th
15 International Photovoltaic Science & Engineering Conference (PVSEC-15) Shanghai China
2005
26-1
Temperature and Irradiance Dependence of the I-V
Curves of Various Kinds of Solar Cells
Yuki Tsuno1, 2, Yoshihiro Hishikawa1 and Kosuke Kurokawa2
1
National Institute of Advanced Industrial Science and Technology (AIST), Research Center for Photovoltaics, Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki, 305-8568, Japan
2.
Tokyo University of Agriculture and Technology (TUAT), 2-24-16 Naka-cho, Koganei, Tokyo, 184-0012, Japan
Phone: +81-42-388-7445, FAX: +81-42-388-7445, E-Mail: kanbai@cc.tuat.ac.jp
Abstract: It is useful to understand the effect of the irradiance and temperature on the solar cell and module performance, in order to
estimate their I-V curves under various climate conditions. In this study, the linear interpolation method for the I-V curves is investigated based on experimental data on various kinds of solar cells. Physical validity of the linear interpolation for temperature is also investigated. Good agreement of the calculations and experiments of within ±1% indicates that the translation of the I-V curve based on
the method is effective for estimating the performance of solar cells, modules and systems under various climatic conditions.
Key Words: solar cell, module, I-V curve, temperature, irradiance, translation.
1 Introduction
3 Experiments and Results
It is useful to understand the effect of the irradiance and
spectrum of the incident light and temperature on the solar cell
and module performance, in order to estimate their performance
under various climate conditions. Although translation equations based on "shifted approximation" are employed on irradiance dependence in some standards [1], those equations can deviate from experiments when the variation in the irradiance
and/or temperature is large. It has been reported that the irradiance dependence of the current-voltage (I–V) curves based on
linear interpolation or extrapolation is valid for various kinds of
solar cells including c-Si, a-Si and thin-film crystalline silicon
solar cells, etc [2]. Recently, Marion et al. [3] reported that the
I-V curves of a solar cell and modules is translated to desired
conditions of irradiance and temperature by means of bilinear
interpolation and four reference I-V curves. In this study, we
investigate the accuracy of the linear interpolation method based
on the experimental I-V curves of various kinds of solar cells.
Physical validity of the linear interpolation for temperature is
also investigated
Typical single-crystalline Si, polycrystalline Si, amorphous
Si and a-Si/thin-film crystalline Si tandem cells were used as
samples. Their sizes ranged 2-10 cm2. They were attached on
metal plates, whose temperature was stabilized at 20°C, 30°C,
40°C, and 50°C by a flow of temperature controlled water. The
temperature was controlled within a nominal accuracy of
±0.2°C. A solar simulator was used as the light source of 100
mW/cm2. Irradiance was controlled by metallic thin film neutral
density filters. For each solar cell, four reference I-V curves
with irradiances of 0 and 100 mW/cm2 and temperatures of
20°C and 50°C. The I-V curves at various irradiances and temperatures were calculated by using equations (1) and (2) from
the reference I-V curves. The calculated I-V curves well agree
with the experiment for all the samples measured in the present study [Fig.1(a)-(d)]. Measured and calculated I-V curve
parameters Isc, Voc, maximum power Pmax and fill factor FF
agreed within ±0.6% for all the samples shown in the figures,
which is good enough for many purposes.
2 The Linear Interpolation Method
The translation of the I-V curve for irradiance and temperature by the linear interpolation method is based on the following two assumptions.
(1) translation for irradiance: The I-V curve is expressed by
the sum of a dark current and a voltage-dependent photocurrent,
which is proportional to the irradiance or the short circuit current Isc (equation (1)).
(2) translation for temperature: The output voltage V is a
linear function of the temperature T when the output current I is
a constant (equation (2)).
E −E
I 3 (V ) = I 1 (V ) + 3 1 ⋅(I 2 (V ) − I 1 (V ) )
(1)
E 2 − E1
(a) single-crystalline Si cell
T3 −T1
⋅(V2 ( I ) −V1 ( I ) )
(2)
T2 −T1
Here, I(V) and V(I) are the I-V curves, Isc is the short circuit
current and T is the device temperature. V(I) I(V) is the inverse
function of I(V). Subscripts 1 and I indicate measured conditions,
and subscript 3 indicates the target condition.
V3 ( I ) =V1 ( I ) +
(b) polycrystalline Si cell
422
also indicates that the output current I, not the irradiance, of
measured two I-V curves should be the same in order to accurately translate the I-V curve. Therefore, the validity of the
translation for the temperature by the linear interpolation is
based on the basic I-V characteristics of the p-n junction. It
should be noted that the I-V curves of amorphous silicon solar
cells (Fig.1(a)) and Si-based multi-junction structure, which are
not expressed by equations (3) and (4), are also very well translated by the linear interpolation. This indicates that the equations (1) and (2) are valid for various kinds of solar cells which
are presently available. It is also noted that parameters such as
series resistance Rs or curve correction factor K are not required
in the present translation equations, which is advantageous because these parameters cannot always be accurately determined.
It is known [2] that the translation equation for the irradiance
(eq. 1) can be modified when the Rs is very large. The translation equation for the temperature (eq. 2) is valid even for very
large value of Rs. As a result, we have confirmed that the linear
interpolation method is applicable to the solar cell which does
not consist of equation (3) such as a-Si or tandem cell. In principle, four I-V curves measured at arbitrary chosen temperature
and irradiance are enough for the calculation.
(c) amorphous Si cell
5 Conclusions
(d) a-Si/thin-film crystalline Si tandem cell
Fig.1 Measured (lines) and calculated (dotted lines) I-V curves
of various kinds of solar cells
We have confirmed the accuracy of the linear interpolation
method for translating the I-V curves of solar cells for irradiance
and temperature, based on the experimental I-V curves of various kinds of solar cells measured under temperature-controlled
conditions. The validity of the linear interpolation for the temperature is based on the basic I-V characteristics of the p-n junction devices. Typical single-crystalline Si, polycrystalline Si,
amorphous Si and a-Si/thin-film crystalline Si tandem cells were
used as samples. Good agreement of the calculations and experiments within ±1% indicates that the translation of the I-V
curve based on the method is effective for estimating the performance of solar cells and modules under various climatic conditions. Therefore, simultaneous translation of the I-V curves for
both the temperature and irradiance is possible.
4 Physical Meaning of The Linear
Interpolation for Temperature
In order to derive an approximate expression for temperature translation, we start with the single-diode model [4] of a p-n
junction cell:
q (V + IR s )
⎛
⎞
) −1⎟⎟
I = I ph − I 0 ⎜⎜ exp(
(3)
kT
⎝
⎠
Where, I is the current, Iph is the photocurrent, I0 is the diode saturation current, q is the electronic charge, V is the voltage,
Rs is the series resistance, k is Boltzmann's constant and T is the
temperature. I0 is also usually expressed as an exponential form:
Eg
)
(4)
I 0 = A exp(−
kT
Where, A is a constant and Eg is the bandgap energy of the
active material. Therefore, the voltage can be rewritten as:
⎛ I ph − I ⎞ E g
⎟+
V = kT ln⎜⎜
− IRs
(5)
q ⎝ A ⎟⎠ q
Equation (5) means the voltage V is linear function of temperature T when current I is a constant. Using equation (5) and
two I-V curves, the final expression for correcting temperature
of typical solar cell is expressed as equation (2). The equation
Acknowledgement
This work was supported in part by NEDO under the Ministry of Economy, Trade and Industry.
References
[1] IEC 60891, 1987.
[2] Hishikawa Y, Imura Y, Oshiro T. Proceedings of the 28th
IEEE PV Specialists Conference, 2000, 1464–1467.
[3] B. Marion, S. Rummel and A, Anderberg. Prog. Photovolt:
Res. Appl. 2004, 12: 593–607.
[4] S. M. Sze. John Wiley & Sons Inc., New York, 1981.
423