Fitting flash test curves with ECN’s I-V Curve fitting Program IVFIT A. R. Burgers Energy research Centre of the Netherlands ECN PO Box 1, 1755 ZG Petten, The Netherlands Phone: +31-224-564959, Fax: +31-224-568214, E-mail:
[email protected] Abstract A procedure is discussed to do fitting of one- and two diode models to I-V curves measured at varying irradiance. An example of such a measurement is a flash test measurement. The procedure is compared to the translation procedure as described in IEC standard 891. This procedure has as draw backs that an estimate for the series resistance is required and that the translation introduces deviations from the diode curve model. These are overcome by direct fitting to the raw data. 1 Introduction Measurement of the I-V curve of solar cells is one of the primary means of obtaining information of a solar cell. Since 1996 the ECN I-V curve fitting program ivfit has been available for download on the ECN website 1 . The program is being downloaded on average 10 times per month. The program fits the 1- and 2-diode models to solar cell I-V curves. V
0
= V − Rse I(V )
(1)
I(V )
= Ilt + V 0 Gsh + I01 e
V0 n1 Vb
−1
(2)
Equations (1) and (2) show the standard one diode model that is commonly used to describe solar cell I-V curves. The program and the methods used are described in [1]. The most important feature of the program is that it takes into account both current- and voltage noise. Voltage noise has a big influence on fitting due to the steep slope of an I-V curve for higher voltage values. This paper reports improvements and extensions to the program. These are • Improved robustness of the numerical method. This is achieved mainly by constraining parameters of the diode model such as I01 and Rsh to positive values; • possibility to fit the 2-diode model with a varying ideality factor of the first diode; • possibility to fit I-V curves where the irradiance varies during the measurement. An example of such a measurement is a flash test measurement; The paper focuses on fitting I-V curves measured at varying irradiance. 2 Flash test measurements When doing a flash test measurement, for every voltage in addition to the current the irradiance E is acquired, for instance with a photo diode. We hence have a set of n data points (Vi , Ii , Ei , i = 1, n). In order to fit such a data set directly, the diode model has to be extended. 1 http://www.ecn.nl/zon/products/ivfit
V0
= V − Rse I(V ) (3) 0 V E(V ) + V 0 Gsh + I01 e n1 Vb − 1 (4) I(V ) = Ilt,ref Eref Equations (3) and (4) show how the 1-diode model can be extended to take into account the varying irradiance. The assumption is that Ilt is the only diode curve parameter that depends on the illumination level E(V ) and that it depends linearly on E(V ). The reference irradiance Eref defines the irradiance at which we want to know Ilt . In order to fit a diode model to a flash test curve one has two options. One option is to first translate the flash test curve to a constant intensity curve. This can be done using the IEC 891 standard. After translation the curve can be fitted in the normal way. The second option is to do curve fitting to the flash test data directly. 3 Comparison with IEC standard 891 A standard way to translate the data points to a different irradiance is prescribed in IEC standard 891 [2]. This standard involves translation both for irradiance and temperature. In this paper we focus on translation for irradiance. The translation procedure for irradiance gives for every data point (Vi , Ii , Ei ) a translated data point (Vt,i , It,i ) as follows: It,i Vt,i
= Ii + Isc (Ei /Eref − 1) = Vi − Rse (It,i − Ii )
Here Isc is the measured short circuit current of the cell and Eref the irradiance of the light we want to translate to. A value for the series resistance is required to carry out the translation. The standard describes a procedure to find an estimate for the series resistance Rse . In order to see the effects of the translation procedure two I-V curves have been calculated based on the same set of diode parameters (See column 2 in table 1 for the values used). One curve is calculated for constant irradiance and satisfies equations (1) and (2). The second curve is calculated for linearly decreasing irradiance and satisfies equations (3) and (4). Figure 1 shows the calculated I-V curves for both constant irradiance and irradiance decreasing linearly with the voltage. An IEC 891 translation of the decreasing irradiance curve is also shown. Figure 2 shows in more detail the influence of the series resistance on the translated I-V curve. For no value of the series resistance used in the translation procedure the constant intensity curve is reproduced exactly. Table 1 shows in column 2 the input values that have been used for the calculated curves. In the last 3 columns the results are shown of fitting to the IEC 891 translated curves for 3 different values of the series resistance used in the translation. The results deviate from the exact values.
4
1.04
3.5
1.02 1
3
0.96
2
0.94
E(V)
0.98
2.5
1.5 0.92 1 0.5 0 -0.2
0.9
exact, varying E(V) exact, constant E(V) IEC891, Rse = 5 mOhm E(V) -0.1
0
0.1 0.2 0.3 Voltage(V)
0.88 0.86 0.4
0.5
0.6
Fit to flashtest I-V curve
Figure 1: calculated I-V curves for both constant and decreasing irradiance. The IEC 891 translation (Rse = 5 mΩ) of the decreasing irradiance curve is shown.
6
1060
5
1040 1020
3.5
0.15
3
0.1
2.5
0.05 0
1.5
-0.05 exact constant E(V) IEC891, Rse = 2.5 mOhm IEC891, Rse = 5 mOhm IEC891, Rse = 10 mOhm Rse = 2.5 mOhm (right axis) Rse = 5 mOhm (right axis) Rse = 10 mOhm (right axis)
1 0.5 0 0.46
0.48
0.5
0.52 0.54 Voltage(V)
1000 3 Data Fit Residual (*10) 1000 W/m2 Irradiance
2 1
I - Iexact (A)
2 I(A)
Current (A)
4
980 960 940
0 -1 -0.2
Irradiance (W/m2)
I(A)
Table 1: Diode curve parameters for exact data compared to fits to IEC 891 translated curves IEC 891 variable exact 2.5 mΩ 5 mΩ 10 mΩ I01 (A) 5.0e-9 5.0e-9 5.2e-9 5.7e-9 I02 (A) 1.0e-5 .78e-5 .80e-5 .81e-5 Gsh (S) .10 .074 .075 .075 Rse (Ω) 5.0e-3 5.2e-3 5.2e-3 5.1e-3 Ilt (A) -3.4 -3.4 -3.4 -3.4 Voc (mV) 579 580 579 577
920 900 -0.1
0
0.1
0.2 0.3 Voltage (V)
0.4
0.5
0.6
0.7
-0.1 -0.15
0.56
0.58
-0.2 0.6
Figure 2: Comparison of the exact I-V curve for constant irradiance and IEC 891 translated curves for different values of the series resistance (left hand side axis). Since the curves are close together, the differences between IEC 891 translated curves and the exact curve have been plotted to the right hand side axis 4 Fit to an actual measurement Figure 3 shows an example of a fit to a measured flash test curve of a solar cell. During the flash, the irradiance of the light (right hand side axis) goes down from 1040 W/m2 to 910 W/m2 . The I-V fit is made to the data points with the model of equations (3) and (4). Fit and data are shown in the graph. The fit results in the diode curve parameters Ilt , Rsh , I01 , n1 , Rse . Once the diode curve parameters are known, the diode curve can be evaluated at 1000 W/m2 . This curve is also shown in the graph with the label “1000 W/m2 ”. With the effect of the decreasing irradiance during the flash thus accounted for, parameters of the cell such as the Voc and fill factor can be calculated. For different cells they can be compared without the influence of the flash on these parameters. 5 Discussion and conclusions In this paper we compare two methods for correcting for varying irradiance during solar cells I-V curve measurements. One
Figure 3: Fit to an actual flash test curve. Data and fit are close together so the difference between fit and data has been plotted too (residuals). method is the procedure described in IEC standard 891. In this paper we propose to fit a diode-curve model directly to the data with varying irradiance. Both methods have their advantages and weak points. A problem in the IEC standard 891 is that it is not easy to find a good value for the series resistance to be used for correction of the voltage values. Another problem is that the translation procedure is not exact for curves described by oneor 2 diode models as shown in table 1. The procedure proposed in this paper has the advantage that no estimate of the series resistance has to be established. The requirement is however that the I-V curve is described well by a diode-curve model, a requirement that is not made in IEC standard 891. If one is going to do a diode fit, then it is better to do the fitting to the raw data than to IEC 891 translated data, since the translation procedure introduces deviations from the diode models. References [1] A.R. Burgers, J.A. Eikelboom, A. Sch¨onecker, and W.C. Sinke. Improved treatment of the strongly varying slope in fitting solar cell I-V curves. In Proceedings 25-th IEEE PVSC Conference, Washington DC, pages 569–72. IEEE, 1996. ECN-RX-96-022. [2] International Electrotechnical Commission. Procedures for temperature and irradiance corrections to measured I-V characteristics of crystalline silicon photovoltaic devices, 1987. IEC 891.
