PV Impedance Characterization Using Square
Wave Method and Frequency Response Analyzer
Chamnan Limsakul, Nattavut Chayavanich, Dhirayut Chenvidhya and Krissanapong Kirtikara
Clean Energy System Group (CES) King Mongkut’s University of Technology Thonburi, Bangkok, Thailand.
Phone: 662 470 8626, Fax: 662 470 8626, Corresponding Author: D. Chenvidhya E-Mail: dhirayut.che@kmutt.ac.th
Abstract: We determine impedance of a crystalline Si solar cell using a frequency response analyzer over 1 Hz to 50 kHz and basic
instruments using square wave inputs from 10 Hz to 50 kHz. Impedance loci are plotted in a complex plane. Derivation of series and
shunt resistance from the measured results are made and results compared. Owing to low resolution of a digital oscilloscope used,
shunt resistance being normally large can be accurately determined, but not series resistance.
Key Words: Solar Cell, Photovoltaic, Impedance Spectroscopy.
1 Introduction
For the study of solar cell dynamic behavior, dynamic parameters replace static parameters. Series resistance (RS) and
shunt resistance (Rsh) are similar to static ones. Dynamic resistance (Rd), diffusion capacitance (CD), and transition capacitance (CT) substitute the diode [1]. In the equivalent dynamic
model, CT is parallel to CD, represented by a parallel capacitance
CP (CT//CD), and Rsh is parallel to Rd, represented by a parallel
resistance RP (Rsh//Rd) [2]. These dynamic parameters can be
determined by using impedance spectroscopy through the use of
a frequency response analyzer, an expensive piece of analytical
equipment.
In previous work, D. Chenvidhya et al had proposed a new
method to characterize solar cell dynamic impedances in the
dark with forward and reverse bias [2][3][4]. The method employs basic instruments and uses square wave inputs instead of
sinusoidal signals reported earlier. The impedance is calculated
from output responses by MATLAB using the FFT technique to
analyze harmonic content. Impedance loci of a polycrystalline
Si cell, obtained from both sinusoidal and square wave input
signals, when plotted in a complex plane, are semicircular and
similar. Using basic instruments and the same method, J.
Thongpron et al worked on single crystal Si module, polycrystalline Si module and amorphous S1 modules, which showed
that results are compatible with previous work [5].
In this paper, we use a frequency response analyzer - FRA
(Impedance gain-phase analyzer - Solartron 1260) of which
highly accurate values of an amplitude and phase of an impedance can be absolutely determined. The aim is to compare analytical results from FRA and the method employing basic instruments and square wave inputs.
2 Experiment
A 10u10 cm2 crystalline Si solar cell was tested under dark
condition, at room temperature with both biasing. This experiment consists of two measurements, the first one with basic instruments, and the second with FRA. In this paper we chose to
compare results at three conditions, in forward bias of 0.10 V
and 0.20 V, and in reverse bias of 0.1 V. The details are as follows.
2.1 Measurement on Basic Instruments
A small square wave voltage signal superimposing on the
dc level is used as an input function. The amplitude of square
wave is about 10% of the dc bias level, in the frequency range
of 10 Hz to 50 kHz. The input and output signals are measured
by a digital oscilloscope (8 bit-resolution at 2 mV/div.) The
waveform data are transferred to a PC, using GPIB data communication. The solar cell impedance is calculated by
MATLAB using the FFT technique to analyze harmonic content.
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Fig.1 Impedance measurement setup with basic instruments
2.2 Measurement on FRA
Solar cell impedance analysis: The amplitude of small ac
signal is about 10% of the dc bias level, in the frequency range
of 1 Hz to 50 kHz. Both forward biasing and reverse biasing can
be used. The results from measurements are analyzed, to determine the frequency response in terms of the amplitude and
phase outputs. Results are plotted and interpreted as impedance
loci of the cell under varying dc biasing.
Fig.2 Impedance measurement by FRA
3 Results and Discussion
Dynamic impedances under forward biasing at 0.10 and
0.20 V are determined from a basic instrument method and FRA.
Impedance loci are plotted in a complex plane, Fig.3. Loci under
reverse bias at 0.10 V are shown, in Fig.4.
From a solar cell impedance equation written in terms of
parallel resistance RP and parallel capacitance CP, RS+RP is
given by an intercept of the impedance locus at low frequency,
and RS is the intercept at high frequency. We bear in mind that
RS+RP is larger than RS by about two orders of magnitude owing to the difference in RS and Rsh. We have not attempted to
derive the two components of RP, i.e. the shunt resistance Rsh
and the dynamic resistance Rd,. J. Thongpron has reported such
derivation. Tab.1 shows the value of RS+RP and RS that are determined from both basic instrument and FRA methods. For
comparison, we show the value of RS+RP and RS determined by
employing a basic instrument but using sinusoidal inputs. We
see that:
Forward Bias
0
Rpv (ohm)
40
20
60
resolution improvement of more than ten times, we could measure series resistance, and other components of dynamic impedance, with improved accuracy. The basic equipment method still
remains less expensive than FRA.
Tab.1 RS+RP and RS determined from basic instrument method
and FRA
80
0
Biasing (V)
Xpv (ohm)
-10
Rs+Rp
-20
Forward
Reverse
-30
Rs
Forward
Reverse
0.10
0.20
0.10
0.10
0.20
0.10
Resistance (ohm)
Basic Instruments
Square
Sinusoidal
wave
64.99
67.82
20.13
20.44
262.30
266.42
0.57
0.54
0.52
0.57
0.53
0.58
FRA
65.91
24.16
265.80
0.17
0.17
0.17
-40
Basic insts : 0.10 V
FRA : 0.10 V
Basic insts : 0.20 V
FRA : 0.20 V
Fig.3 Impedance loci under forward bias at 0.1 and 0.2 V
Reverse Bias
Rpv (ohm)
0
50
100
150
200
250
300
0
-20
Xpv (ohm)
-40
-60
-80
-100
4 Conclusions
We determine impedance of a single crystalline Si solar
cell using a frequency response analyzer and basic instruments
using square wave inputs. Impedance loci are plotted in a complex plane. We also derive series and shunt resistance from the
measured results. Owing to low resolution of a digital oscilloscope used, shunt resistance (being normally large) can be accurately determined, but not series resistance.
-120
-140
Basic insts : 0.10 V
FRA : 0.10 V
Fig.4 Impedance loci under reverse biasing at 0.1 V
(a) RS determined by FRA and basic instrument methods
are quite different, although those values obtained from basic
instrument method but using sinusoidal and square wave inputs
are quite close. Due to the resolution of basic equipment and
impedance at high frequency being quite low, reading of values
becomes difficult. Thus FRA results should yield more accurate
results.
(b) On the other hand, RS+RP determined by FRA and basic instrument methods are nearly equal (less than 1% difference)
when impedances are large, at low frequency and low dc biasing
of 0.1 V. With smaller impedance, biasing at 0.2 V, the two
methods yield a difference of about 15 %. Under reverse biasing
when the shunt resistance is large and dominant, its value can be
determined accurately by basic instrument method.
We therefore conclude that the method using basic instruments, which costs much less than FRA, can provide fairly accurate values of parallel resistance, hence shunt resistance, but
not series resistance. If we replace the existing oscilloscope with
one with higher resolution, now commercially available with a
References
[1] H.S. Rauschenbach, Solar cell array design handbook, Van
Nostrand Reinhold, 1980, pp.52-63 .
[2] D. Chenvidhya, K. Kirtikara, and C. Jivacate, “A new characterization method for solar cell dynamic impedance”, Solar
Energy Materials and Solar Cells, 2003, 80: 459.
[3] D. Chenvidhya, K. Kirtikara, C. Jivacate, D. Chenvidya, K.
Kirtikara and C. Jivacate, “ On dynamic and static characteristics of solar cells modules having low and high fill factors”,
Proceedings of the 3rd World Conference on Photovoltaic Energy Conversion WCPEC3, 12-16 May 2003, Osaka, Japan.
[4] D. Chenvidhya, C. Limsakul, J. Thongpron, K. Kirtikara and
C. Jivacate, “Determination of solar cell dynamic parameters
from time domain responses”, Technical Digest of the 14th International Photovoltaic Science and Engineering Conference
PVSEC14, 26-30 January 2004, Bangkok, Thailand.
[5] J. Thongpron. K. Kirtikara and C. Jivacate, “ A method for
the determination of dynamic resistance of photovoltaic modules under illumination”, Technical Digest of the 14th International Photovoltaic Science and Engineering Conference
PVSEC14, 26-30 January 2004, Bangkok, Thailand.