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Solar Energy Materials & Solar Cells 112 (2013) 65–72
Contents lists available at SciVerse ScienceDirect
Solar Energy Materials & Solar Cells
journal homepage: www.elsevier.com/locate/solmat
Estimation of steady state and dynamic parameters of low concentration
photovoltaic system
Pankaj Yadav a, Brijesh Tripathi a,b, Makarand Lokhande b, Manoj Kumar b,n
a
b
School of Solar Energy, Pandit Deendayal Petroleum University, Gandhinagar 382007, Gujarat, India
School of Technology, Pandit Deendayal Petroleum University, Gandhinagar 382007, Gujarat, India
a r t i c l e i n f o
abstract
Article history:
Received 14 September 2012
Received in revised form
20 December 2012
Accepted 9 January 2013
The estimation of steady state and dynamic parameters is indispensable to extract maximum power
from solar photovoltaic system. This article aims to extract steady state and dynamic parameters for a
low-concentration photovoltaic system under actual test conditions. A theoretical model is reported to
estimate dynamic resistance under varying concentration and temperature for low-concentration
photovoltaic system. When the concentration ratio is changed from 1 sun to 5.17 suns the maximum
power delivered by low-concentration photovoltaic system increased by threefold. The results show
that the higher solar PV module temperature has negative impact on the open circuit voltage for a given
concentration with negative temperature coefficient of E 0.021 V/K. The observed dynamic resistance was in the range of 17.99 to 24.84 O for the low-concentration photovoltaic system under actual
test conditions.
& 2013 Elsevier B.V. All rights reserved.
Keywords:
Low-concentration photovoltaic (LCPV)
system
Concentration photovoltaic (CPV)
Dynamic resistance
Silicon solar PV module
Modelling
Simulation
1. Introduction
In last few decades, there is an increased awareness to reduce
global warming which encourages many countries around the
world to promote renewable energy applications. In this scenario,
solar energy has emerged as a promising source of green energy
alternative to non-renewable energy sources. Solar energy is
effectively utilized in two ways, i.e., either by using it directly
for heating or cooling of air and water without using an intermediate electric circuitry (i.e., solar thermal), or by converting it
into electrical energy by using solar photovoltaic (PV) modules.
Direct conversion of solar radiation into electrical energy is the
most suitable way of utilizing solar energy. Among the various PV
technologies, Si is one of the widely used semiconductors for the
fabrication of solar cells. About 80% to 90% of PV cell manufactured worldwide is Si wafer-based solar cell. Even though the
electricity generated from solar cells is quite high as compared
with the conventional electricity price. Further cost reduction of
the solar cell is possible by using thin c-Si wafers [1], thin film c-Si
[2], Si in the form of ribbon [3,4], and concentrator Si solar cell
[5,6]. In the last decade, price of silicon-based solar module is
reduced by a factor of 1/5 making it more relevant to develop
low-concentration photovoltaics using these cells.
Concentration solar cell technology is developed for concentration ratio as low as 2 suns to higher concentrations as high as
1000 suns. The efficiency of III–V material-based solar cells, which
are generally used for high concentration ration ( 4100), is in the
range of 35% to 43.5% at 500 suns but they are quite expensive.
For medium concentration (20–100 suns) applications, modified
c-Si solar cells are used. These solar cells are fabricated using
specialized techniques like laser grooving, selective diffusion for
selective emitter formation, photo-lithography and metal evaporations for contact placement [2]. The efficiency of these solar
cells is in range of 22% to 27% at concentration level of about 100
suns. The major hindrance in medium and high concentration is
as follows:
(A) The cell temperature increases with the increase in concentration of light and being a semiconductor material it has
negative temperature coefficient of open-circuit voltage. As a
result the solar cell losses its efficiency.
(B) Concentrating system uses direct sunlight, so they require an
accurate sun tracking system. With the increase in concentration a high precision in tracking and optics is required [7].
n
Corresponding author. Tel.: þ91 79 2327 5328; fax: þ 91 79 2327 5030.
E-mail addresses: [email protected],
[email protected] (M. Kumar).
0927-0248/$ - see front matter & 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.solmat.2013.01.012
Recently, there has been a renewed interest in the low concentration Si solar PV systems. In this technology, the commercial Si solar
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P. Yadav et al. / Solar Energy Materials & Solar Cells 112 (2013) 65–72
cell is used under the concentration of 2 suns to 10 suns. The
improvement in performance is obtained by reducing the series
resistance of the solar cell by using commercial techniques like
electro-deposition of front metal contacts with Ag [2]. A lot of work
has been done in designing and analysis of the low concentration
photovoltaic system (LCPV). In the beginning of this decade Sala et al.
[8] 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 5 sun to
extract maximum power. An industrialization potential of siliconbased concentrator photovoltaic system with an estimated cost of
$0.5/Wp is reported by Castro et al. [9], where the group uses back
contact solar cells under 100 suns. A detailed review of modeling in
relation to low-concentration solar concentrating photovoltaic is
presented by Zahedi [7]. Ming et al. have studied the performance
of solar cell array based on a trough concentrating photovoltaic/
thermal system [10]. Recently, Schuetz et al. [11] have reported
design and construction of 7 low-concentration CPV system
based on compound parabolic concentrators.
For a practical purpose, it is assumed that the power delivered
by solar PV module connected to maximum power point tracking
(MPPT) system is always maximum [12]. The solar PV module
exhibits nonlinear voltage current-characteristics which vary
with module temperature and solar radiation. Under concentration conditions, it becomes difficult to track maximum power
point due to extended effect offered by small variation in sunlight.
The continuous variation in solar PV module output under actual
test conditions (ATC) leads to improper tracking of maximum
power point (MPP) [13]. In this situation, it is important to
analyze static and dynamic parameters of solar PV module
accurately for designing better MPP tracker. Very few reports
exist in the literature on the estimation of dynamic parameters of
a PV system [14–17], and there is no report on the estimation of
dynamic resistance for a LCPV system in our knowledge. The
objective of this paper is to develop a simplified simulation model
for LCPV system to estimate the static and dynamic parameter
for ATC.
Fig. 1. Impedance spectra of LCPV module under different reverse bias conditions.
2. Material science aspects
A solar PV module is fabricated for LCPV application using a
string of 16 mono-crystalline silicon solar cells (size:
14 mm 64 mm, efficiency 14%) cut from commercially available solar cells. The material science aspects are explored using
impedance spectroscopy (IS) and capacitance–voltage (C–V)
characterization.
2.1. Impedance spectra of LCPV module
The impedance spectroscopy is an excellent characterization
technique to discriminate between series, parallel resistances and
capacitance of a semiconductor device. For impedance measurements, an ac signal, with varying frequency in the range of 1 Hz to
0.1 MHz with an amplitude of 5 mV is used. The impedance
spectra were plotted in a complex plane (i.e., Z0 versus Z00 , also
known as Nyquist or Cole–Cole plot [18]). The measurements
were carried out on the developed LCPV module under forward
and reverse bias ( þ0.5 V to 0.5 V) conditions in the dark. Fig. 1
shows the impedance spectrum of the LCPV module under
reverse bias conditions (from 0 to 0.5 V). The impedance
spectrum is nearly semicircular in shape under the zero and
reverse bias conditions, which implies that the equivalent circuit
of the device consists of a single RC network with a single time
constant. The radius of the semicircle increases with the increase
in bias voltage as compared to that of zero bias demonstrating the
Fig. 2. Impedance spectra of LCPV module under different forward bias
conditions.
bias dependence of resistance and capacitance [18]. The increase
in the radius of semicircle during reverse bias is observed due to
expansion of depletion region of the solar cell, which increases
the resistance offered by the cell.
Fig. 2 shows the impedance spectrum under the forward bias
conditions (from 0 to 0.5 V) where in contrast to the reverse bias,
the opposite behavior is observed. Here the radius of the semicircle decreases with increasing positive bias from its maximum
value at the zero bias. The decrease in the radius of semicircle
during forward bias is observed due to shrinking of depletion
region of the solar cell, which decreases the resistance offered by
the cell.
The commercial silicon solar cell possess n þ –p–p þ structure
with high phosphorus concentration at the front (n þ ), p-type
silicon in the middle and high aluminum concentration at the
back contact (p þ ) [19]. The ac equivalent circuit of the n þ –p–p þ
structure under consideration is shown in Fig. 3, which incorporates the capacitive effect owing to the excess minority carriers
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P. Yadav et al. / Solar Energy Materials & Solar Cells 112 (2013) 65–72
67
Fig. 3. The ac equivalent circuit of LCPV module to explain observed impedance
spectra.
Table 1
The value of R, C and corresponding t obtained from the measured impedance
spectra under different bias voltage conditions.
Applied (V)
R (kX)
C (nF)
t (ms)
0.5
0.2
0
0.2
0.5
70
55
45
37
28
49
51.4
36.2
35.1
32.1
3.43
2.83
1.63
1.30
0.90
Fig. 4. The capacitance–voltage characterization of LCPV module.
(Cd commonly known as the diffusion capacitance) in parallel
with the depletion layer capacitance Ct (Fig. 3). Resistive effects
arising from the minority carrier recombination are shown as the
diffusion resistance (Rd) in parallel with a shunt (RSH) resistance
and a series resistance, RS, connected in the circuit [18].
Under forward bias condition, due to the accumulation of
minority carriers in the bulk, the magnitude of the diffusion
capacitance is large compared to the depletion region capacitance
[20]. The ac impedance of the circuit is given by
ZðoÞ ¼ Z 0 ðoÞjZ 00 ðoÞ
0
ð1Þ
00
where Z and Z are the magnitudes of the real and imaginary
parts of impedance, and a minus sign arises due to capacitive
reactance involved in the circuit. On analyzing the circuit, Z 0 and
Z 00 can be written as
Z 0 ðoÞ ¼ Rs þ
Z 00 ðoÞ ¼
R
1 þðoRCÞ2
oCR2
1 þðoRCÞ2
ð2Þ
ð3Þ
For the case of very low RS, when Z 0 and Z 00 are plotted on a
complex plane, by varying the frequency (o), a semicircle of
radius R/2 with its center at (R/2, 0) is obtained. Further, because
of the semicircular geometry, the maximum value of Z 00 arises
when om RC ¼ 1, where om is the frequency at which Z 00 becomes
maximum. Thus, we have C ¼ 1=om R and the presence of RS shifts
the semicircle, by its value, on the x-axis. The analysis of the
impedance diagram on the complex plane, therefore, give values
of all the three parameters i.e., R, C and RS used in the equivalent
circuit. The product of resistance and capacitance (RC) represents
the time constant (t). The value of R, C and corresponding t
obtained from the measured impedance spectra under different
bias voltage conditions is listed in Table 1. These values are in
good agreement with existing literature for silicon solar cells
[18,19].
2.2. Capacitance–voltage characterization of LCPV module
Capacitance–voltage (C–V) measurement is an important tool
to understand the material properties of a semiconductor device.
Generally capacitance is measured in the reversed bias (Mott–
Schottky) condition to determine barrier potential and effective
doping concentration. Capacitance–voltage characterization is
done for the developed LCPV module as shown in Fig. 4.
The dependence of barrier potential and doping concentration
on the depletion region capacitance per unit area is given by [21]:
1
2
2kB T
ð4Þ
V
¼
V
bi
qK e0 N
q
C2
dð1=C 2 Þ
2
¼
dV
qK e0 N
ð5Þ
where q is the electron charge, K is the dielectric constant of
silicon, e0 is the permittivity of free space, Vbi is the barrier
potential, kB is Boltzmann’s constant, T is equal to 300 K, N is the
doping concentration and V represents applied potential.
The slope and its intersection on the abscissa in the Mott–
Schottky plot, shown in Fig. 4 for the LCPV module, gives the
doping concentration (N) and barrier potential (Vbi), respectively.
The N value is found as 7.79 1016 cm 3 and the value of
Vbi 2 kT/q is equal to 0.56 eV, which corresponds to Vbi ¼0.61 eV.
The calculated values are in agreement with the reported values
for commercially available silicon solar cells [21,22].
3. Performance predction model
3.1. Prediction of I–V curve of LCPV module
Solar PV module is an integral part of solar power generation
system. A solar PV module is made of series connected solar cells.
Solar cell is basically a semiconductor p–n junction device
fabricated using a thin wafer or layers of p-type, n-type and
intrinsic semiconductor material. The solar radiation is directly
converted into electricity through solar photovoltaic effect exhibited by the p–n junction. Being exposed to the sunlight, photons
with energy greater than the band-gap energy of the semiconductor are absorbed and create electron–hole pairs proportional
to the incident radiation wavelength. When a solar PV module is
exposed to solar radiation, it shows non-linear current–voltage
characteristics. The output current–voltage characteristic of solar
PV module is mainly influenced by the solar insolation and cell
temperature. There exist many mathematical models used for
computer simulation, which describe the effect of solar insolation
and cell temperature on output current–voltage characteristics of
solar PV module [23–25]. A generalized model for LCPV solar
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P. Yadav et al. / Solar Energy Materials & Solar Cells 112 (2013) 65–72
system, using MATLAB/Simulink is reported model here, which is
used to predict expected I–V of LCPV system under ATC.
A crystalline silicon wafer-based solar photovoltaic (PV) cell of
size 125 mm 125 mm typically produces around 2.5 W at a
voltage of 560 mV. These cells are connected in series and/or
parallel configuration on a module to produce required power.
The equivalent circuit for solar PV module, having NP numbers of
cells arranged in parallel and NS number of cells arranged in
series, is shown in Fig. 5.
The terminal equation for current and voltage of the solar PV
array is mentioned below as described by many groups [26–29]:
q½ðV=NS Þ þ ðIRS =NP Þ
NP V
I ¼ NP IPH N P IS exp
1 þIRS =RSH
kB T C A
NS
ð6Þ
Ideally in a solar PV module lower series resistance and very
high shunt resistance is expected for higher power generation. In
solar PV modules the PV cells are generally connected in series in
order to obtain adequate working voltage. The solar PV modules
can be arranged in series–parallel combination to make an array,
which produces desired power. The current–voltage characteristic
of such array is described by Eq. (6). Generally, for the solar PV
modules IPH cIS , so in Eq. (6), the small diode and ground-leakage
currents can be ignored under zero-terminal voltage. Therefore
the short-circuit current is approximately equal to the photocurrent. The expression for IPH is given by Eq. (7):
IPH ¼ ½ISC þK I ðT C T Ref Þl
ð7Þ
where l ¼ r CR Global Irradiation in W=m2 Þ, r represents
reflection coefficient of mirrors.
The photocurrent (IPH ) mainly depends on the solar insolation
and cell’s working temperature. The saturation current of a solar
cell varies with the cell temperature, which is described
by Eq. (8):
IS ¼ IRS
TC
T Ref
3
qEg ½ð1=T Ref Þð1=T C Þ
exp
kB A
ð8Þ
ð9Þ
Based on the theoretical model described above, the LCPV
system is simulated using MATLAB/Simulink.
The maximum power output of LCPV module is related to the
ISC and VOC by the following equation:
P MAX ¼ FFV OC ISC
A dynamic model for LCPV solar PV module is developed.
A solar PV module mainly consists of three types of resistance:
series resistance (RS), shunt resistance (RSH) and dynamic resistance (rd). The series resistance, RS, can be determine by various
illumination conditions such as dark, constant illumination and
varying illumination and they yield different results [31]. Practically, RS is determined by using two different illumination levels,
the so-called two-curve method. Shunts resistance, RSH, can be
obtained from only one illuminated I–V curve, or single curve
method. Both RS and RSH do not depend on illumination levels and
operating voltages [31]. The output impedance of solar PV
module, i.e., dynamic resistance is usually composed of the series
resistance and shunt resistance. In this paper dynamic resistance
of LCPV module is quantified by using direct estimation method
reported by Wang et.al [13]. The equivalent circuit for solar PV
module is shown in Fig. 5.
In order to estimate the dynamic resistance which is defined as
the negative reciprocal of dI/dV, Eq. (6) is differentiated with
respect to V, i.e.,
dI
NP
dI
RS NP IS q 1
dI
RS
¼
þ
dV
kTA NS dV NP
N S RSH dV RSH
q
V
IRS
þ
ð11Þ
exp
kTA NS
NP
For the open circuit condition and short-circuit conditions of
LCPV module, following two expressions are given using the slope
of one I–V characteristics at the points (VOC, 0) and (0, ISC) by
!1
dI Rs0 ¼ ð12Þ
dV V ¼ V OC
and
Rsh0 ¼ Reverse saturation current of the cell at reference temperature
depends on the open-circuit voltage (VOC) and can be approximately obtained by following equation as given by Tsai et al. [30]:
IRS ¼ ISC =½exp ðqV OC =N S kB AT C Þ1
3.2. Prediction of dynamic resistance of LCPV module
ð10Þ
The values of ISC, VOC and FF can be determined from the I–V
characteristics obtained by Eq. (6).
!1
dI dV I ¼ ISC
ð13Þ
respectively. When the load is disconnected from the LCPV
module and the output current (I) is equal to zero, Eq. (11) can
be expressed by
dI NP
dI ¼
dV V ¼ V OC
N S RSH dV V ¼ V OC
"
#
RS N P IS q 1
dI RS
q
V
þ exp
kTA NS dV V ¼ V OC NP
kTA NS
RSH
ð14Þ
Eq. (14) is further simplified to
q
V OC
1
dI RS
1 kTA dI exp þ ffi
N P IS q dV V ¼ V OC
kTA
NS dV V ¼ V OC N P
NS
Therefore series resistance RS is expressed by Eq. (16)
Rs0 NP kTA
q
V OC
exp RS ¼
qIS
kTA
NS
NS
ð15Þ
ð16Þ
For short-circuit condition the output voltage of LCPV module
is zero so Eq. (11) is reduced to
Fig. 5. The general model for solar PV module.
dI NP
dI ¼
dV I ¼ ISC
N S RSH dV I ¼ ISC
"
#
RS N P I S q 1
dI RS
þ
kTA NS dV I ¼ ISC N P
RSH
q
ISC RS
exp
kTA
NP
ð17Þ
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P. Yadav et al. / Solar Energy Materials & Solar Cells 112 (2013) 65–72
Eq. (17) can be further simplified as
dI NP
dI RS
¼
dV I ¼ ISC
NS RSH dV I ¼ ISC RSH
ð18Þ
Therefore the shunt resistance can be expressed by
!1
NS dI RSH ¼ NP dV I ¼ ISC
RSH ¼
NS
R
NP sh0
ð19Þ
ð20Þ
By analysis of Eq. (11) we conclude that the dynamic resistance of LCPV module is dependent on the solar irradiance and
solar PV module temperature. It is observed that with the increase
of the solar irradiation the dynamic resistance of solar PV module
increases. This is primarily caused by increase in VOC and a linear
increase in solar PV module photocurrent. The dynamic resistance
increases with the increase in temperature because of marginal
increase in short-circuit current [32–35].
4. Description of experiment
A piecewise linear parabolic LCPV system is developed as
shown in Fig. 6. The effective aperture area available using eight
mirrors is 0.211 m2, and the effective receiver area is 0.027 m2,
which gives the geometric concentration ratio of 8. In this LCPV
system, the reflecting mirrors can be added or removed so that
effective aperture area can be changed and as a result concentration ratio can be varied. The receiver is made of a solar PV module
fabricated by a string of 16 silicon cell pieces (material: monocrystalline silicon, size: 14 mm 64 mm, efficiency 14%) cut
from commercially available solar cell. The reason behind the
selection of the specific size of the cells mentioned here is to solve
the current handling problem of the solar cells under concentration. A typical solar cell of size 125 mm 125 mm producing
2.5 W at a voltage of 560 mV would have a current handling
capability of around 4.5 A. This cell, when used under 10 sun
Fig. 6. The constructed prototype of low concentrator photovoltaic (LCPV) system.
69
concentration may produce 45 A current by assuming a linear
relationship between the current increment and concentration
ratio (CR). But if the size of the cell is reduced to 1/10th of normal
size, then the current generated under 10 sun concentration
would be less than or equal to 4.5 A, then it will be easily handled
without damaging the solar cell contacts. This module was tested
under standard test conditions (STC) and detailed parameters are
given in Table 2. The incident solar radiation is reflected by the
piecewise linear parabolic trough concentrator (PLPTC) and concentrated on the focal plane having width of 0.64 mm. The
receiver is mounted at the focal plane to intercept all the reflected
radiation from PLPTC. The effective concentration is dependent on
the reflectivity of the mirrors used in PLPTC. In this case the
reflectivity of the mirrors used is measured as 80%. At CR 8
the cell temperature increases above 100 1C for solar irradiance
above 900 W/m2. Due to increased temperature the open-circuit
voltage decreases considerably to produce quite low power. This
problem is generally avoided by using either passive or active
cooling methods. In this case, an active cooling mechanism is
employed by flowing normal water behind the encapsulated solar
PV module which is shown in Fig. 6. By employing this mechanism, module temperature could be lowered down to 45 1C. A
light-dependent resistor (LDR) based one axis tracking system is
developed for sun tracking with a provision of manual tracking on
second axis with an accuracy of 7 31 as shown in Fig. 6.
5. Validation and analysis of developed model
A MATLAB/Simulink computer code is developed using the
mathematical model reported in Section 3 to simulate LCPV
system. The concentrated light is received by the solar PV module
which is placed at the focal plane of the PLPTC. To simulate the
electrical power generated from this PV module the computer
program needs the value of series resistance, shunt resistance,
energy band gap, number of cells connected in series, number of
strings connected parallel to each other, cell temperature, ambient temperature, short-circuit current of module, open-circuit
voltage of the module etc.
In this LCPV system, a solar PV module manufactured at
WAAREE Energies Pvt. Ltd. is used. The open-circuit voltage and
short-circuit current of this module are measured as VOC ¼9.86 V
and ISC ¼0.259 A, respectively, under AM1.5 spectrum at 25 1C.
This module consists of only one string of 16 cells of dimensions
64 mm 14 mm connected in series. The current–voltage output
characteristic of generalized solar PV module under AM1.5 solar
spectrum is shown in Fig. 7. The simulated current–voltage
characteristic of developed solar PV module for the LCPV system
is in accordance with the experimental current–voltage characteristics of this PV module as can be observed from Fig. 7. In the
simulation short-circuit current, open-circuit voltage, series resistance and cell temperature measured under standard test conditions (STC) by manufacturer are taken as input parameters. The
current–voltage characteristic generated from simulation program match well with the experimental current–voltage
characteristic.
Looking at the current–voltage curve, it can be stated that the
photovoltaic module is a constant current source at lower values
of voltage with current equal to the short-circuit current (ISC).
Table 2
The parameters used for simulation under 1 sun concentration.
Module parameter
RS (O)
Eg (eV)
NS
NP
A
Tc (K)
Tref (K)
K (J/K)
KI
Q (C)
ISC (A)
IRS (A)
VOC (V)
For 1 sun
0.071
1.12
16
1
1.3
298
298
1.38 10 23
0.65 10 3
1.602 10 19
0.259
0.86 10 12
9.86
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P. Yadav et al. / Solar Energy Materials & Solar Cells 112 (2013) 65–72
With further increase in voltage values, the current starts
decreasing exponentially at certain point. The value of current
becomes zero at open-circuit voltage (VOC). Over the entire
voltage range the point where the module operates at the highest
efficiency, is called maximum power point (PMAX). By comparing
experimental and theoretical results, it is demonstrated that the
proposed method is accurate and practicable for LCPV modules.
Table 3
Parameter estimated from I–V curves plotted under various CR.
CR
1
1.85
3.56
4.72
5.17
Experimental results
Theoretical estimation
VOC
(V)
ISC
(A)
RS
(X )
rd
(X)
VOC
(V)
ISC
(A)
RS
(O)
rd
(X )
9.86
8.48
8.39
8.31
8.24
0.25
0.33
0.63
0.91
1.07
1.12
1.20
1.29
1.39
1.55
17.99
19.23
20.73
22.27
24.84
9.85
8.50
8.40
8.34
8.31
0.25
0.33
0.62
0.90
1.07
1.13
1.24
1.34
1.44
1.52
18.24
20.01
21.50
23.04
24.32
Error
(%)
1.3
3.8
3.5
3.3
2.1
6. Results and discussion
The proposed model in Section 3.1 is used to estimate the I–V
characteristics of the LCPV module having 16 cells connected in
series. The static parameters (ISC, VOC, PMAX and RS) of the LCPV
module are measured in ATC conditions as well as calculated by
the proposed theoretical model. The measured and simulated
current–voltage characteristics of LCPV module is shown in Fig. 8
with varying concentration and corresponding temperature. The
measured/calculated values of solar irradiation, ISC, VOC, PMAX, RS,
temperature, FF, RD and efficiency are listed in Tables 3 and 4.
Generally, the output current of the solar PV modules increases
with the radiation intensity. A positive increment in current is
mainly due to increase in solar irradiance on LCPV module. With
increase in the solar irradiance the higher number of photons
Fig. 7. I–V characteristics of the designed LCPV module under 1 sun, AM1.5 at
25 1C.
Fig. 8. Simulated and experimental I–V characteristics of LCPV system under ATC.
Table 4
The static parameters of LCPV module.
CR
Experimental results
Theoretical estimation
Error (%)
TC (K) PMAX (W) FF (%) g (%) PMAX (W) FF (%) g (%)
1
1.85
3.56
4.72
5.17
298
321
328
331
332.5
1.91
2.07
3.72
5
5.84
74.58
73.97
70.37
67.00
66.23
7.07
6.26
6.11
5.73
5.66
1.91
2.00
3.55
4.91
5.54
74.86
70.02
67.29
64.85
62.30
7.07
6.05
5.83
5.62
5.37
0.0
3.4
4.8
1.9
5.4
strikes the solar PV module which results in enhanced electron–
hole pair production and higher photocurrent [32].
The values of the dynamic resistance at MPP are computed
using the values of IPH, ISC and RS. The dynamic resistance of LCPV
module is calculated in an effective manner using Eq. (6) as listed
in Table 3. Approximate error between experimental and theoretical dynamic resistance of the LCPV modules is found within
practically acceptable limits ( 1.3–2.1%).
The plot shown in Fig. 8 and extracted data listed in Tables 3
and 4 describe the dependence of the FF and efficiency of LCPV
module on the change in CR. From the observed results, it is
concluded that the FF and efficiency of LCPV module decreases as
the concentration ratio increases. The decrease in FF and efficiency of solar PV module with the concentration ratio is highly
dependent on the increase in series resistance of LCPV module
due to increase in CR and temperature. As a result of increased
concentration ratio, higher series resistance offers greater resistive power losses equivalent to I2RS in LCPV module and thus
reduces its performance by reducing the FF and efficiency.
The effects of the series resistance on I–V characteristics of
LCPV module is simulated using proposed theoretical model as
shown in Fig. 9. The maximum power point shifts towards lower
values with the increase in series resistance. The current output of
LCPV module in the range of ISC to IMAX is dependent on the RSH of
the solar cells. For this study sufficient high RSH is considered for
modeling (and the experimental value of RSH is also quite high), so
there is negligible variation in the current between ISC to IMAX
with respect to varying voltage at the output terminal of LCPV
module. The voltage output of LCPV module in the range of VMAX
to VOC is dependent on series resistance. Although both resistances (RS and RSH) contribute to the degradation of the I–V curve,
but effect of RS is dominant because the current loss ( I2RS) is
directly dependent on RS. At higher current, which is the case for
LCPV systems, the loss term is more prominent.
The effects of the cell temperature (TC) on I–V curve of LCPV
module is estimated from the proposed model as shown in
Fig. 10. As the device temperature increases, small increase in
short-circuit current is observed, however the open-circuit voltage rapidly decreases due to the exponential dependence of the
reverse saturation current on the temperature as given by Eq. (8)
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P. Yadav et al. / Solar Energy Materials & Solar Cells 112 (2013) 65–72
71
threefold increase. The proposed model is simple and useful to
predict the steady state and dynamic parameters of LCPV module
and can also be used to simulate the I–V curves of the medium
and high concentration solar PV module with certain
considerations.
Acknowledgements
The authors acknowledge the financial support provided by
Gujarat Energy Development Agency (GEDA) to develop CPV
system by grant number: GEDA\EC:REC\March-2010/3/9174. The
authors also acknowledge WAAREE Energies Pvt. Ltd., India for
providing encapsulated crystalline silicon solar PV modules for
this study.
References
Fig. 9. Effect of series resistance on the I–V characteristics of PV module.
Fig. 10. Variation of PMAX with the cell temperature TC.
[32]. In the actual experiments, similar effect of temperature on
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decreases from 9.86 to 8.24 V with temperature coefficient of
voltage 0.021 V/K under ATC as shown in Fig. 8.
A decrease in the PMAX with the increase in TC is observed
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for a given irradiance because of high injection of electrons from
valance band to conduction band of semiconductor material [32].
7. Conclusion
A simple model for estimating the static and dynamic parameters of LCPV system is presented. Experimental results show
that commercially available Si solar cell designed for 1 sun
applications can be used in LCPV system. The static and dynamic
parameters affecting the LCPV module performance under ATC
conditions are explored experimentally and validated theoretically with the help of proposed model. When the CR increased
from 1 sun to 5.17 suns the PMAX of the LCPV module registered a
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