the 119909-axis The analysis of the impedancediagram on the complex plane therefore gives values ofall the three parameters that is 119877 119862 and 119877119878 used in theequivalent circuit The product of resistance and capacitance(119877119862) represents the time constant (120591) The value of 119877 119862and corresponding 120591 obtained from themeasured impedancespectra under different bias voltage conditions is listed inTable 3These values are in good agreement with the existingliterature for silicon solar cells [33 35]
Capacitance-voltage (119862-119881) measurement is an importanttool to understand the transient behavior of a semiconductordevice Generally capacitance is measured in the reversedbias (Mott-Schottky) condition to determine barrier poten-tial and effective doping concentration Capacitance-voltagecharacterization is done for the developed LCPV module asshown in Figure 8
8 International Journal of Photoenergy
minus08 minus06 minus04 minus02 0 02 04 06 08Voltage (V)
times1014
0
05
1
15
2
25
3
1C
2(1F2)
Figure 8 The capacitance-voltage characterization of LCPV mod-ule
The dependence of barrier potential and doping concen-tration on the depletion region capacitance per unit area isgiven by [30]
1
1198622=
2
1199021198701205760119873
(119881bi minus 119881 minus
2119896119861119879
119902
)
119889 (1119862
2)
119889119881
= minus
2
1199021198701205760119873
(33)
where 119902 is the electron charge 119870 is dielectric constant ofsilicon 1205760 is the permittivity of free space 119881bi is barrierpotential 119896119861 is Boltzmannrsquos constant119879 is equal to 29814 K119873is doping concentration and 119881 represents applied potential
The slope and its intersection on the abscissa in theMott-Schottky plot shown in Figure 8 for the LCPV module givesthe doping concentration (119873) and barrier potential (119881bi)respectivelyThe119873 value is found as 779 times 1016 cmminus3 and thevalue of119881bi minus2119896119879119902 is equal to 056 eV which corresponds to119881bi = 061 eV The calculated values are in good agreementwith the reported values for commercially available siliconsolar cells [36 37]
4 LCPV Experiment under ATC
The experiments were carried out in the campus of Schoolof Solar Energy located in Gandhinagar India (Lat 2322∘Long 7268E) in the month of December (Year 2012) Themodule temperature was measured with the digital ther-mometer having an accuracy of plusmn01∘C during experimentswind speed was measured by anemometer as 085ms withan accuracy of plusmn5 Solar radiation and ambient temperaturewere recorded at the weather station located in the universitycampus The following parameters were measured duringexperiments ambient temperature solar radiation LCPVmodule and ambient temperature load current load voltageshort-circuit current and open-circuit voltage During theexperiments the module temperature was varied in the
range of 300ndash350K by controlling the flow rate of waterbehind the LCPV module Since the aim of this paper is toextract maximum electrical output from LCPV systems thethermodynamic analysis of flowingwater is avoided hereThecurrent-voltage measurements of an LCPV system are takenby Agilent SMU 6632B and by using multimeters and loadrheostat The sensitivity of the current-voltage measurementinstrument is given as plusmn3 The developed LCPV system isstudied by varying the number of reflecting mirrors arrangedin PLPTC
5 Result and Discussion
51 Exergy and Energy Analysis The effect of the lightconcentration and module temperature on the input exergyrate electrical exergy output rate and thermal exergy outputrate of LCPV module is estimated from the proposed modelin Section 2 It is found that with the increase in CR the inputexergy rate increases which results in increased amount ofenergy available to do useful work by the system The datalisted in Table 4 shows that the exergy efficiency decreaseswith the increase in the input exergy rate This decrease ismainly due to the increase in cell temperature which resultsin electrical exergy destruction with a rate of ldquo119881OC119868SC minus
119881mp119868mprdquo [38] Further the increase in the cell temperatureaffects 119881OC with a negative temperature coefficient as shownin the Figure 9 Figure 9 shows that 119881OC decreases from848V to 824V with increase in input exergy rate from3081W to 9612W when the cell temperature changesfrom 321 K to 3325 K The influence of the cell temperatureon exergy efficiency is clearly observed (Table 4) whichdecreases with the increase in the cell temperature Similareffect is observed by other researchers [15 38] Since the celltemperature changes with the increase in the input exergyrate it is imperative to design the LCPV system based on thisinformation so that useful exergy can bemaximized For thispurpose it is very important to track maximum power pointwhich depends on dynamic resistance of LCPV system
The proposed model in Section 2 is used to performenergy analysis of the LCPV module having 16 cells con-nected in series The static parameters (119868SC 119881OC 119875MAX and119877119878) of the LCPV module are measured in ATC conditionsas well as calculated by the proposed theoretical model Themeasured and simulated current-voltage characteristics ofLCPVmodule is shown in Figure 9 with varying input energyrate and corresponding temperature
It can be seen from Figure 9 that there is good agreementbetween the experimental and theoretical current-voltagecharacteristics which include 119868SC 119881OC 119875MAX 119877119878 FF 119903119889and efficiency The mean square of percentage deviation (119890)
is in the range of 274ndash843 and the linear coefficient ofcorrelation (119903) is in the range of 0995ndash0999
The measured values of solar irradiation 119868SC 119881OC 119875MAX119877119878 temperature FF 119903119889 and efficiency are listed in Table 5Generally the output current of the solar PV modulesincreases with the increase in input energy rate (ie solarirradiance received at focal point of PLPTC) With increasein the solar irradiance the higher number of photons strikes
International Journal of Photoenergy 9
Table 4 Exergy analysis of LCPV system
Solar irradiation(Wm2)
Cell temperature 119879119862 (K) Input exergy rate (W)Output exergy rate (W)
Exergy efficiency 120578ex ()Electricalexergy rate (W)
Thermal exergyrate (W)
1225 321 3081 2 043 5102254 328 5668 355 070 5033234 331 8133 491 083 5013822 3325 9612 554 091 482
Table 5 Parameter estimated from 119868-119881 curves plotted under various CR
Solarirradiation(Wm2)
Celltemperature
119879119862 (K)
Short-circuitcurrent 119868SC
(A)
Seriesresistance 119877119878
(Ω)
Dynamicresistance 119903119889
(Ω)
Open-circuitvoltage 119881OC
(V)
Maximumpower 119875MAX
(W)
Fill factor FF()
Energyefficiency 120578
()1000 298 025 112 1799 986 191 7458 7071225 321 033 120 1923 848 207 7397 6262254 328 063 129 2073 839 372 7037 6113234 331 091 139 2227 831 500 6700 5733822 3325 107 155 2484 824 584 6623 566
0 2 4 6 8 10Voltage (V)
Curr
ent (
A)
0
02
04
06
08
1
12
Simulation (2 mirrors)Experimental (2 mirrors)Simulation (4 mirrors)Experimental (4 mirrors)
Simulation (6 mirrors)Experimental (6 mirrors)Simulation (8 mirrors)Experimental (8 mirrors)
Figure 9 Simulated and experimental 119868-119881 characteristics of LCPVsystem under ATC
the solar PVmodule which results in enhanced electron-holepair production and higher photocurrent [39] The valuesof the dynamic resistance at MPP are computed using thevalues of 119868PH 119868SC and 119877119878 The dynamic resistance of LCPVmodule is calculated in an effective manner using (21) andis listed in Table 5 Approximate error between experimentaland theoretical dynamic resistance of the LCPV module isfound as sim13ndash21 which shows the uncertainty is wellwithin the practically acceptable limits
The plot shown in Figure 9 and extracted data listed inTable 5 describe the dependence of FF and efficiency of LCPV
module on the change in input energy rate and moduletemperature From the observed results it can be concludedthat the FF and efficiency of LCPV module decrease as theinput energy rate increasesThe decrease in FF and efficiencyof solar PV module with the increasing energy rate is highlydependent on the increase in electrical exergy destructionof LCPV module due to the increase in input energy rateand temperature As a result of increased input energy ratedynamic resistance offers greater resistive power losses inLCPV module and thus reduces its performance by reducingthe FF and efficiency The increase in the dynamic resistanceand reduction in the FF of LCPV module are foremostparameters for the decrease in the electrical energy efficiency
The effects of the cell temperature (119879119862) on 119868-119881 curveof LCPV module is estimated from the proposed model asshown in Figure 10 As the device temperature increasessmall increase in short-circuit current is observed how-ever the open-circuit voltage rapidly decreases due to theexponential dependence of the saturation current on thetemperature as given by (18) [39] In the actual experimentssimilar effect of temperature on open-circuit voltage (119881OC) isobserved and it is found that the 119881OC decreases from 986 to824V with temperature coefficient of voltage asymp minus0021 VKunder ATC as shown in Figure 9
A decrease in the 119875MAX with the increase in 119879119862 isobserved because with the increase in temperature the bandgap of the intrinsic semiconductor shrinks The increasedtemperature causes reduction in open-circuit voltage (119881OC)and the increase in the photocurrent for a given irradiancebecause of high injection of electrons from valance band toconduction band of semiconductor material [39]
52 Economical Analysis of LCPV System Net Present Value(NPV) method allows analyzing the economic aspects of anyengineering system and is used for the economic analysis of
10 International Journal of Photoenergy
Table 6 Cost of various components of LCPV system (asymp1 kWP) to find initial investment cost (numbers provided here are in accordancewith the current market price)lowast
Components Module BOSBattery Charge controller Support structure Tracker Cabling
Cost (in US$) 206 800 48 320 590 120Total initial investment cost (in US$) 2084
lowastThe price is based on market survey which may vary depending on specific location or company
Table 7 Economical analysis of LCPV system (having a lifetime of 25 years [24])
Period (year) 0 1 2 3 4 5 6 7 8Initial investment cost minus2084
Benefitslowastlowast 29043 29043 29043 29043 29043 29043 29043 29043O and M costlowastlowastlowast minus218 minus230 minus243 minus257 minus272 minus288 minus304 minus321
Discount rate 001 001 001 001 001 001 001 001 001Net cash flow 28825 28813 287995 28786 28771 28755 28739 28721119886 099 099 098 097 096 095 094 093 092Discounted net cash flow 28539 28245 27953 27662 27374 27089 26805 26524NPV minus17986 minus15162 minus12366 minus960 minus68626 minus41537 minus14732 11792lowastlowastBenefits are based on the tariff policy of Gujarat Electricity Regulatory Commission released for projects commissioned in 2012 [24]lowastlowastlowastEscalation in operating cost is taken as 572 annually [24]
300K325K
350K375K
0 2 4 6 8 100
005
01
015
02
025
03
Voltage (V)
Curr
ent (
A)
Figure 10 Variation of current-voltage characteristics with the celltemperature 119879119862
developed LCPV system of 1 kWP As the system presented inthis paper is very small for economic analysis the calculationsare done for 1 kWP system NPV method allows accountingfor the present value of annual capital expenditures andsavings during the lifetime of the system Net present value(NPV) includes sum of all the current values (costs are shownas negative and net savings are shown as positive) Foracceptance of any engineering project the positive NPV is
desiredThe formulas for calculatingNPVand correspondingfactor are given as [16]
NPV =
119899
sum
119894=1
(119861 minus 119862)119894
119886 =
1
(1 + 119894)
119901
(34)
where ldquo119886rdquo represents net present value factor ldquo119861rdquo representsgain ldquo119901rdquo represents the period and ldquo119894rdquo represents discountrate in the equation given previously
The initial investment cost is required in order to calculateNPV which includes module cost and balance of systems(BOS) cost The components of BOS include battery storagecharge controllers support structure tracking system andtransmission cables Cost of all these components is listedin Table 6 Using the initial investment cost and the formulaoutlined in (34) the NPV is calculated (Table 7) Operationandmaintenance (O andM) cost is taken as 075 of the totalinvestment cost with escalation in operating cost as 572 perannum [24] The feasibility of this project is demonstrated bya positive value of NPV obtained within 8 years
6 Conclusions
A theoretical model is used to perform electrical energy andexergy analyses of low-concentration photovoltaic (LCPV)system working under actual test conditions (ATC) Theexergy efficiency of LCPV system is in the range from51 to 482 with increasing rate of input exergy ratefrom 3081W to 9612W when concentration ratio changes
International Journal of Photoenergy 11
from 185 to 517 Sun Short-circuit current shows increasingtrend with increasing input exergy rate of asymp0011 AW Powerconversion efficiency decreases from 707 to 566 and open-circuit voltage decreases from986 to 824Vwith temperaturecoefficient of voltage asymp minus0021 VK under ATC The resultsconfirm that the commercially available silicon solar PVmodule performs satisfactorily under low concentration
Nomenclature
CR Concentration ratio119882 Width of the profile119863 Depth of the profile0119903 Rim angle120579119888 Acceptance angle119865 Focus point120588mirror Reflectivity of mirrors119877min Half width of the solar panel119871 Parabolic trough length120572 Absorption coefficient119860119886 Aperture area119896119861 Boltzmannrsquos constant (138 times 10minus23)119868PH Light generated current119868119878 Cell saturation or dark current119902 Electron charge (16 times 10minus19 C)119860 Ideality factor119880rad Radiative heat loss coefficient119880con Convective heat loss coefficient119879119862 Working temperature of solar cell (Kelvin)119877SH Shunt resistance119877119878 Series resistance119873119878 Series number of cells in a PV module119873119875 Parallel number of modules for a PV array119868SC Cellrsquos short-circuit current at 29814 K and
1 kWm2119870119868 Cellrsquos short-circuit current temperature
coefficient119879Ref Cellrsquos reference temperature120582 Solar insolation in kWm2119868RS Cellrsquos reverse saturation current at a
reference temperature and solar radiation119864119892 Band gap energy of the semiconductor119868mp Current at maximum power point119881mp Voltage at maximum power point
Acknowledgments
The authors acknowledge the financial support providedby Gujarat Energy Development Agency (GEDA) todevelop CPV system by Grant no GEDAECRECMarch-201039174 Authors also acknowledge WAAREE EnergiesPvt Ltd India for providing encapsulated crystallinesilicon solar PV modules for this study
References
[1] G Sala D Pachon I Anton and Test Test Rating andSpecification of PV Concentrator Components and Systems
(C-Rating Project) Book1 Classification of PV ConcentratorsUniversidad Politecnica de Madrid Madrid Spain 2002httpwwwies-defupmesiesCRATINGDocumentshtm
[2] M Yamaguchi andA Luque ldquoHigh efficiency and high concen-tration in photovoltaicsrdquo IEEE Transactions on Electron Devicesvol 46 no 10 pp 2139ndash2144 1999
[3] M A Green and A Ho-Baillie ldquoForty three per cent compositesplit-spectrum concentrator solar cell efficiencyrdquo Progress inPhotovoltaics vol 18 no 1 pp 42ndash47 2010
[4] H Cotal C Fetzer J Boisvert et al ldquoIII-V multijunction solarcells for concentrating photovoltaicsrdquo Energy and Environmen-tal Science vol 2 no 2 pp 174ndash192 2009
[5] G Sala I Anton J Monedero et al ldquoThe euclides-thermieconcentrator power plant in continuous operationrdquo in Proceed-ings of the 17th European Photovoltaic Solar Energy Conference(EUPVSEC rsquo01) pp 488ndash491 Munich Germany 2001
[6] V Garboushian S Yoon G Turner A Gunn and D FairldquoNovel high-concentration PV technology for cost competitiveutility bulk power generationrdquo in Proceedings of the 24th IEEEPhotovoltaic Specialists Conference Part 2 (of 2) pp 1060ndash1063December 1994
[7] M Castro I Anton and G Sala ldquoPilot production of concen-trator silicon solar cells approaching industrializationrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1697ndash17052008
[8] A Zahedi ldquoReview of modelling details in relation to low-concentration solar concentrating photovoltaicrdquoRenewable andSustainable Energy Reviews vol 15 no 3 pp 1609ndash1614 2011
[9] M Li X Ji G Li S Wei Y Li and F Shi ldquoPerformancestudy of solar cell arrays based on a trough concentratingphotovoltaicthermal systemrdquoApplied Energy vol 88 no 9 pp3218ndash3227 2011
[10] M A Schuetz K A Shell S A Brown G S Reinbolt RH French and R J Davis ldquoDesign and construction of a sim
7times low-concentration photovoltaic system based on compoundparabolic concentratorsrdquo IEEE Journal of Photovoltaics vol 2no 3 pp 382ndash386 2012
[11] H G Riveros and A I Oliva ldquoGraphical analysis of sunconcentrating collectorsrdquo Solar Energy vol 36 no 4 pp 313ndash322 1986
[12] O A Jaramillo J A Del Rıo and G Huelsz ldquoThermal study ofoptical fibres transmitting concentrated solar energyrdquo Journal ofPhysics D vol 32 no 9 pp 1000ndash1005 1999
[13] O A Jaramillo G Huelsz and J A Del Rıo ldquoA theoretical andexperimental thermal study of SiO2 optical fibres transmittingconcentrated radiative energyrdquo Journal of Physics D vol 35 no2 pp 95ndash102 2002
[14] C Kandilli and K Ulgen ldquoReview and modelling the systemsof transmission concentrated solar energy via optical fibresrdquoRenewable and Sustainable Energy Reviews vol 13 no 1 pp 67ndash84 2009
[15] A S Joshi I Dincer and B V Reddy ldquoThermodynamicassessment of photovoltaic systemsrdquo Solar Energy vol 83 no8 pp 1139ndash1149 2009
[16] C Kandilli ldquoPerformance analysis of novel concentrating solarphotovoltaic combined systemrdquo Energy Conversion and Man-agement vol 67 pp 186ndash196 2013
[17] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part I the concept of net exergyflow and the modeling of solar air heatersrdquo Solar Energy vol 41no 2 pp 127ndash132 1988
12 International Journal of Photoenergy
[18] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part 2 results of optimizationand analysis of sensibility to variations of operating conditionsrdquoSolar Energy vol 41 no 4 pp 309ndash317 1988
[19] S Farahat F Sarhaddi and H Ajam ldquoExergetic optimization offlat plate solar collectorsrdquo Renewable Energy vol 34 no 4 pp1169ndash1174 2009
[20] H Ajam S Farahat and F Sarhaddi ldquoExergetic optimizationof solar air heaters and comparison with energy analysisrdquoInternational Journal of Thermodynamics vol 8 no 4 pp 183ndash190 2005
[21] M J Kerr and A Cuevas ldquoGeneralized analysis of the illumi-nation intensity versus open-circuit voltage of solar cellsrdquo SolarEnergy vol 76 no 1ndash3 pp 263ndash267 2004
[22] E Radziemska and E Klugmann ldquoThermally affected parame-ters of the current-voltage characteristics of silicon photocellrdquoEnergy Conversion and Management vol 43 no 14 pp 1889ndash1900 2002
[23] E E van Dyk B J Scott E L Meyer and A W R LeitchldquoTemperature dependence of performance of crystalline siliconphotovoltaic modulesrdquo South African Journal of Science vol 96no 4 pp 198ndash200 2000
[24] httpwwwgercinorgrenewablepdfSolar20Tariff20Order20120of202012pdf 2013
[25] M Veerachary T Senjyu and K Uezato ldquoVoltage-basedmaximum power point tracking control of PV systemrdquo IEEETransactions on Aerospace and Electronic Systems vol 38 no1 pp 262ndash270 2002
[26] M Veerachary and K S Shinoy ldquoV2-based power tracking fornonlinear PV sourcesrdquo IEE Proceedings-Electric Power Applica-tions vol 152 no 5 pp 1263ndash1270 2005
[27] I S Kim and M J Youn ldquoVariable-structure observer for solararray current estimation in a photovoltaic power-generationsystemrdquo IEE Proceedings-Electric Power Applications vol 152no 4 pp 953ndash959 2005
[28] I S Kim M B Kim and M J Youn ldquoNew maximum powerpoint tracker using sliding-mode observer for estimation ofsolar array current in the grid-connected photovoltaic systemrdquoIEEE Transactions on Industrial Electronics vol 53 no 4 pp1027ndash1035 2006
[29] H L Tsai C S Tu and Y J Su ldquoDevelopment of generalizedphotovoltaic model using MATLABSIMULINKrdquo in Proceed-ings of theWorld Congress on Engineering and Computer ScienceSan Francisco NC USA October 2008
[30] J CThongpron K Kirtikara and C Jivacate ldquoAmethod for thedetermination of dynamic resistance of photovoltaic modulesunder illuminationrdquo Solar Energy Materials and Solar Cells vol90 no 18-19 pp 3078ndash3084 2006
[31] J C Wang J C Shieh Y L Su et al ldquoA novel method for thedetermination of dynamic resistance for photovoltaicmodulesrdquoEnergy vol 36 no 10 pp 5968ndash5974 2011
[32] S Dubey G S Sandhu andG N Tiwari ldquoAnalytical expressionfor electrical efficiency of PVT hybrid air collectorrdquo AppliedEnergy vol 86 no 5 pp 697ndash705 2009
[33] S Kumar P K Singh G S Chilana and S R Dhariwal ldquoGen-eration and recombination lifetime measurement in siliconwafers using impedance spectroscopyrdquo Semiconductor Scienceand Technology vol 24 no 9 Article ID 095001 pp 1ndash8 2009
[34] J Millman and C C Halkias Integrated Electronics McGraw-Hill New York NY USA 1972
[35] S Kumar P K Singh and G S Chilana ldquoStudy of siliconsolar cell at different intensities of illumination andwavelengthsusing impedance spectroscopyrdquo Solar Energy Materials andSolar Cells vol 93 no 10 pp 1881ndash1884 2009
[36] S Kumar V Sareen N Batra and P K Singh ldquoStudy of C-Vcharacteristics in thin n+-p-p+ silicon solar cells and inducedjunction n-p-p+ cell structuresrdquo Solar Energy Materials andSolar Cells vol 94 no 9 pp 1469ndash1472 2010
[37] I Mora-Sero G Garcia-Belmonte P P Boix M A Vazquezand J Bisquert ldquoImpedance spectroscopy characterisation ofhighly efficient silicon solar cells under different light illumina-tion intensitiesrdquo Energy and Environmental Science vol 2 no 6pp 678ndash686 2009
[38] F Sarhaddi S Farahat H Ajam andA Behzadmehr ldquoExergeticoptimization of a solar photovoltaic arrayrdquo Journal of Thermo-dynamics vol 2009 Article ID 313561 11 pages 2009
[39] S M Sze Physics of Semiconductor Devices Wiley New YorkNY USA 2nd edition 1981
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
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Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
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Journal of
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Analytical ChemistryInternational Journal of
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Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
International Journal of Photoenergy 7
0 2 4 6 8
times104
times104
0
05
1
15
2
25
3
35
Bias = 0VBias = minus02VBias = minus05V
Z998400 (Ohm)
Z998400998400
(Ohm
)
Figure 5 Impedance spectra of LCPV module under reverse biasconditions
times104
times104
0
05
1
15
2
25
Z998400 (Ohm)
Z998400998400
(Ohm
)
Bias = 0V
0 1 2 3 4 5
Bias = 02VBias = 05V
Figure 6 Impedance spectra of LCPV module under forward biasconditions
of depletion region of the solar cell which decreases theresistance offered by the cell
The ac equivalent circuit of the n+-p-p+structure underconsideration is shown in Figure 7 which incorporates thecapacitive effect owing to the excess minority carriers (119862119889commonly known as the diffusion capacitance) in parallelwith the depletion layer capacitance 119862119905 (Figure 7) Resistiveeffects arising from the minority carrier recombination areshown as the diffusion resistance (119877119889) in parallel with a shunt
RS
C = (Cd + Ct)
R = (RSH Rd)
Figure 7 The ac equivalent circuit of LCPV module to explainobserved impedance spectra
(119877SH) resistance and a series resistance 119877119878 connected in thecircuit [33]
Under forward bias condition due to the accumulationof minority carriers in the bulk the magnitude of thediffusion capacitance is large compared to the depletionregion capacitance [34] The ac impedance of the circuit isgiven by
119885 (120596) = 119885
1015840(120596) minus 119895119885
10158401015840(120596) (31)
where 119885
1015840 and 119885
10158401015840 are the magnitudes of the real andimaginary parts of impedance and a minus sign arises dueto capacitive reactance involved in the circuit On analyzingthe circuit 1198851015840 and 119885
10158401015840 can be written as
119885
1015840(120596) = 119877119904 +
119877
1 + (120596119877119862)
2
119885
10158401015840(120596) =
120596119862119877
2
1 + (120596119877119862)
2
(32)
For the case of very low 119877119878 when 119885
1015840 and 119885
10158401015840 are plotted ina complex plane by varying the frequency (120596) a semicircleof radius 1198772 with its center at (1198772 0) is obtained Furtherbecause of the semicircular geometry the maximum valueof 11988510158401015840 arises when 120596119898119877119862 = 1 where 120596119898 is the frequencyat which 119885
10158401015840 becomes maximum Thus we have that 119862 =
1120596119898119877 and the presence of 119877119878 shifts the semicircle byits value on the 119909-axis The analysis of the impedancediagram on the complex plane therefore gives values ofall the three parameters that is 119877 119862 and 119877119878 used in theequivalent circuit The product of resistance and capacitance(119877119862) represents the time constant (120591) The value of 119877 119862and corresponding 120591 obtained from themeasured impedancespectra under different bias voltage conditions is listed inTable 3These values are in good agreement with the existingliterature for silicon solar cells [33 35]
Capacitance-voltage (119862-119881) measurement is an importanttool to understand the transient behavior of a semiconductordevice Generally capacitance is measured in the reversedbias (Mott-Schottky) condition to determine barrier poten-tial and effective doping concentration Capacitance-voltagecharacterization is done for the developed LCPV module asshown in Figure 8
8 International Journal of Photoenergy
minus08 minus06 minus04 minus02 0 02 04 06 08Voltage (V)
times1014
0
05
1
15
2
25
3
1C
2(1F2)
Figure 8 The capacitance-voltage characterization of LCPV mod-ule
The dependence of barrier potential and doping concen-tration on the depletion region capacitance per unit area isgiven by [30]
1
1198622=
2
1199021198701205760119873
(119881bi minus 119881 minus
2119896119861119879
119902
)
119889 (1119862
2)
119889119881
= minus
2
1199021198701205760119873
(33)
where 119902 is the electron charge 119870 is dielectric constant ofsilicon 1205760 is the permittivity of free space 119881bi is barrierpotential 119896119861 is Boltzmannrsquos constant119879 is equal to 29814 K119873is doping concentration and 119881 represents applied potential
The slope and its intersection on the abscissa in theMott-Schottky plot shown in Figure 8 for the LCPV module givesthe doping concentration (119873) and barrier potential (119881bi)respectivelyThe119873 value is found as 779 times 1016 cmminus3 and thevalue of119881bi minus2119896119879119902 is equal to 056 eV which corresponds to119881bi = 061 eV The calculated values are in good agreementwith the reported values for commercially available siliconsolar cells [36 37]
4 LCPV Experiment under ATC
The experiments were carried out in the campus of Schoolof Solar Energy located in Gandhinagar India (Lat 2322∘Long 7268E) in the month of December (Year 2012) Themodule temperature was measured with the digital ther-mometer having an accuracy of plusmn01∘C during experimentswind speed was measured by anemometer as 085ms withan accuracy of plusmn5 Solar radiation and ambient temperaturewere recorded at the weather station located in the universitycampus The following parameters were measured duringexperiments ambient temperature solar radiation LCPVmodule and ambient temperature load current load voltageshort-circuit current and open-circuit voltage During theexperiments the module temperature was varied in the
range of 300ndash350K by controlling the flow rate of waterbehind the LCPV module Since the aim of this paper is toextract maximum electrical output from LCPV systems thethermodynamic analysis of flowingwater is avoided hereThecurrent-voltage measurements of an LCPV system are takenby Agilent SMU 6632B and by using multimeters and loadrheostat The sensitivity of the current-voltage measurementinstrument is given as plusmn3 The developed LCPV system isstudied by varying the number of reflecting mirrors arrangedin PLPTC
5 Result and Discussion
51 Exergy and Energy Analysis The effect of the lightconcentration and module temperature on the input exergyrate electrical exergy output rate and thermal exergy outputrate of LCPV module is estimated from the proposed modelin Section 2 It is found that with the increase in CR the inputexergy rate increases which results in increased amount ofenergy available to do useful work by the system The datalisted in Table 4 shows that the exergy efficiency decreaseswith the increase in the input exergy rate This decrease ismainly due to the increase in cell temperature which resultsin electrical exergy destruction with a rate of ldquo119881OC119868SC minus
119881mp119868mprdquo [38] Further the increase in the cell temperatureaffects 119881OC with a negative temperature coefficient as shownin the Figure 9 Figure 9 shows that 119881OC decreases from848V to 824V with increase in input exergy rate from3081W to 9612W when the cell temperature changesfrom 321 K to 3325 K The influence of the cell temperatureon exergy efficiency is clearly observed (Table 4) whichdecreases with the increase in the cell temperature Similareffect is observed by other researchers [15 38] Since the celltemperature changes with the increase in the input exergyrate it is imperative to design the LCPV system based on thisinformation so that useful exergy can bemaximized For thispurpose it is very important to track maximum power pointwhich depends on dynamic resistance of LCPV system
The proposed model in Section 2 is used to performenergy analysis of the LCPV module having 16 cells con-nected in series The static parameters (119868SC 119881OC 119875MAX and119877119878) of the LCPV module are measured in ATC conditionsas well as calculated by the proposed theoretical model Themeasured and simulated current-voltage characteristics ofLCPVmodule is shown in Figure 9 with varying input energyrate and corresponding temperature
It can be seen from Figure 9 that there is good agreementbetween the experimental and theoretical current-voltagecharacteristics which include 119868SC 119881OC 119875MAX 119877119878 FF 119903119889and efficiency The mean square of percentage deviation (119890)
is in the range of 274ndash843 and the linear coefficient ofcorrelation (119903) is in the range of 0995ndash0999
The measured values of solar irradiation 119868SC 119881OC 119875MAX119877119878 temperature FF 119903119889 and efficiency are listed in Table 5Generally the output current of the solar PV modulesincreases with the increase in input energy rate (ie solarirradiance received at focal point of PLPTC) With increasein the solar irradiance the higher number of photons strikes
International Journal of Photoenergy 9
Table 4 Exergy analysis of LCPV system
Solar irradiation(Wm2)
Cell temperature 119879119862 (K) Input exergy rate (W)Output exergy rate (W)
Exergy efficiency 120578ex ()Electricalexergy rate (W)
Thermal exergyrate (W)
1225 321 3081 2 043 5102254 328 5668 355 070 5033234 331 8133 491 083 5013822 3325 9612 554 091 482
Table 5 Parameter estimated from 119868-119881 curves plotted under various CR
Solarirradiation(Wm2)
Celltemperature
119879119862 (K)
Short-circuitcurrent 119868SC
(A)
Seriesresistance 119877119878
(Ω)
Dynamicresistance 119903119889
(Ω)
Open-circuitvoltage 119881OC
(V)
Maximumpower 119875MAX
(W)
Fill factor FF()
Energyefficiency 120578
()1000 298 025 112 1799 986 191 7458 7071225 321 033 120 1923 848 207 7397 6262254 328 063 129 2073 839 372 7037 6113234 331 091 139 2227 831 500 6700 5733822 3325 107 155 2484 824 584 6623 566
0 2 4 6 8 10Voltage (V)
Curr
ent (
A)
0
02
04
06
08
1
12
Simulation (2 mirrors)Experimental (2 mirrors)Simulation (4 mirrors)Experimental (4 mirrors)
Simulation (6 mirrors)Experimental (6 mirrors)Simulation (8 mirrors)Experimental (8 mirrors)
Figure 9 Simulated and experimental 119868-119881 characteristics of LCPVsystem under ATC
the solar PVmodule which results in enhanced electron-holepair production and higher photocurrent [39] The valuesof the dynamic resistance at MPP are computed using thevalues of 119868PH 119868SC and 119877119878 The dynamic resistance of LCPVmodule is calculated in an effective manner using (21) andis listed in Table 5 Approximate error between experimentaland theoretical dynamic resistance of the LCPV module isfound as sim13ndash21 which shows the uncertainty is wellwithin the practically acceptable limits
The plot shown in Figure 9 and extracted data listed inTable 5 describe the dependence of FF and efficiency of LCPV
module on the change in input energy rate and moduletemperature From the observed results it can be concludedthat the FF and efficiency of LCPV module decrease as theinput energy rate increasesThe decrease in FF and efficiencyof solar PV module with the increasing energy rate is highlydependent on the increase in electrical exergy destructionof LCPV module due to the increase in input energy rateand temperature As a result of increased input energy ratedynamic resistance offers greater resistive power losses inLCPV module and thus reduces its performance by reducingthe FF and efficiency The increase in the dynamic resistanceand reduction in the FF of LCPV module are foremostparameters for the decrease in the electrical energy efficiency
The effects of the cell temperature (119879119862) on 119868-119881 curveof LCPV module is estimated from the proposed model asshown in Figure 10 As the device temperature increasessmall increase in short-circuit current is observed how-ever the open-circuit voltage rapidly decreases due to theexponential dependence of the saturation current on thetemperature as given by (18) [39] In the actual experimentssimilar effect of temperature on open-circuit voltage (119881OC) isobserved and it is found that the 119881OC decreases from 986 to824V with temperature coefficient of voltage asymp minus0021 VKunder ATC as shown in Figure 9
A decrease in the 119875MAX with the increase in 119879119862 isobserved because with the increase in temperature the bandgap of the intrinsic semiconductor shrinks The increasedtemperature causes reduction in open-circuit voltage (119881OC)and the increase in the photocurrent for a given irradiancebecause of high injection of electrons from valance band toconduction band of semiconductor material [39]
52 Economical Analysis of LCPV System Net Present Value(NPV) method allows analyzing the economic aspects of anyengineering system and is used for the economic analysis of
10 International Journal of Photoenergy
Table 6 Cost of various components of LCPV system (asymp1 kWP) to find initial investment cost (numbers provided here are in accordancewith the current market price)lowast
Components Module BOSBattery Charge controller Support structure Tracker Cabling
Cost (in US$) 206 800 48 320 590 120Total initial investment cost (in US$) 2084
lowastThe price is based on market survey which may vary depending on specific location or company
Table 7 Economical analysis of LCPV system (having a lifetime of 25 years [24])
Period (year) 0 1 2 3 4 5 6 7 8Initial investment cost minus2084
Benefitslowastlowast 29043 29043 29043 29043 29043 29043 29043 29043O and M costlowastlowastlowast minus218 minus230 minus243 minus257 minus272 minus288 minus304 minus321
Discount rate 001 001 001 001 001 001 001 001 001Net cash flow 28825 28813 287995 28786 28771 28755 28739 28721119886 099 099 098 097 096 095 094 093 092Discounted net cash flow 28539 28245 27953 27662 27374 27089 26805 26524NPV minus17986 minus15162 minus12366 minus960 minus68626 minus41537 minus14732 11792lowastlowastBenefits are based on the tariff policy of Gujarat Electricity Regulatory Commission released for projects commissioned in 2012 [24]lowastlowastlowastEscalation in operating cost is taken as 572 annually [24]
300K325K
350K375K
0 2 4 6 8 100
005
01
015
02
025
03
Voltage (V)
Curr
ent (
A)
Figure 10 Variation of current-voltage characteristics with the celltemperature 119879119862
developed LCPV system of 1 kWP As the system presented inthis paper is very small for economic analysis the calculationsare done for 1 kWP system NPV method allows accountingfor the present value of annual capital expenditures andsavings during the lifetime of the system Net present value(NPV) includes sum of all the current values (costs are shownas negative and net savings are shown as positive) Foracceptance of any engineering project the positive NPV is
desiredThe formulas for calculatingNPVand correspondingfactor are given as [16]
NPV =
119899
sum
119894=1
(119861 minus 119862)119894
119886 =
1
(1 + 119894)
119901
(34)
where ldquo119886rdquo represents net present value factor ldquo119861rdquo representsgain ldquo119901rdquo represents the period and ldquo119894rdquo represents discountrate in the equation given previously
The initial investment cost is required in order to calculateNPV which includes module cost and balance of systems(BOS) cost The components of BOS include battery storagecharge controllers support structure tracking system andtransmission cables Cost of all these components is listedin Table 6 Using the initial investment cost and the formulaoutlined in (34) the NPV is calculated (Table 7) Operationandmaintenance (O andM) cost is taken as 075 of the totalinvestment cost with escalation in operating cost as 572 perannum [24] The feasibility of this project is demonstrated bya positive value of NPV obtained within 8 years
6 Conclusions
A theoretical model is used to perform electrical energy andexergy analyses of low-concentration photovoltaic (LCPV)system working under actual test conditions (ATC) Theexergy efficiency of LCPV system is in the range from51 to 482 with increasing rate of input exergy ratefrom 3081W to 9612W when concentration ratio changes
International Journal of Photoenergy 11
from 185 to 517 Sun Short-circuit current shows increasingtrend with increasing input exergy rate of asymp0011 AW Powerconversion efficiency decreases from 707 to 566 and open-circuit voltage decreases from986 to 824Vwith temperaturecoefficient of voltage asymp minus0021 VK under ATC The resultsconfirm that the commercially available silicon solar PVmodule performs satisfactorily under low concentration
Nomenclature
CR Concentration ratio119882 Width of the profile119863 Depth of the profile0119903 Rim angle120579119888 Acceptance angle119865 Focus point120588mirror Reflectivity of mirrors119877min Half width of the solar panel119871 Parabolic trough length120572 Absorption coefficient119860119886 Aperture area119896119861 Boltzmannrsquos constant (138 times 10minus23)119868PH Light generated current119868119878 Cell saturation or dark current119902 Electron charge (16 times 10minus19 C)119860 Ideality factor119880rad Radiative heat loss coefficient119880con Convective heat loss coefficient119879119862 Working temperature of solar cell (Kelvin)119877SH Shunt resistance119877119878 Series resistance119873119878 Series number of cells in a PV module119873119875 Parallel number of modules for a PV array119868SC Cellrsquos short-circuit current at 29814 K and
1 kWm2119870119868 Cellrsquos short-circuit current temperature
coefficient119879Ref Cellrsquos reference temperature120582 Solar insolation in kWm2119868RS Cellrsquos reverse saturation current at a
reference temperature and solar radiation119864119892 Band gap energy of the semiconductor119868mp Current at maximum power point119881mp Voltage at maximum power point
Acknowledgments
The authors acknowledge the financial support providedby Gujarat Energy Development Agency (GEDA) todevelop CPV system by Grant no GEDAECRECMarch-201039174 Authors also acknowledge WAAREE EnergiesPvt Ltd India for providing encapsulated crystallinesilicon solar PV modules for this study
References
[1] G Sala D Pachon I Anton and Test Test Rating andSpecification of PV Concentrator Components and Systems
(C-Rating Project) Book1 Classification of PV ConcentratorsUniversidad Politecnica de Madrid Madrid Spain 2002httpwwwies-defupmesiesCRATINGDocumentshtm
[2] M Yamaguchi andA Luque ldquoHigh efficiency and high concen-tration in photovoltaicsrdquo IEEE Transactions on Electron Devicesvol 46 no 10 pp 2139ndash2144 1999
[3] M A Green and A Ho-Baillie ldquoForty three per cent compositesplit-spectrum concentrator solar cell efficiencyrdquo Progress inPhotovoltaics vol 18 no 1 pp 42ndash47 2010
[4] H Cotal C Fetzer J Boisvert et al ldquoIII-V multijunction solarcells for concentrating photovoltaicsrdquo Energy and Environmen-tal Science vol 2 no 2 pp 174ndash192 2009
[5] G Sala I Anton J Monedero et al ldquoThe euclides-thermieconcentrator power plant in continuous operationrdquo in Proceed-ings of the 17th European Photovoltaic Solar Energy Conference(EUPVSEC rsquo01) pp 488ndash491 Munich Germany 2001
[6] V Garboushian S Yoon G Turner A Gunn and D FairldquoNovel high-concentration PV technology for cost competitiveutility bulk power generationrdquo in Proceedings of the 24th IEEEPhotovoltaic Specialists Conference Part 2 (of 2) pp 1060ndash1063December 1994
[7] M Castro I Anton and G Sala ldquoPilot production of concen-trator silicon solar cells approaching industrializationrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1697ndash17052008
[8] A Zahedi ldquoReview of modelling details in relation to low-concentration solar concentrating photovoltaicrdquoRenewable andSustainable Energy Reviews vol 15 no 3 pp 1609ndash1614 2011
[9] M Li X Ji G Li S Wei Y Li and F Shi ldquoPerformancestudy of solar cell arrays based on a trough concentratingphotovoltaicthermal systemrdquoApplied Energy vol 88 no 9 pp3218ndash3227 2011
[10] M A Schuetz K A Shell S A Brown G S Reinbolt RH French and R J Davis ldquoDesign and construction of a sim
7times low-concentration photovoltaic system based on compoundparabolic concentratorsrdquo IEEE Journal of Photovoltaics vol 2no 3 pp 382ndash386 2012
[11] H G Riveros and A I Oliva ldquoGraphical analysis of sunconcentrating collectorsrdquo Solar Energy vol 36 no 4 pp 313ndash322 1986
[12] O A Jaramillo J A Del Rıo and G Huelsz ldquoThermal study ofoptical fibres transmitting concentrated solar energyrdquo Journal ofPhysics D vol 32 no 9 pp 1000ndash1005 1999
[13] O A Jaramillo G Huelsz and J A Del Rıo ldquoA theoretical andexperimental thermal study of SiO2 optical fibres transmittingconcentrated radiative energyrdquo Journal of Physics D vol 35 no2 pp 95ndash102 2002
[14] C Kandilli and K Ulgen ldquoReview and modelling the systemsof transmission concentrated solar energy via optical fibresrdquoRenewable and Sustainable Energy Reviews vol 13 no 1 pp 67ndash84 2009
[15] A S Joshi I Dincer and B V Reddy ldquoThermodynamicassessment of photovoltaic systemsrdquo Solar Energy vol 83 no8 pp 1139ndash1149 2009
[16] C Kandilli ldquoPerformance analysis of novel concentrating solarphotovoltaic combined systemrdquo Energy Conversion and Man-agement vol 67 pp 186ndash196 2013
[17] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part I the concept of net exergyflow and the modeling of solar air heatersrdquo Solar Energy vol 41no 2 pp 127ndash132 1988
12 International Journal of Photoenergy
[18] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part 2 results of optimizationand analysis of sensibility to variations of operating conditionsrdquoSolar Energy vol 41 no 4 pp 309ndash317 1988
[19] S Farahat F Sarhaddi and H Ajam ldquoExergetic optimization offlat plate solar collectorsrdquo Renewable Energy vol 34 no 4 pp1169ndash1174 2009
[20] H Ajam S Farahat and F Sarhaddi ldquoExergetic optimizationof solar air heaters and comparison with energy analysisrdquoInternational Journal of Thermodynamics vol 8 no 4 pp 183ndash190 2005
[21] M J Kerr and A Cuevas ldquoGeneralized analysis of the illumi-nation intensity versus open-circuit voltage of solar cellsrdquo SolarEnergy vol 76 no 1ndash3 pp 263ndash267 2004
[22] E Radziemska and E Klugmann ldquoThermally affected parame-ters of the current-voltage characteristics of silicon photocellrdquoEnergy Conversion and Management vol 43 no 14 pp 1889ndash1900 2002
[23] E E van Dyk B J Scott E L Meyer and A W R LeitchldquoTemperature dependence of performance of crystalline siliconphotovoltaic modulesrdquo South African Journal of Science vol 96no 4 pp 198ndash200 2000
[24] httpwwwgercinorgrenewablepdfSolar20Tariff20Order20120of202012pdf 2013
[25] M Veerachary T Senjyu and K Uezato ldquoVoltage-basedmaximum power point tracking control of PV systemrdquo IEEETransactions on Aerospace and Electronic Systems vol 38 no1 pp 262ndash270 2002
[26] M Veerachary and K S Shinoy ldquoV2-based power tracking fornonlinear PV sourcesrdquo IEE Proceedings-Electric Power Applica-tions vol 152 no 5 pp 1263ndash1270 2005
[27] I S Kim and M J Youn ldquoVariable-structure observer for solararray current estimation in a photovoltaic power-generationsystemrdquo IEE Proceedings-Electric Power Applications vol 152no 4 pp 953ndash959 2005
[28] I S Kim M B Kim and M J Youn ldquoNew maximum powerpoint tracker using sliding-mode observer for estimation ofsolar array current in the grid-connected photovoltaic systemrdquoIEEE Transactions on Industrial Electronics vol 53 no 4 pp1027ndash1035 2006
[29] H L Tsai C S Tu and Y J Su ldquoDevelopment of generalizedphotovoltaic model using MATLABSIMULINKrdquo in Proceed-ings of theWorld Congress on Engineering and Computer ScienceSan Francisco NC USA October 2008
[30] J CThongpron K Kirtikara and C Jivacate ldquoAmethod for thedetermination of dynamic resistance of photovoltaic modulesunder illuminationrdquo Solar Energy Materials and Solar Cells vol90 no 18-19 pp 3078ndash3084 2006
[31] J C Wang J C Shieh Y L Su et al ldquoA novel method for thedetermination of dynamic resistance for photovoltaicmodulesrdquoEnergy vol 36 no 10 pp 5968ndash5974 2011
[32] S Dubey G S Sandhu andG N Tiwari ldquoAnalytical expressionfor electrical efficiency of PVT hybrid air collectorrdquo AppliedEnergy vol 86 no 5 pp 697ndash705 2009
[33] S Kumar P K Singh G S Chilana and S R Dhariwal ldquoGen-eration and recombination lifetime measurement in siliconwafers using impedance spectroscopyrdquo Semiconductor Scienceand Technology vol 24 no 9 Article ID 095001 pp 1ndash8 2009
[34] J Millman and C C Halkias Integrated Electronics McGraw-Hill New York NY USA 1972
[35] S Kumar P K Singh and G S Chilana ldquoStudy of siliconsolar cell at different intensities of illumination andwavelengthsusing impedance spectroscopyrdquo Solar Energy Materials andSolar Cells vol 93 no 10 pp 1881ndash1884 2009
[36] S Kumar V Sareen N Batra and P K Singh ldquoStudy of C-Vcharacteristics in thin n+-p-p+ silicon solar cells and inducedjunction n-p-p+ cell structuresrdquo Solar Energy Materials andSolar Cells vol 94 no 9 pp 1469ndash1472 2010
[37] I Mora-Sero G Garcia-Belmonte P P Boix M A Vazquezand J Bisquert ldquoImpedance spectroscopy characterisation ofhighly efficient silicon solar cells under different light illumina-tion intensitiesrdquo Energy and Environmental Science vol 2 no 6pp 678ndash686 2009
[38] F Sarhaddi S Farahat H Ajam andA Behzadmehr ldquoExergeticoptimization of a solar photovoltaic arrayrdquo Journal of Thermo-dynamics vol 2009 Article ID 313561 11 pages 2009
[39] S M Sze Physics of Semiconductor Devices Wiley New YorkNY USA 2nd edition 1981
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
8 International Journal of Photoenergy
minus08 minus06 minus04 minus02 0 02 04 06 08Voltage (V)
times1014
0
05
1
15
2
25
3
1C
2(1F2)
Figure 8 The capacitance-voltage characterization of LCPV mod-ule
The dependence of barrier potential and doping concen-tration on the depletion region capacitance per unit area isgiven by [30]
1
1198622=
2
1199021198701205760119873
(119881bi minus 119881 minus
2119896119861119879
119902
)
119889 (1119862
2)
119889119881
= minus
2
1199021198701205760119873
(33)
where 119902 is the electron charge 119870 is dielectric constant ofsilicon 1205760 is the permittivity of free space 119881bi is barrierpotential 119896119861 is Boltzmannrsquos constant119879 is equal to 29814 K119873is doping concentration and 119881 represents applied potential
The slope and its intersection on the abscissa in theMott-Schottky plot shown in Figure 8 for the LCPV module givesthe doping concentration (119873) and barrier potential (119881bi)respectivelyThe119873 value is found as 779 times 1016 cmminus3 and thevalue of119881bi minus2119896119879119902 is equal to 056 eV which corresponds to119881bi = 061 eV The calculated values are in good agreementwith the reported values for commercially available siliconsolar cells [36 37]
4 LCPV Experiment under ATC
The experiments were carried out in the campus of Schoolof Solar Energy located in Gandhinagar India (Lat 2322∘Long 7268E) in the month of December (Year 2012) Themodule temperature was measured with the digital ther-mometer having an accuracy of plusmn01∘C during experimentswind speed was measured by anemometer as 085ms withan accuracy of plusmn5 Solar radiation and ambient temperaturewere recorded at the weather station located in the universitycampus The following parameters were measured duringexperiments ambient temperature solar radiation LCPVmodule and ambient temperature load current load voltageshort-circuit current and open-circuit voltage During theexperiments the module temperature was varied in the
range of 300ndash350K by controlling the flow rate of waterbehind the LCPV module Since the aim of this paper is toextract maximum electrical output from LCPV systems thethermodynamic analysis of flowingwater is avoided hereThecurrent-voltage measurements of an LCPV system are takenby Agilent SMU 6632B and by using multimeters and loadrheostat The sensitivity of the current-voltage measurementinstrument is given as plusmn3 The developed LCPV system isstudied by varying the number of reflecting mirrors arrangedin PLPTC
5 Result and Discussion
51 Exergy and Energy Analysis The effect of the lightconcentration and module temperature on the input exergyrate electrical exergy output rate and thermal exergy outputrate of LCPV module is estimated from the proposed modelin Section 2 It is found that with the increase in CR the inputexergy rate increases which results in increased amount ofenergy available to do useful work by the system The datalisted in Table 4 shows that the exergy efficiency decreaseswith the increase in the input exergy rate This decrease ismainly due to the increase in cell temperature which resultsin electrical exergy destruction with a rate of ldquo119881OC119868SC minus
119881mp119868mprdquo [38] Further the increase in the cell temperatureaffects 119881OC with a negative temperature coefficient as shownin the Figure 9 Figure 9 shows that 119881OC decreases from848V to 824V with increase in input exergy rate from3081W to 9612W when the cell temperature changesfrom 321 K to 3325 K The influence of the cell temperatureon exergy efficiency is clearly observed (Table 4) whichdecreases with the increase in the cell temperature Similareffect is observed by other researchers [15 38] Since the celltemperature changes with the increase in the input exergyrate it is imperative to design the LCPV system based on thisinformation so that useful exergy can bemaximized For thispurpose it is very important to track maximum power pointwhich depends on dynamic resistance of LCPV system
The proposed model in Section 2 is used to performenergy analysis of the LCPV module having 16 cells con-nected in series The static parameters (119868SC 119881OC 119875MAX and119877119878) of the LCPV module are measured in ATC conditionsas well as calculated by the proposed theoretical model Themeasured and simulated current-voltage characteristics ofLCPVmodule is shown in Figure 9 with varying input energyrate and corresponding temperature
It can be seen from Figure 9 that there is good agreementbetween the experimental and theoretical current-voltagecharacteristics which include 119868SC 119881OC 119875MAX 119877119878 FF 119903119889and efficiency The mean square of percentage deviation (119890)
is in the range of 274ndash843 and the linear coefficient ofcorrelation (119903) is in the range of 0995ndash0999
The measured values of solar irradiation 119868SC 119881OC 119875MAX119877119878 temperature FF 119903119889 and efficiency are listed in Table 5Generally the output current of the solar PV modulesincreases with the increase in input energy rate (ie solarirradiance received at focal point of PLPTC) With increasein the solar irradiance the higher number of photons strikes
International Journal of Photoenergy 9
Table 4 Exergy analysis of LCPV system
Solar irradiation(Wm2)
Cell temperature 119879119862 (K) Input exergy rate (W)Output exergy rate (W)
Exergy efficiency 120578ex ()Electricalexergy rate (W)
Thermal exergyrate (W)
1225 321 3081 2 043 5102254 328 5668 355 070 5033234 331 8133 491 083 5013822 3325 9612 554 091 482
Table 5 Parameter estimated from 119868-119881 curves plotted under various CR
Solarirradiation(Wm2)
Celltemperature
119879119862 (K)
Short-circuitcurrent 119868SC
(A)
Seriesresistance 119877119878
(Ω)
Dynamicresistance 119903119889
(Ω)
Open-circuitvoltage 119881OC
(V)
Maximumpower 119875MAX
(W)
Fill factor FF()
Energyefficiency 120578
()1000 298 025 112 1799 986 191 7458 7071225 321 033 120 1923 848 207 7397 6262254 328 063 129 2073 839 372 7037 6113234 331 091 139 2227 831 500 6700 5733822 3325 107 155 2484 824 584 6623 566
0 2 4 6 8 10Voltage (V)
Curr
ent (
A)
0
02
04
06
08
1
12
Simulation (2 mirrors)Experimental (2 mirrors)Simulation (4 mirrors)Experimental (4 mirrors)
Simulation (6 mirrors)Experimental (6 mirrors)Simulation (8 mirrors)Experimental (8 mirrors)
Figure 9 Simulated and experimental 119868-119881 characteristics of LCPVsystem under ATC
the solar PVmodule which results in enhanced electron-holepair production and higher photocurrent [39] The valuesof the dynamic resistance at MPP are computed using thevalues of 119868PH 119868SC and 119877119878 The dynamic resistance of LCPVmodule is calculated in an effective manner using (21) andis listed in Table 5 Approximate error between experimentaland theoretical dynamic resistance of the LCPV module isfound as sim13ndash21 which shows the uncertainty is wellwithin the practically acceptable limits
The plot shown in Figure 9 and extracted data listed inTable 5 describe the dependence of FF and efficiency of LCPV
module on the change in input energy rate and moduletemperature From the observed results it can be concludedthat the FF and efficiency of LCPV module decrease as theinput energy rate increasesThe decrease in FF and efficiencyof solar PV module with the increasing energy rate is highlydependent on the increase in electrical exergy destructionof LCPV module due to the increase in input energy rateand temperature As a result of increased input energy ratedynamic resistance offers greater resistive power losses inLCPV module and thus reduces its performance by reducingthe FF and efficiency The increase in the dynamic resistanceand reduction in the FF of LCPV module are foremostparameters for the decrease in the electrical energy efficiency
The effects of the cell temperature (119879119862) on 119868-119881 curveof LCPV module is estimated from the proposed model asshown in Figure 10 As the device temperature increasessmall increase in short-circuit current is observed how-ever the open-circuit voltage rapidly decreases due to theexponential dependence of the saturation current on thetemperature as given by (18) [39] In the actual experimentssimilar effect of temperature on open-circuit voltage (119881OC) isobserved and it is found that the 119881OC decreases from 986 to824V with temperature coefficient of voltage asymp minus0021 VKunder ATC as shown in Figure 9
A decrease in the 119875MAX with the increase in 119879119862 isobserved because with the increase in temperature the bandgap of the intrinsic semiconductor shrinks The increasedtemperature causes reduction in open-circuit voltage (119881OC)and the increase in the photocurrent for a given irradiancebecause of high injection of electrons from valance band toconduction band of semiconductor material [39]
52 Economical Analysis of LCPV System Net Present Value(NPV) method allows analyzing the economic aspects of anyengineering system and is used for the economic analysis of
10 International Journal of Photoenergy
Table 6 Cost of various components of LCPV system (asymp1 kWP) to find initial investment cost (numbers provided here are in accordancewith the current market price)lowast
Components Module BOSBattery Charge controller Support structure Tracker Cabling
Cost (in US$) 206 800 48 320 590 120Total initial investment cost (in US$) 2084
lowastThe price is based on market survey which may vary depending on specific location or company
Table 7 Economical analysis of LCPV system (having a lifetime of 25 years [24])
Period (year) 0 1 2 3 4 5 6 7 8Initial investment cost minus2084
Benefitslowastlowast 29043 29043 29043 29043 29043 29043 29043 29043O and M costlowastlowastlowast minus218 minus230 minus243 minus257 minus272 minus288 minus304 minus321
Discount rate 001 001 001 001 001 001 001 001 001Net cash flow 28825 28813 287995 28786 28771 28755 28739 28721119886 099 099 098 097 096 095 094 093 092Discounted net cash flow 28539 28245 27953 27662 27374 27089 26805 26524NPV minus17986 minus15162 minus12366 minus960 minus68626 minus41537 minus14732 11792lowastlowastBenefits are based on the tariff policy of Gujarat Electricity Regulatory Commission released for projects commissioned in 2012 [24]lowastlowastlowastEscalation in operating cost is taken as 572 annually [24]
300K325K
350K375K
0 2 4 6 8 100
005
01
015
02
025
03
Voltage (V)
Curr
ent (
A)
Figure 10 Variation of current-voltage characteristics with the celltemperature 119879119862
developed LCPV system of 1 kWP As the system presented inthis paper is very small for economic analysis the calculationsare done for 1 kWP system NPV method allows accountingfor the present value of annual capital expenditures andsavings during the lifetime of the system Net present value(NPV) includes sum of all the current values (costs are shownas negative and net savings are shown as positive) Foracceptance of any engineering project the positive NPV is
desiredThe formulas for calculatingNPVand correspondingfactor are given as [16]
NPV =
119899
sum
119894=1
(119861 minus 119862)119894
119886 =
1
(1 + 119894)
119901
(34)
where ldquo119886rdquo represents net present value factor ldquo119861rdquo representsgain ldquo119901rdquo represents the period and ldquo119894rdquo represents discountrate in the equation given previously
The initial investment cost is required in order to calculateNPV which includes module cost and balance of systems(BOS) cost The components of BOS include battery storagecharge controllers support structure tracking system andtransmission cables Cost of all these components is listedin Table 6 Using the initial investment cost and the formulaoutlined in (34) the NPV is calculated (Table 7) Operationandmaintenance (O andM) cost is taken as 075 of the totalinvestment cost with escalation in operating cost as 572 perannum [24] The feasibility of this project is demonstrated bya positive value of NPV obtained within 8 years
6 Conclusions
A theoretical model is used to perform electrical energy andexergy analyses of low-concentration photovoltaic (LCPV)system working under actual test conditions (ATC) Theexergy efficiency of LCPV system is in the range from51 to 482 with increasing rate of input exergy ratefrom 3081W to 9612W when concentration ratio changes
International Journal of Photoenergy 11
from 185 to 517 Sun Short-circuit current shows increasingtrend with increasing input exergy rate of asymp0011 AW Powerconversion efficiency decreases from 707 to 566 and open-circuit voltage decreases from986 to 824Vwith temperaturecoefficient of voltage asymp minus0021 VK under ATC The resultsconfirm that the commercially available silicon solar PVmodule performs satisfactorily under low concentration
Nomenclature
CR Concentration ratio119882 Width of the profile119863 Depth of the profile0119903 Rim angle120579119888 Acceptance angle119865 Focus point120588mirror Reflectivity of mirrors119877min Half width of the solar panel119871 Parabolic trough length120572 Absorption coefficient119860119886 Aperture area119896119861 Boltzmannrsquos constant (138 times 10minus23)119868PH Light generated current119868119878 Cell saturation or dark current119902 Electron charge (16 times 10minus19 C)119860 Ideality factor119880rad Radiative heat loss coefficient119880con Convective heat loss coefficient119879119862 Working temperature of solar cell (Kelvin)119877SH Shunt resistance119877119878 Series resistance119873119878 Series number of cells in a PV module119873119875 Parallel number of modules for a PV array119868SC Cellrsquos short-circuit current at 29814 K and
1 kWm2119870119868 Cellrsquos short-circuit current temperature
coefficient119879Ref Cellrsquos reference temperature120582 Solar insolation in kWm2119868RS Cellrsquos reverse saturation current at a
reference temperature and solar radiation119864119892 Band gap energy of the semiconductor119868mp Current at maximum power point119881mp Voltage at maximum power point
Acknowledgments
The authors acknowledge the financial support providedby Gujarat Energy Development Agency (GEDA) todevelop CPV system by Grant no GEDAECRECMarch-201039174 Authors also acknowledge WAAREE EnergiesPvt Ltd India for providing encapsulated crystallinesilicon solar PV modules for this study
References
[1] G Sala D Pachon I Anton and Test Test Rating andSpecification of PV Concentrator Components and Systems
(C-Rating Project) Book1 Classification of PV ConcentratorsUniversidad Politecnica de Madrid Madrid Spain 2002httpwwwies-defupmesiesCRATINGDocumentshtm
[2] M Yamaguchi andA Luque ldquoHigh efficiency and high concen-tration in photovoltaicsrdquo IEEE Transactions on Electron Devicesvol 46 no 10 pp 2139ndash2144 1999
[3] M A Green and A Ho-Baillie ldquoForty three per cent compositesplit-spectrum concentrator solar cell efficiencyrdquo Progress inPhotovoltaics vol 18 no 1 pp 42ndash47 2010
[4] H Cotal C Fetzer J Boisvert et al ldquoIII-V multijunction solarcells for concentrating photovoltaicsrdquo Energy and Environmen-tal Science vol 2 no 2 pp 174ndash192 2009
[5] G Sala I Anton J Monedero et al ldquoThe euclides-thermieconcentrator power plant in continuous operationrdquo in Proceed-ings of the 17th European Photovoltaic Solar Energy Conference(EUPVSEC rsquo01) pp 488ndash491 Munich Germany 2001
[6] V Garboushian S Yoon G Turner A Gunn and D FairldquoNovel high-concentration PV technology for cost competitiveutility bulk power generationrdquo in Proceedings of the 24th IEEEPhotovoltaic Specialists Conference Part 2 (of 2) pp 1060ndash1063December 1994
[7] M Castro I Anton and G Sala ldquoPilot production of concen-trator silicon solar cells approaching industrializationrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1697ndash17052008
[8] A Zahedi ldquoReview of modelling details in relation to low-concentration solar concentrating photovoltaicrdquoRenewable andSustainable Energy Reviews vol 15 no 3 pp 1609ndash1614 2011
[9] M Li X Ji G Li S Wei Y Li and F Shi ldquoPerformancestudy of solar cell arrays based on a trough concentratingphotovoltaicthermal systemrdquoApplied Energy vol 88 no 9 pp3218ndash3227 2011
[10] M A Schuetz K A Shell S A Brown G S Reinbolt RH French and R J Davis ldquoDesign and construction of a sim
7times low-concentration photovoltaic system based on compoundparabolic concentratorsrdquo IEEE Journal of Photovoltaics vol 2no 3 pp 382ndash386 2012
[11] H G Riveros and A I Oliva ldquoGraphical analysis of sunconcentrating collectorsrdquo Solar Energy vol 36 no 4 pp 313ndash322 1986
[12] O A Jaramillo J A Del Rıo and G Huelsz ldquoThermal study ofoptical fibres transmitting concentrated solar energyrdquo Journal ofPhysics D vol 32 no 9 pp 1000ndash1005 1999
[13] O A Jaramillo G Huelsz and J A Del Rıo ldquoA theoretical andexperimental thermal study of SiO2 optical fibres transmittingconcentrated radiative energyrdquo Journal of Physics D vol 35 no2 pp 95ndash102 2002
[14] C Kandilli and K Ulgen ldquoReview and modelling the systemsof transmission concentrated solar energy via optical fibresrdquoRenewable and Sustainable Energy Reviews vol 13 no 1 pp 67ndash84 2009
[15] A S Joshi I Dincer and B V Reddy ldquoThermodynamicassessment of photovoltaic systemsrdquo Solar Energy vol 83 no8 pp 1139ndash1149 2009
[16] C Kandilli ldquoPerformance analysis of novel concentrating solarphotovoltaic combined systemrdquo Energy Conversion and Man-agement vol 67 pp 186ndash196 2013
[17] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part I the concept of net exergyflow and the modeling of solar air heatersrdquo Solar Energy vol 41no 2 pp 127ndash132 1988
12 International Journal of Photoenergy
[18] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part 2 results of optimizationand analysis of sensibility to variations of operating conditionsrdquoSolar Energy vol 41 no 4 pp 309ndash317 1988
[19] S Farahat F Sarhaddi and H Ajam ldquoExergetic optimization offlat plate solar collectorsrdquo Renewable Energy vol 34 no 4 pp1169ndash1174 2009
[20] H Ajam S Farahat and F Sarhaddi ldquoExergetic optimizationof solar air heaters and comparison with energy analysisrdquoInternational Journal of Thermodynamics vol 8 no 4 pp 183ndash190 2005
[21] M J Kerr and A Cuevas ldquoGeneralized analysis of the illumi-nation intensity versus open-circuit voltage of solar cellsrdquo SolarEnergy vol 76 no 1ndash3 pp 263ndash267 2004
[22] E Radziemska and E Klugmann ldquoThermally affected parame-ters of the current-voltage characteristics of silicon photocellrdquoEnergy Conversion and Management vol 43 no 14 pp 1889ndash1900 2002
[23] E E van Dyk B J Scott E L Meyer and A W R LeitchldquoTemperature dependence of performance of crystalline siliconphotovoltaic modulesrdquo South African Journal of Science vol 96no 4 pp 198ndash200 2000
[24] httpwwwgercinorgrenewablepdfSolar20Tariff20Order20120of202012pdf 2013
[25] M Veerachary T Senjyu and K Uezato ldquoVoltage-basedmaximum power point tracking control of PV systemrdquo IEEETransactions on Aerospace and Electronic Systems vol 38 no1 pp 262ndash270 2002
[26] M Veerachary and K S Shinoy ldquoV2-based power tracking fornonlinear PV sourcesrdquo IEE Proceedings-Electric Power Applica-tions vol 152 no 5 pp 1263ndash1270 2005
[27] I S Kim and M J Youn ldquoVariable-structure observer for solararray current estimation in a photovoltaic power-generationsystemrdquo IEE Proceedings-Electric Power Applications vol 152no 4 pp 953ndash959 2005
[28] I S Kim M B Kim and M J Youn ldquoNew maximum powerpoint tracker using sliding-mode observer for estimation ofsolar array current in the grid-connected photovoltaic systemrdquoIEEE Transactions on Industrial Electronics vol 53 no 4 pp1027ndash1035 2006
[29] H L Tsai C S Tu and Y J Su ldquoDevelopment of generalizedphotovoltaic model using MATLABSIMULINKrdquo in Proceed-ings of theWorld Congress on Engineering and Computer ScienceSan Francisco NC USA October 2008
[30] J CThongpron K Kirtikara and C Jivacate ldquoAmethod for thedetermination of dynamic resistance of photovoltaic modulesunder illuminationrdquo Solar Energy Materials and Solar Cells vol90 no 18-19 pp 3078ndash3084 2006
[31] J C Wang J C Shieh Y L Su et al ldquoA novel method for thedetermination of dynamic resistance for photovoltaicmodulesrdquoEnergy vol 36 no 10 pp 5968ndash5974 2011
[32] S Dubey G S Sandhu andG N Tiwari ldquoAnalytical expressionfor electrical efficiency of PVT hybrid air collectorrdquo AppliedEnergy vol 86 no 5 pp 697ndash705 2009
[33] S Kumar P K Singh G S Chilana and S R Dhariwal ldquoGen-eration and recombination lifetime measurement in siliconwafers using impedance spectroscopyrdquo Semiconductor Scienceand Technology vol 24 no 9 Article ID 095001 pp 1ndash8 2009
[34] J Millman and C C Halkias Integrated Electronics McGraw-Hill New York NY USA 1972
[35] S Kumar P K Singh and G S Chilana ldquoStudy of siliconsolar cell at different intensities of illumination andwavelengthsusing impedance spectroscopyrdquo Solar Energy Materials andSolar Cells vol 93 no 10 pp 1881ndash1884 2009
[36] S Kumar V Sareen N Batra and P K Singh ldquoStudy of C-Vcharacteristics in thin n+-p-p+ silicon solar cells and inducedjunction n-p-p+ cell structuresrdquo Solar Energy Materials andSolar Cells vol 94 no 9 pp 1469ndash1472 2010
[37] I Mora-Sero G Garcia-Belmonte P P Boix M A Vazquezand J Bisquert ldquoImpedance spectroscopy characterisation ofhighly efficient silicon solar cells under different light illumina-tion intensitiesrdquo Energy and Environmental Science vol 2 no 6pp 678ndash686 2009
[38] F Sarhaddi S Farahat H Ajam andA Behzadmehr ldquoExergeticoptimization of a solar photovoltaic arrayrdquo Journal of Thermo-dynamics vol 2009 Article ID 313561 11 pages 2009
[39] S M Sze Physics of Semiconductor Devices Wiley New YorkNY USA 2nd edition 1981
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
International Journal of Photoenergy 9
Table 4 Exergy analysis of LCPV system
Solar irradiation(Wm2)
Cell temperature 119879119862 (K) Input exergy rate (W)Output exergy rate (W)
Exergy efficiency 120578ex ()Electricalexergy rate (W)
Thermal exergyrate (W)
1225 321 3081 2 043 5102254 328 5668 355 070 5033234 331 8133 491 083 5013822 3325 9612 554 091 482
Table 5 Parameter estimated from 119868-119881 curves plotted under various CR
Solarirradiation(Wm2)
Celltemperature
119879119862 (K)
Short-circuitcurrent 119868SC
(A)
Seriesresistance 119877119878
(Ω)
Dynamicresistance 119903119889
(Ω)
Open-circuitvoltage 119881OC
(V)
Maximumpower 119875MAX
(W)
Fill factor FF()
Energyefficiency 120578
()1000 298 025 112 1799 986 191 7458 7071225 321 033 120 1923 848 207 7397 6262254 328 063 129 2073 839 372 7037 6113234 331 091 139 2227 831 500 6700 5733822 3325 107 155 2484 824 584 6623 566
0 2 4 6 8 10Voltage (V)
Curr
ent (
A)
0
02
04
06
08
1
12
Simulation (2 mirrors)Experimental (2 mirrors)Simulation (4 mirrors)Experimental (4 mirrors)
Simulation (6 mirrors)Experimental (6 mirrors)Simulation (8 mirrors)Experimental (8 mirrors)
Figure 9 Simulated and experimental 119868-119881 characteristics of LCPVsystem under ATC
the solar PVmodule which results in enhanced electron-holepair production and higher photocurrent [39] The valuesof the dynamic resistance at MPP are computed using thevalues of 119868PH 119868SC and 119877119878 The dynamic resistance of LCPVmodule is calculated in an effective manner using (21) andis listed in Table 5 Approximate error between experimentaland theoretical dynamic resistance of the LCPV module isfound as sim13ndash21 which shows the uncertainty is wellwithin the practically acceptable limits
The plot shown in Figure 9 and extracted data listed inTable 5 describe the dependence of FF and efficiency of LCPV
module on the change in input energy rate and moduletemperature From the observed results it can be concludedthat the FF and efficiency of LCPV module decrease as theinput energy rate increasesThe decrease in FF and efficiencyof solar PV module with the increasing energy rate is highlydependent on the increase in electrical exergy destructionof LCPV module due to the increase in input energy rateand temperature As a result of increased input energy ratedynamic resistance offers greater resistive power losses inLCPV module and thus reduces its performance by reducingthe FF and efficiency The increase in the dynamic resistanceand reduction in the FF of LCPV module are foremostparameters for the decrease in the electrical energy efficiency
The effects of the cell temperature (119879119862) on 119868-119881 curveof LCPV module is estimated from the proposed model asshown in Figure 10 As the device temperature increasessmall increase in short-circuit current is observed how-ever the open-circuit voltage rapidly decreases due to theexponential dependence of the saturation current on thetemperature as given by (18) [39] In the actual experimentssimilar effect of temperature on open-circuit voltage (119881OC) isobserved and it is found that the 119881OC decreases from 986 to824V with temperature coefficient of voltage asymp minus0021 VKunder ATC as shown in Figure 9
A decrease in the 119875MAX with the increase in 119879119862 isobserved because with the increase in temperature the bandgap of the intrinsic semiconductor shrinks The increasedtemperature causes reduction in open-circuit voltage (119881OC)and the increase in the photocurrent for a given irradiancebecause of high injection of electrons from valance band toconduction band of semiconductor material [39]
52 Economical Analysis of LCPV System Net Present Value(NPV) method allows analyzing the economic aspects of anyengineering system and is used for the economic analysis of
10 International Journal of Photoenergy
Table 6 Cost of various components of LCPV system (asymp1 kWP) to find initial investment cost (numbers provided here are in accordancewith the current market price)lowast
Components Module BOSBattery Charge controller Support structure Tracker Cabling
Cost (in US$) 206 800 48 320 590 120Total initial investment cost (in US$) 2084
lowastThe price is based on market survey which may vary depending on specific location or company
Table 7 Economical analysis of LCPV system (having a lifetime of 25 years [24])
Period (year) 0 1 2 3 4 5 6 7 8Initial investment cost minus2084
Benefitslowastlowast 29043 29043 29043 29043 29043 29043 29043 29043O and M costlowastlowastlowast minus218 minus230 minus243 minus257 minus272 minus288 minus304 minus321
Discount rate 001 001 001 001 001 001 001 001 001Net cash flow 28825 28813 287995 28786 28771 28755 28739 28721119886 099 099 098 097 096 095 094 093 092Discounted net cash flow 28539 28245 27953 27662 27374 27089 26805 26524NPV minus17986 minus15162 minus12366 minus960 minus68626 minus41537 minus14732 11792lowastlowastBenefits are based on the tariff policy of Gujarat Electricity Regulatory Commission released for projects commissioned in 2012 [24]lowastlowastlowastEscalation in operating cost is taken as 572 annually [24]
300K325K
350K375K
0 2 4 6 8 100
005
01
015
02
025
03
Voltage (V)
Curr
ent (
A)
Figure 10 Variation of current-voltage characteristics with the celltemperature 119879119862
developed LCPV system of 1 kWP As the system presented inthis paper is very small for economic analysis the calculationsare done for 1 kWP system NPV method allows accountingfor the present value of annual capital expenditures andsavings during the lifetime of the system Net present value(NPV) includes sum of all the current values (costs are shownas negative and net savings are shown as positive) Foracceptance of any engineering project the positive NPV is
desiredThe formulas for calculatingNPVand correspondingfactor are given as [16]
NPV =
119899
sum
119894=1
(119861 minus 119862)119894
119886 =
1
(1 + 119894)
119901
(34)
where ldquo119886rdquo represents net present value factor ldquo119861rdquo representsgain ldquo119901rdquo represents the period and ldquo119894rdquo represents discountrate in the equation given previously
The initial investment cost is required in order to calculateNPV which includes module cost and balance of systems(BOS) cost The components of BOS include battery storagecharge controllers support structure tracking system andtransmission cables Cost of all these components is listedin Table 6 Using the initial investment cost and the formulaoutlined in (34) the NPV is calculated (Table 7) Operationandmaintenance (O andM) cost is taken as 075 of the totalinvestment cost with escalation in operating cost as 572 perannum [24] The feasibility of this project is demonstrated bya positive value of NPV obtained within 8 years
6 Conclusions
A theoretical model is used to perform electrical energy andexergy analyses of low-concentration photovoltaic (LCPV)system working under actual test conditions (ATC) Theexergy efficiency of LCPV system is in the range from51 to 482 with increasing rate of input exergy ratefrom 3081W to 9612W when concentration ratio changes
International Journal of Photoenergy 11
from 185 to 517 Sun Short-circuit current shows increasingtrend with increasing input exergy rate of asymp0011 AW Powerconversion efficiency decreases from 707 to 566 and open-circuit voltage decreases from986 to 824Vwith temperaturecoefficient of voltage asymp minus0021 VK under ATC The resultsconfirm that the commercially available silicon solar PVmodule performs satisfactorily under low concentration
Nomenclature
CR Concentration ratio119882 Width of the profile119863 Depth of the profile0119903 Rim angle120579119888 Acceptance angle119865 Focus point120588mirror Reflectivity of mirrors119877min Half width of the solar panel119871 Parabolic trough length120572 Absorption coefficient119860119886 Aperture area119896119861 Boltzmannrsquos constant (138 times 10minus23)119868PH Light generated current119868119878 Cell saturation or dark current119902 Electron charge (16 times 10minus19 C)119860 Ideality factor119880rad Radiative heat loss coefficient119880con Convective heat loss coefficient119879119862 Working temperature of solar cell (Kelvin)119877SH Shunt resistance119877119878 Series resistance119873119878 Series number of cells in a PV module119873119875 Parallel number of modules for a PV array119868SC Cellrsquos short-circuit current at 29814 K and
1 kWm2119870119868 Cellrsquos short-circuit current temperature
coefficient119879Ref Cellrsquos reference temperature120582 Solar insolation in kWm2119868RS Cellrsquos reverse saturation current at a
reference temperature and solar radiation119864119892 Band gap energy of the semiconductor119868mp Current at maximum power point119881mp Voltage at maximum power point
Acknowledgments
The authors acknowledge the financial support providedby Gujarat Energy Development Agency (GEDA) todevelop CPV system by Grant no GEDAECRECMarch-201039174 Authors also acknowledge WAAREE EnergiesPvt Ltd India for providing encapsulated crystallinesilicon solar PV modules for this study
References
[1] G Sala D Pachon I Anton and Test Test Rating andSpecification of PV Concentrator Components and Systems
(C-Rating Project) Book1 Classification of PV ConcentratorsUniversidad Politecnica de Madrid Madrid Spain 2002httpwwwies-defupmesiesCRATINGDocumentshtm
[2] M Yamaguchi andA Luque ldquoHigh efficiency and high concen-tration in photovoltaicsrdquo IEEE Transactions on Electron Devicesvol 46 no 10 pp 2139ndash2144 1999
[3] M A Green and A Ho-Baillie ldquoForty three per cent compositesplit-spectrum concentrator solar cell efficiencyrdquo Progress inPhotovoltaics vol 18 no 1 pp 42ndash47 2010
[4] H Cotal C Fetzer J Boisvert et al ldquoIII-V multijunction solarcells for concentrating photovoltaicsrdquo Energy and Environmen-tal Science vol 2 no 2 pp 174ndash192 2009
[5] G Sala I Anton J Monedero et al ldquoThe euclides-thermieconcentrator power plant in continuous operationrdquo in Proceed-ings of the 17th European Photovoltaic Solar Energy Conference(EUPVSEC rsquo01) pp 488ndash491 Munich Germany 2001
[6] V Garboushian S Yoon G Turner A Gunn and D FairldquoNovel high-concentration PV technology for cost competitiveutility bulk power generationrdquo in Proceedings of the 24th IEEEPhotovoltaic Specialists Conference Part 2 (of 2) pp 1060ndash1063December 1994
[7] M Castro I Anton and G Sala ldquoPilot production of concen-trator silicon solar cells approaching industrializationrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1697ndash17052008
[8] A Zahedi ldquoReview of modelling details in relation to low-concentration solar concentrating photovoltaicrdquoRenewable andSustainable Energy Reviews vol 15 no 3 pp 1609ndash1614 2011
[9] M Li X Ji G Li S Wei Y Li and F Shi ldquoPerformancestudy of solar cell arrays based on a trough concentratingphotovoltaicthermal systemrdquoApplied Energy vol 88 no 9 pp3218ndash3227 2011
[10] M A Schuetz K A Shell S A Brown G S Reinbolt RH French and R J Davis ldquoDesign and construction of a sim
7times low-concentration photovoltaic system based on compoundparabolic concentratorsrdquo IEEE Journal of Photovoltaics vol 2no 3 pp 382ndash386 2012
[11] H G Riveros and A I Oliva ldquoGraphical analysis of sunconcentrating collectorsrdquo Solar Energy vol 36 no 4 pp 313ndash322 1986
[12] O A Jaramillo J A Del Rıo and G Huelsz ldquoThermal study ofoptical fibres transmitting concentrated solar energyrdquo Journal ofPhysics D vol 32 no 9 pp 1000ndash1005 1999
[13] O A Jaramillo G Huelsz and J A Del Rıo ldquoA theoretical andexperimental thermal study of SiO2 optical fibres transmittingconcentrated radiative energyrdquo Journal of Physics D vol 35 no2 pp 95ndash102 2002
[14] C Kandilli and K Ulgen ldquoReview and modelling the systemsof transmission concentrated solar energy via optical fibresrdquoRenewable and Sustainable Energy Reviews vol 13 no 1 pp 67ndash84 2009
[15] A S Joshi I Dincer and B V Reddy ldquoThermodynamicassessment of photovoltaic systemsrdquo Solar Energy vol 83 no8 pp 1139ndash1149 2009
[16] C Kandilli ldquoPerformance analysis of novel concentrating solarphotovoltaic combined systemrdquo Energy Conversion and Man-agement vol 67 pp 186ndash196 2013
[17] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part I the concept of net exergyflow and the modeling of solar air heatersrdquo Solar Energy vol 41no 2 pp 127ndash132 1988
12 International Journal of Photoenergy
[18] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part 2 results of optimizationand analysis of sensibility to variations of operating conditionsrdquoSolar Energy vol 41 no 4 pp 309ndash317 1988
[19] S Farahat F Sarhaddi and H Ajam ldquoExergetic optimization offlat plate solar collectorsrdquo Renewable Energy vol 34 no 4 pp1169ndash1174 2009
[20] H Ajam S Farahat and F Sarhaddi ldquoExergetic optimizationof solar air heaters and comparison with energy analysisrdquoInternational Journal of Thermodynamics vol 8 no 4 pp 183ndash190 2005
[21] M J Kerr and A Cuevas ldquoGeneralized analysis of the illumi-nation intensity versus open-circuit voltage of solar cellsrdquo SolarEnergy vol 76 no 1ndash3 pp 263ndash267 2004
[22] E Radziemska and E Klugmann ldquoThermally affected parame-ters of the current-voltage characteristics of silicon photocellrdquoEnergy Conversion and Management vol 43 no 14 pp 1889ndash1900 2002
[23] E E van Dyk B J Scott E L Meyer and A W R LeitchldquoTemperature dependence of performance of crystalline siliconphotovoltaic modulesrdquo South African Journal of Science vol 96no 4 pp 198ndash200 2000
[24] httpwwwgercinorgrenewablepdfSolar20Tariff20Order20120of202012pdf 2013
[25] M Veerachary T Senjyu and K Uezato ldquoVoltage-basedmaximum power point tracking control of PV systemrdquo IEEETransactions on Aerospace and Electronic Systems vol 38 no1 pp 262ndash270 2002
[26] M Veerachary and K S Shinoy ldquoV2-based power tracking fornonlinear PV sourcesrdquo IEE Proceedings-Electric Power Applica-tions vol 152 no 5 pp 1263ndash1270 2005
[27] I S Kim and M J Youn ldquoVariable-structure observer for solararray current estimation in a photovoltaic power-generationsystemrdquo IEE Proceedings-Electric Power Applications vol 152no 4 pp 953ndash959 2005
[28] I S Kim M B Kim and M J Youn ldquoNew maximum powerpoint tracker using sliding-mode observer for estimation ofsolar array current in the grid-connected photovoltaic systemrdquoIEEE Transactions on Industrial Electronics vol 53 no 4 pp1027ndash1035 2006
[29] H L Tsai C S Tu and Y J Su ldquoDevelopment of generalizedphotovoltaic model using MATLABSIMULINKrdquo in Proceed-ings of theWorld Congress on Engineering and Computer ScienceSan Francisco NC USA October 2008
[30] J CThongpron K Kirtikara and C Jivacate ldquoAmethod for thedetermination of dynamic resistance of photovoltaic modulesunder illuminationrdquo Solar Energy Materials and Solar Cells vol90 no 18-19 pp 3078ndash3084 2006
[31] J C Wang J C Shieh Y L Su et al ldquoA novel method for thedetermination of dynamic resistance for photovoltaicmodulesrdquoEnergy vol 36 no 10 pp 5968ndash5974 2011
[32] S Dubey G S Sandhu andG N Tiwari ldquoAnalytical expressionfor electrical efficiency of PVT hybrid air collectorrdquo AppliedEnergy vol 86 no 5 pp 697ndash705 2009
[33] S Kumar P K Singh G S Chilana and S R Dhariwal ldquoGen-eration and recombination lifetime measurement in siliconwafers using impedance spectroscopyrdquo Semiconductor Scienceand Technology vol 24 no 9 Article ID 095001 pp 1ndash8 2009
[34] J Millman and C C Halkias Integrated Electronics McGraw-Hill New York NY USA 1972
[35] S Kumar P K Singh and G S Chilana ldquoStudy of siliconsolar cell at different intensities of illumination andwavelengthsusing impedance spectroscopyrdquo Solar Energy Materials andSolar Cells vol 93 no 10 pp 1881ndash1884 2009
[36] S Kumar V Sareen N Batra and P K Singh ldquoStudy of C-Vcharacteristics in thin n+-p-p+ silicon solar cells and inducedjunction n-p-p+ cell structuresrdquo Solar Energy Materials andSolar Cells vol 94 no 9 pp 1469ndash1472 2010
[37] I Mora-Sero G Garcia-Belmonte P P Boix M A Vazquezand J Bisquert ldquoImpedance spectroscopy characterisation ofhighly efficient silicon solar cells under different light illumina-tion intensitiesrdquo Energy and Environmental Science vol 2 no 6pp 678ndash686 2009
[38] F Sarhaddi S Farahat H Ajam andA Behzadmehr ldquoExergeticoptimization of a solar photovoltaic arrayrdquo Journal of Thermo-dynamics vol 2009 Article ID 313561 11 pages 2009
[39] S M Sze Physics of Semiconductor Devices Wiley New YorkNY USA 2nd edition 1981
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
10 International Journal of Photoenergy
Table 6 Cost of various components of LCPV system (asymp1 kWP) to find initial investment cost (numbers provided here are in accordancewith the current market price)lowast
Components Module BOSBattery Charge controller Support structure Tracker Cabling
Cost (in US$) 206 800 48 320 590 120Total initial investment cost (in US$) 2084
lowastThe price is based on market survey which may vary depending on specific location or company
Table 7 Economical analysis of LCPV system (having a lifetime of 25 years [24])
Period (year) 0 1 2 3 4 5 6 7 8Initial investment cost minus2084
Benefitslowastlowast 29043 29043 29043 29043 29043 29043 29043 29043O and M costlowastlowastlowast minus218 minus230 minus243 minus257 minus272 minus288 minus304 minus321
Discount rate 001 001 001 001 001 001 001 001 001Net cash flow 28825 28813 287995 28786 28771 28755 28739 28721119886 099 099 098 097 096 095 094 093 092Discounted net cash flow 28539 28245 27953 27662 27374 27089 26805 26524NPV minus17986 minus15162 minus12366 minus960 minus68626 minus41537 minus14732 11792lowastlowastBenefits are based on the tariff policy of Gujarat Electricity Regulatory Commission released for projects commissioned in 2012 [24]lowastlowastlowastEscalation in operating cost is taken as 572 annually [24]
300K325K
350K375K
0 2 4 6 8 100
005
01
015
02
025
03
Voltage (V)
Curr
ent (
A)
Figure 10 Variation of current-voltage characteristics with the celltemperature 119879119862
developed LCPV system of 1 kWP As the system presented inthis paper is very small for economic analysis the calculationsare done for 1 kWP system NPV method allows accountingfor the present value of annual capital expenditures andsavings during the lifetime of the system Net present value(NPV) includes sum of all the current values (costs are shownas negative and net savings are shown as positive) Foracceptance of any engineering project the positive NPV is
desiredThe formulas for calculatingNPVand correspondingfactor are given as [16]
NPV =
119899
sum
119894=1
(119861 minus 119862)119894
119886 =
1
(1 + 119894)
119901
(34)
where ldquo119886rdquo represents net present value factor ldquo119861rdquo representsgain ldquo119901rdquo represents the period and ldquo119894rdquo represents discountrate in the equation given previously
The initial investment cost is required in order to calculateNPV which includes module cost and balance of systems(BOS) cost The components of BOS include battery storagecharge controllers support structure tracking system andtransmission cables Cost of all these components is listedin Table 6 Using the initial investment cost and the formulaoutlined in (34) the NPV is calculated (Table 7) Operationandmaintenance (O andM) cost is taken as 075 of the totalinvestment cost with escalation in operating cost as 572 perannum [24] The feasibility of this project is demonstrated bya positive value of NPV obtained within 8 years
6 Conclusions
A theoretical model is used to perform electrical energy andexergy analyses of low-concentration photovoltaic (LCPV)system working under actual test conditions (ATC) Theexergy efficiency of LCPV system is in the range from51 to 482 with increasing rate of input exergy ratefrom 3081W to 9612W when concentration ratio changes
International Journal of Photoenergy 11
from 185 to 517 Sun Short-circuit current shows increasingtrend with increasing input exergy rate of asymp0011 AW Powerconversion efficiency decreases from 707 to 566 and open-circuit voltage decreases from986 to 824Vwith temperaturecoefficient of voltage asymp minus0021 VK under ATC The resultsconfirm that the commercially available silicon solar PVmodule performs satisfactorily under low concentration
Nomenclature
CR Concentration ratio119882 Width of the profile119863 Depth of the profile0119903 Rim angle120579119888 Acceptance angle119865 Focus point120588mirror Reflectivity of mirrors119877min Half width of the solar panel119871 Parabolic trough length120572 Absorption coefficient119860119886 Aperture area119896119861 Boltzmannrsquos constant (138 times 10minus23)119868PH Light generated current119868119878 Cell saturation or dark current119902 Electron charge (16 times 10minus19 C)119860 Ideality factor119880rad Radiative heat loss coefficient119880con Convective heat loss coefficient119879119862 Working temperature of solar cell (Kelvin)119877SH Shunt resistance119877119878 Series resistance119873119878 Series number of cells in a PV module119873119875 Parallel number of modules for a PV array119868SC Cellrsquos short-circuit current at 29814 K and
1 kWm2119870119868 Cellrsquos short-circuit current temperature
coefficient119879Ref Cellrsquos reference temperature120582 Solar insolation in kWm2119868RS Cellrsquos reverse saturation current at a
reference temperature and solar radiation119864119892 Band gap energy of the semiconductor119868mp Current at maximum power point119881mp Voltage at maximum power point
Acknowledgments
The authors acknowledge the financial support providedby Gujarat Energy Development Agency (GEDA) todevelop CPV system by Grant no GEDAECRECMarch-201039174 Authors also acknowledge WAAREE EnergiesPvt Ltd India for providing encapsulated crystallinesilicon solar PV modules for this study
References
[1] G Sala D Pachon I Anton and Test Test Rating andSpecification of PV Concentrator Components and Systems
(C-Rating Project) Book1 Classification of PV ConcentratorsUniversidad Politecnica de Madrid Madrid Spain 2002httpwwwies-defupmesiesCRATINGDocumentshtm
[2] M Yamaguchi andA Luque ldquoHigh efficiency and high concen-tration in photovoltaicsrdquo IEEE Transactions on Electron Devicesvol 46 no 10 pp 2139ndash2144 1999
[3] M A Green and A Ho-Baillie ldquoForty three per cent compositesplit-spectrum concentrator solar cell efficiencyrdquo Progress inPhotovoltaics vol 18 no 1 pp 42ndash47 2010
[4] H Cotal C Fetzer J Boisvert et al ldquoIII-V multijunction solarcells for concentrating photovoltaicsrdquo Energy and Environmen-tal Science vol 2 no 2 pp 174ndash192 2009
[5] G Sala I Anton J Monedero et al ldquoThe euclides-thermieconcentrator power plant in continuous operationrdquo in Proceed-ings of the 17th European Photovoltaic Solar Energy Conference(EUPVSEC rsquo01) pp 488ndash491 Munich Germany 2001
[6] V Garboushian S Yoon G Turner A Gunn and D FairldquoNovel high-concentration PV technology for cost competitiveutility bulk power generationrdquo in Proceedings of the 24th IEEEPhotovoltaic Specialists Conference Part 2 (of 2) pp 1060ndash1063December 1994
[7] M Castro I Anton and G Sala ldquoPilot production of concen-trator silicon solar cells approaching industrializationrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1697ndash17052008
[8] A Zahedi ldquoReview of modelling details in relation to low-concentration solar concentrating photovoltaicrdquoRenewable andSustainable Energy Reviews vol 15 no 3 pp 1609ndash1614 2011
[9] M Li X Ji G Li S Wei Y Li and F Shi ldquoPerformancestudy of solar cell arrays based on a trough concentratingphotovoltaicthermal systemrdquoApplied Energy vol 88 no 9 pp3218ndash3227 2011
[10] M A Schuetz K A Shell S A Brown G S Reinbolt RH French and R J Davis ldquoDesign and construction of a sim
7times low-concentration photovoltaic system based on compoundparabolic concentratorsrdquo IEEE Journal of Photovoltaics vol 2no 3 pp 382ndash386 2012
[11] H G Riveros and A I Oliva ldquoGraphical analysis of sunconcentrating collectorsrdquo Solar Energy vol 36 no 4 pp 313ndash322 1986
[12] O A Jaramillo J A Del Rıo and G Huelsz ldquoThermal study ofoptical fibres transmitting concentrated solar energyrdquo Journal ofPhysics D vol 32 no 9 pp 1000ndash1005 1999
[13] O A Jaramillo G Huelsz and J A Del Rıo ldquoA theoretical andexperimental thermal study of SiO2 optical fibres transmittingconcentrated radiative energyrdquo Journal of Physics D vol 35 no2 pp 95ndash102 2002
[14] C Kandilli and K Ulgen ldquoReview and modelling the systemsof transmission concentrated solar energy via optical fibresrdquoRenewable and Sustainable Energy Reviews vol 13 no 1 pp 67ndash84 2009
[15] A S Joshi I Dincer and B V Reddy ldquoThermodynamicassessment of photovoltaic systemsrdquo Solar Energy vol 83 no8 pp 1139ndash1149 2009
[16] C Kandilli ldquoPerformance analysis of novel concentrating solarphotovoltaic combined systemrdquo Energy Conversion and Man-agement vol 67 pp 186ndash196 2013
[17] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part I the concept of net exergyflow and the modeling of solar air heatersrdquo Solar Energy vol 41no 2 pp 127ndash132 1988
12 International Journal of Photoenergy
[18] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part 2 results of optimizationand analysis of sensibility to variations of operating conditionsrdquoSolar Energy vol 41 no 4 pp 309ndash317 1988
[19] S Farahat F Sarhaddi and H Ajam ldquoExergetic optimization offlat plate solar collectorsrdquo Renewable Energy vol 34 no 4 pp1169ndash1174 2009
[20] H Ajam S Farahat and F Sarhaddi ldquoExergetic optimizationof solar air heaters and comparison with energy analysisrdquoInternational Journal of Thermodynamics vol 8 no 4 pp 183ndash190 2005
[21] M J Kerr and A Cuevas ldquoGeneralized analysis of the illumi-nation intensity versus open-circuit voltage of solar cellsrdquo SolarEnergy vol 76 no 1ndash3 pp 263ndash267 2004
[22] E Radziemska and E Klugmann ldquoThermally affected parame-ters of the current-voltage characteristics of silicon photocellrdquoEnergy Conversion and Management vol 43 no 14 pp 1889ndash1900 2002
[23] E E van Dyk B J Scott E L Meyer and A W R LeitchldquoTemperature dependence of performance of crystalline siliconphotovoltaic modulesrdquo South African Journal of Science vol 96no 4 pp 198ndash200 2000
[24] httpwwwgercinorgrenewablepdfSolar20Tariff20Order20120of202012pdf 2013
[25] M Veerachary T Senjyu and K Uezato ldquoVoltage-basedmaximum power point tracking control of PV systemrdquo IEEETransactions on Aerospace and Electronic Systems vol 38 no1 pp 262ndash270 2002
[26] M Veerachary and K S Shinoy ldquoV2-based power tracking fornonlinear PV sourcesrdquo IEE Proceedings-Electric Power Applica-tions vol 152 no 5 pp 1263ndash1270 2005
[27] I S Kim and M J Youn ldquoVariable-structure observer for solararray current estimation in a photovoltaic power-generationsystemrdquo IEE Proceedings-Electric Power Applications vol 152no 4 pp 953ndash959 2005
[28] I S Kim M B Kim and M J Youn ldquoNew maximum powerpoint tracker using sliding-mode observer for estimation ofsolar array current in the grid-connected photovoltaic systemrdquoIEEE Transactions on Industrial Electronics vol 53 no 4 pp1027ndash1035 2006
[29] H L Tsai C S Tu and Y J Su ldquoDevelopment of generalizedphotovoltaic model using MATLABSIMULINKrdquo in Proceed-ings of theWorld Congress on Engineering and Computer ScienceSan Francisco NC USA October 2008
[30] J CThongpron K Kirtikara and C Jivacate ldquoAmethod for thedetermination of dynamic resistance of photovoltaic modulesunder illuminationrdquo Solar Energy Materials and Solar Cells vol90 no 18-19 pp 3078ndash3084 2006
[31] J C Wang J C Shieh Y L Su et al ldquoA novel method for thedetermination of dynamic resistance for photovoltaicmodulesrdquoEnergy vol 36 no 10 pp 5968ndash5974 2011
[32] S Dubey G S Sandhu andG N Tiwari ldquoAnalytical expressionfor electrical efficiency of PVT hybrid air collectorrdquo AppliedEnergy vol 86 no 5 pp 697ndash705 2009
[33] S Kumar P K Singh G S Chilana and S R Dhariwal ldquoGen-eration and recombination lifetime measurement in siliconwafers using impedance spectroscopyrdquo Semiconductor Scienceand Technology vol 24 no 9 Article ID 095001 pp 1ndash8 2009
[34] J Millman and C C Halkias Integrated Electronics McGraw-Hill New York NY USA 1972
[35] S Kumar P K Singh and G S Chilana ldquoStudy of siliconsolar cell at different intensities of illumination andwavelengthsusing impedance spectroscopyrdquo Solar Energy Materials andSolar Cells vol 93 no 10 pp 1881ndash1884 2009
[36] S Kumar V Sareen N Batra and P K Singh ldquoStudy of C-Vcharacteristics in thin n+-p-p+ silicon solar cells and inducedjunction n-p-p+ cell structuresrdquo Solar Energy Materials andSolar Cells vol 94 no 9 pp 1469ndash1472 2010
[37] I Mora-Sero G Garcia-Belmonte P P Boix M A Vazquezand J Bisquert ldquoImpedance spectroscopy characterisation ofhighly efficient silicon solar cells under different light illumina-tion intensitiesrdquo Energy and Environmental Science vol 2 no 6pp 678ndash686 2009
[38] F Sarhaddi S Farahat H Ajam andA Behzadmehr ldquoExergeticoptimization of a solar photovoltaic arrayrdquo Journal of Thermo-dynamics vol 2009 Article ID 313561 11 pages 2009
[39] S M Sze Physics of Semiconductor Devices Wiley New YorkNY USA 2nd edition 1981
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
International Journal of Photoenergy 11
from 185 to 517 Sun Short-circuit current shows increasingtrend with increasing input exergy rate of asymp0011 AW Powerconversion efficiency decreases from 707 to 566 and open-circuit voltage decreases from986 to 824Vwith temperaturecoefficient of voltage asymp minus0021 VK under ATC The resultsconfirm that the commercially available silicon solar PVmodule performs satisfactorily under low concentration
Nomenclature
CR Concentration ratio119882 Width of the profile119863 Depth of the profile0119903 Rim angle120579119888 Acceptance angle119865 Focus point120588mirror Reflectivity of mirrors119877min Half width of the solar panel119871 Parabolic trough length120572 Absorption coefficient119860119886 Aperture area119896119861 Boltzmannrsquos constant (138 times 10minus23)119868PH Light generated current119868119878 Cell saturation or dark current119902 Electron charge (16 times 10minus19 C)119860 Ideality factor119880rad Radiative heat loss coefficient119880con Convective heat loss coefficient119879119862 Working temperature of solar cell (Kelvin)119877SH Shunt resistance119877119878 Series resistance119873119878 Series number of cells in a PV module119873119875 Parallel number of modules for a PV array119868SC Cellrsquos short-circuit current at 29814 K and
1 kWm2119870119868 Cellrsquos short-circuit current temperature
coefficient119879Ref Cellrsquos reference temperature120582 Solar insolation in kWm2119868RS Cellrsquos reverse saturation current at a
reference temperature and solar radiation119864119892 Band gap energy of the semiconductor119868mp Current at maximum power point119881mp Voltage at maximum power point
Acknowledgments
The authors acknowledge the financial support providedby Gujarat Energy Development Agency (GEDA) todevelop CPV system by Grant no GEDAECRECMarch-201039174 Authors also acknowledge WAAREE EnergiesPvt Ltd India for providing encapsulated crystallinesilicon solar PV modules for this study
References
[1] G Sala D Pachon I Anton and Test Test Rating andSpecification of PV Concentrator Components and Systems
(C-Rating Project) Book1 Classification of PV ConcentratorsUniversidad Politecnica de Madrid Madrid Spain 2002httpwwwies-defupmesiesCRATINGDocumentshtm
[2] M Yamaguchi andA Luque ldquoHigh efficiency and high concen-tration in photovoltaicsrdquo IEEE Transactions on Electron Devicesvol 46 no 10 pp 2139ndash2144 1999
[3] M A Green and A Ho-Baillie ldquoForty three per cent compositesplit-spectrum concentrator solar cell efficiencyrdquo Progress inPhotovoltaics vol 18 no 1 pp 42ndash47 2010
[4] H Cotal C Fetzer J Boisvert et al ldquoIII-V multijunction solarcells for concentrating photovoltaicsrdquo Energy and Environmen-tal Science vol 2 no 2 pp 174ndash192 2009
[5] G Sala I Anton J Monedero et al ldquoThe euclides-thermieconcentrator power plant in continuous operationrdquo in Proceed-ings of the 17th European Photovoltaic Solar Energy Conference(EUPVSEC rsquo01) pp 488ndash491 Munich Germany 2001
[6] V Garboushian S Yoon G Turner A Gunn and D FairldquoNovel high-concentration PV technology for cost competitiveutility bulk power generationrdquo in Proceedings of the 24th IEEEPhotovoltaic Specialists Conference Part 2 (of 2) pp 1060ndash1063December 1994
[7] M Castro I Anton and G Sala ldquoPilot production of concen-trator silicon solar cells approaching industrializationrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1697ndash17052008
[8] A Zahedi ldquoReview of modelling details in relation to low-concentration solar concentrating photovoltaicrdquoRenewable andSustainable Energy Reviews vol 15 no 3 pp 1609ndash1614 2011
[9] M Li X Ji G Li S Wei Y Li and F Shi ldquoPerformancestudy of solar cell arrays based on a trough concentratingphotovoltaicthermal systemrdquoApplied Energy vol 88 no 9 pp3218ndash3227 2011
[10] M A Schuetz K A Shell S A Brown G S Reinbolt RH French and R J Davis ldquoDesign and construction of a sim
7times low-concentration photovoltaic system based on compoundparabolic concentratorsrdquo IEEE Journal of Photovoltaics vol 2no 3 pp 382ndash386 2012
[11] H G Riveros and A I Oliva ldquoGraphical analysis of sunconcentrating collectorsrdquo Solar Energy vol 36 no 4 pp 313ndash322 1986
[12] O A Jaramillo J A Del Rıo and G Huelsz ldquoThermal study ofoptical fibres transmitting concentrated solar energyrdquo Journal ofPhysics D vol 32 no 9 pp 1000ndash1005 1999
[13] O A Jaramillo G Huelsz and J A Del Rıo ldquoA theoretical andexperimental thermal study of SiO2 optical fibres transmittingconcentrated radiative energyrdquo Journal of Physics D vol 35 no2 pp 95ndash102 2002
[14] C Kandilli and K Ulgen ldquoReview and modelling the systemsof transmission concentrated solar energy via optical fibresrdquoRenewable and Sustainable Energy Reviews vol 13 no 1 pp 67ndash84 2009
[15] A S Joshi I Dincer and B V Reddy ldquoThermodynamicassessment of photovoltaic systemsrdquo Solar Energy vol 83 no8 pp 1139ndash1149 2009
[16] C Kandilli ldquoPerformance analysis of novel concentrating solarphotovoltaic combined systemrdquo Energy Conversion and Man-agement vol 67 pp 186ndash196 2013
[17] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part I the concept of net exergyflow and the modeling of solar air heatersrdquo Solar Energy vol 41no 2 pp 127ndash132 1988
12 International Journal of Photoenergy
[18] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part 2 results of optimizationand analysis of sensibility to variations of operating conditionsrdquoSolar Energy vol 41 no 4 pp 309ndash317 1988
[19] S Farahat F Sarhaddi and H Ajam ldquoExergetic optimization offlat plate solar collectorsrdquo Renewable Energy vol 34 no 4 pp1169ndash1174 2009
[20] H Ajam S Farahat and F Sarhaddi ldquoExergetic optimizationof solar air heaters and comparison with energy analysisrdquoInternational Journal of Thermodynamics vol 8 no 4 pp 183ndash190 2005
[21] M J Kerr and A Cuevas ldquoGeneralized analysis of the illumi-nation intensity versus open-circuit voltage of solar cellsrdquo SolarEnergy vol 76 no 1ndash3 pp 263ndash267 2004
[22] E Radziemska and E Klugmann ldquoThermally affected parame-ters of the current-voltage characteristics of silicon photocellrdquoEnergy Conversion and Management vol 43 no 14 pp 1889ndash1900 2002
[23] E E van Dyk B J Scott E L Meyer and A W R LeitchldquoTemperature dependence of performance of crystalline siliconphotovoltaic modulesrdquo South African Journal of Science vol 96no 4 pp 198ndash200 2000
[24] httpwwwgercinorgrenewablepdfSolar20Tariff20Order20120of202012pdf 2013
[25] M Veerachary T Senjyu and K Uezato ldquoVoltage-basedmaximum power point tracking control of PV systemrdquo IEEETransactions on Aerospace and Electronic Systems vol 38 no1 pp 262ndash270 2002
[26] M Veerachary and K S Shinoy ldquoV2-based power tracking fornonlinear PV sourcesrdquo IEE Proceedings-Electric Power Applica-tions vol 152 no 5 pp 1263ndash1270 2005
[27] I S Kim and M J Youn ldquoVariable-structure observer for solararray current estimation in a photovoltaic power-generationsystemrdquo IEE Proceedings-Electric Power Applications vol 152no 4 pp 953ndash959 2005
[28] I S Kim M B Kim and M J Youn ldquoNew maximum powerpoint tracker using sliding-mode observer for estimation ofsolar array current in the grid-connected photovoltaic systemrdquoIEEE Transactions on Industrial Electronics vol 53 no 4 pp1027ndash1035 2006
[29] H L Tsai C S Tu and Y J Su ldquoDevelopment of generalizedphotovoltaic model using MATLABSIMULINKrdquo in Proceed-ings of theWorld Congress on Engineering and Computer ScienceSan Francisco NC USA October 2008
[30] J CThongpron K Kirtikara and C Jivacate ldquoAmethod for thedetermination of dynamic resistance of photovoltaic modulesunder illuminationrdquo Solar Energy Materials and Solar Cells vol90 no 18-19 pp 3078ndash3084 2006
[31] J C Wang J C Shieh Y L Su et al ldquoA novel method for thedetermination of dynamic resistance for photovoltaicmodulesrdquoEnergy vol 36 no 10 pp 5968ndash5974 2011
[32] S Dubey G S Sandhu andG N Tiwari ldquoAnalytical expressionfor electrical efficiency of PVT hybrid air collectorrdquo AppliedEnergy vol 86 no 5 pp 697ndash705 2009
[33] S Kumar P K Singh G S Chilana and S R Dhariwal ldquoGen-eration and recombination lifetime measurement in siliconwafers using impedance spectroscopyrdquo Semiconductor Scienceand Technology vol 24 no 9 Article ID 095001 pp 1ndash8 2009
[34] J Millman and C C Halkias Integrated Electronics McGraw-Hill New York NY USA 1972
[35] S Kumar P K Singh and G S Chilana ldquoStudy of siliconsolar cell at different intensities of illumination andwavelengthsusing impedance spectroscopyrdquo Solar Energy Materials andSolar Cells vol 93 no 10 pp 1881ndash1884 2009
[36] S Kumar V Sareen N Batra and P K Singh ldquoStudy of C-Vcharacteristics in thin n+-p-p+ silicon solar cells and inducedjunction n-p-p+ cell structuresrdquo Solar Energy Materials andSolar Cells vol 94 no 9 pp 1469ndash1472 2010
[37] I Mora-Sero G Garcia-Belmonte P P Boix M A Vazquezand J Bisquert ldquoImpedance spectroscopy characterisation ofhighly efficient silicon solar cells under different light illumina-tion intensitiesrdquo Energy and Environmental Science vol 2 no 6pp 678ndash686 2009
[38] F Sarhaddi S Farahat H Ajam andA Behzadmehr ldquoExergeticoptimization of a solar photovoltaic arrayrdquo Journal of Thermo-dynamics vol 2009 Article ID 313561 11 pages 2009
[39] S M Sze Physics of Semiconductor Devices Wiley New YorkNY USA 2nd edition 1981
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
12 International Journal of Photoenergy
[18] K Altfeld W Leiner and M Fiebig ldquoSecond law optimizationof flat-plate solar air heaters Part 2 results of optimizationand analysis of sensibility to variations of operating conditionsrdquoSolar Energy vol 41 no 4 pp 309ndash317 1988
[19] S Farahat F Sarhaddi and H Ajam ldquoExergetic optimization offlat plate solar collectorsrdquo Renewable Energy vol 34 no 4 pp1169ndash1174 2009
[20] H Ajam S Farahat and F Sarhaddi ldquoExergetic optimizationof solar air heaters and comparison with energy analysisrdquoInternational Journal of Thermodynamics vol 8 no 4 pp 183ndash190 2005
[21] M J Kerr and A Cuevas ldquoGeneralized analysis of the illumi-nation intensity versus open-circuit voltage of solar cellsrdquo SolarEnergy vol 76 no 1ndash3 pp 263ndash267 2004
[22] E Radziemska and E Klugmann ldquoThermally affected parame-ters of the current-voltage characteristics of silicon photocellrdquoEnergy Conversion and Management vol 43 no 14 pp 1889ndash1900 2002
[23] E E van Dyk B J Scott E L Meyer and A W R LeitchldquoTemperature dependence of performance of crystalline siliconphotovoltaic modulesrdquo South African Journal of Science vol 96no 4 pp 198ndash200 2000
[24] httpwwwgercinorgrenewablepdfSolar20Tariff20Order20120of202012pdf 2013
[25] M Veerachary T Senjyu and K Uezato ldquoVoltage-basedmaximum power point tracking control of PV systemrdquo IEEETransactions on Aerospace and Electronic Systems vol 38 no1 pp 262ndash270 2002
[26] M Veerachary and K S Shinoy ldquoV2-based power tracking fornonlinear PV sourcesrdquo IEE Proceedings-Electric Power Applica-tions vol 152 no 5 pp 1263ndash1270 2005
[27] I S Kim and M J Youn ldquoVariable-structure observer for solararray current estimation in a photovoltaic power-generationsystemrdquo IEE Proceedings-Electric Power Applications vol 152no 4 pp 953ndash959 2005
[28] I S Kim M B Kim and M J Youn ldquoNew maximum powerpoint tracker using sliding-mode observer for estimation ofsolar array current in the grid-connected photovoltaic systemrdquoIEEE Transactions on Industrial Electronics vol 53 no 4 pp1027ndash1035 2006
[29] H L Tsai C S Tu and Y J Su ldquoDevelopment of generalizedphotovoltaic model using MATLABSIMULINKrdquo in Proceed-ings of theWorld Congress on Engineering and Computer ScienceSan Francisco NC USA October 2008
[30] J CThongpron K Kirtikara and C Jivacate ldquoAmethod for thedetermination of dynamic resistance of photovoltaic modulesunder illuminationrdquo Solar Energy Materials and Solar Cells vol90 no 18-19 pp 3078ndash3084 2006
[31] J C Wang J C Shieh Y L Su et al ldquoA novel method for thedetermination of dynamic resistance for photovoltaicmodulesrdquoEnergy vol 36 no 10 pp 5968ndash5974 2011
[32] S Dubey G S Sandhu andG N Tiwari ldquoAnalytical expressionfor electrical efficiency of PVT hybrid air collectorrdquo AppliedEnergy vol 86 no 5 pp 697ndash705 2009
[33] S Kumar P K Singh G S Chilana and S R Dhariwal ldquoGen-eration and recombination lifetime measurement in siliconwafers using impedance spectroscopyrdquo Semiconductor Scienceand Technology vol 24 no 9 Article ID 095001 pp 1ndash8 2009
[34] J Millman and C C Halkias Integrated Electronics McGraw-Hill New York NY USA 1972
[35] S Kumar P K Singh and G S Chilana ldquoStudy of siliconsolar cell at different intensities of illumination andwavelengthsusing impedance spectroscopyrdquo Solar Energy Materials andSolar Cells vol 93 no 10 pp 1881ndash1884 2009
[36] S Kumar V Sareen N Batra and P K Singh ldquoStudy of C-Vcharacteristics in thin n+-p-p+ silicon solar cells and inducedjunction n-p-p+ cell structuresrdquo Solar Energy Materials andSolar Cells vol 94 no 9 pp 1469ndash1472 2010
[37] I Mora-Sero G Garcia-Belmonte P P Boix M A Vazquezand J Bisquert ldquoImpedance spectroscopy characterisation ofhighly efficient silicon solar cells under different light illumina-tion intensitiesrdquo Energy and Environmental Science vol 2 no 6pp 678ndash686 2009
[38] F Sarhaddi S Farahat H Ajam andA Behzadmehr ldquoExergeticoptimization of a solar photovoltaic arrayrdquo Journal of Thermo-dynamics vol 2009 Article ID 313561 11 pages 2009
[39] S M Sze Physics of Semiconductor Devices Wiley New YorkNY USA 2nd edition 1981
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Inorganic ChemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Carbohydrate Chemistry
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Physical Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom
Analytical Methods in Chemistry
Journal of
Volume 2014
Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
SpectroscopyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Medicinal ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chromatography Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Theoretical ChemistryJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Spectroscopy
Analytical ChemistryInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Quantum Chemistry
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Organic Chemistry International
ElectrochemistryInternational Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CatalystsJournal of
