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Outdoor testing of photovoltaic arrays in the Saharan region
ARTICLE IN PRESS Renewable Energy 33 (2008) 2516– 2524
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Outdoor testing of photovoltaic arrays in the Saharan region Mohammed Sadok , Ahmed Mehdaoui Research Unit of Renewable Energy in Saharan Middle (URER/MS), B.P. 478, Adrar 01000, Algeria
a r t i c l e in f o
a b s t r a c t
Article history: Received 17 April 2007 Accepted 10 February 2008 Available online 15 May 2008
This article presents the results obtained from the analysis of the I– V electrical characteristics of photovoltaic arrays that were tested in a region of the Sahara. Experiments were carried out at Adrar in the southern part of Algeria. The study includes the determination of the most representative parameters of the arrays by using numerical methods for the one exponential model. After having determined these parameters, they were numerically used in order to carry out the plotting of the theoretical I– V characteristics of modules for the considered environmental variables such as ambient temperature and solar irradiance. Other model (Rauschenbach’s model) has also been considered in this article to make a comparison with the previous one. The study has been completed by carrying out the translation of the experimental characteristics for the standard conditions. This translation allowed the comparison to be made between the performances of tested modules. In the last part of the paper, some elements related to the degradation of arrays performances have been presented. & 2008 Elsevier Ltd. All rights reserved.
Keywords: Photovoltaic array Numerical method Electrical characteristic Standard test conditions Degradation
1. Introduction In any photovoltaic system, the array plays a main role in the setting of its energy balance. Consequently, when analysing the functioning of a photovoltaic system, the array must be looked into. The study of a photovoltaic array particularly aims at determining the principal parameters of the equation governing its electrical characteristic. Once these parameters are known, they can more easily be used in evaluating the performances of the considered photovoltaic array (yield, maximum power, fill factor,y). However, it is important to note that a standardized presentation of the modules’ performances makes them more significant. This work intends to present and analyse some of the results obtained from the outdoor testing of a photovoltaic array of a nominal 1.6 kWp stand alone photovoltaic system. This task includes two parts. The first part is detailed in the present paper whereas the second one essentially deals with the performances of the modules when they are associated together. The photovoltaic modules forming the generator of the SAPVS have been tested in outdoor conditions. Measurements were taken at Adrar in the southern part of Algeria. This site of experiments is considered as a very important location since it is often exposed to high levels of solar radiation. The mean annual of the daily
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global irradiance measured on tilted surface exceeds the value of 7 kWh/m2 [1].
2. Performance of the system The tested photovoltaic modules were associated together to constitute a generator of a nominal 1.6 kWp stand alone photovoltaic system with battery storage. In previous studies, the performances of this SAPVS have been determined for a considered functioning period. Though not sufficiently long, this period gave important information on the behaviour of the system and allowed to make the determination of the system performances. Some values of yield and performance indices, determined for three months of operating of the SAPVS, are given in Table 1 [2]. The formulas used for the determination of these parameters have already been detailed in previous Ref. [2]. The study of the monthly evolution of the generator daily yield shows that its values have not exceeded the threshold of 10% [2]. So it was obvious that these array yield values influence the global performances of all the system. For this reason, it was projected to perform outdoor characterization testing of modules which form the photovoltaic generator of the SAPVS. Experimental electrical characteristics have been obtained for different values of solar irradiance and ambient temperature. After plotting these characteristics, a code program was implemented in order to analyse data files and fit the I– V curves. The determination of the principal parameters of modules has therefore been achieved as well as the translation of the characteristics for the standard test conditions.
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Table 1 Some values of yield and performance indices of the SAPVS Month
Z (%)
YA
YR
YF
PR (%)
November December January
8.74 9.36 10.64
4.50 4.58 4.50
5.95 5.68 4.95
3.73 3.77 3.20
65.87 69.17 69.48
3. Experimentation The photovoltaic array of the studied SAPVS is presented by Fig. 1. The experimental setup used for the outdoor measurements consists of the module to test, a capacitive electronic load and a scopemeter. The values of the solar radiation and the ambient temperature are given by a CM11 Kipp & Zonen Pyranometer and a digital thermometer, respectively. The total number of the modules under test is 32. They were facing towards the equator and mounted on a fixed structure which was tilted at an angle equalling the latitude of the site. All modules are of UDTS-50 type which utilizes single crystal silicon cells laminated to tempered glass with ethylene vinyl acetate (EVA). Each module consists of 36 solar cells wired in serial connection. The tests of modules were repeated for different values of solar radiation and ambient temperature. While undertaking a module test, the corresponding values of environmental parameters were recorded. All of this information was saved to files named according to the serial type reference of the module in question. The obtained data files have been treated to eliminate erroneous points. The plotting of the electrical I– V characteristic of the module was then carried out. Thus it can be seen in these characteristics that the current–voltage pairs are presented in the form of cloud points (see Fig. 2).
4. Numerical method and validation The determination of the tested module parameters has been quite difficult because of the above-mentioned shape of the obtained I– V curves and the distribution of current–voltage points. Then it was necessary to have recourse to numerical methods so as to result in a best graphical representation of curves and quite accurate values of the module parameters. This task required the use of a computer model having the ability to mathematically describe the I– V curve of the module. Such a model must be combined with the experimental data to make the resolution of the equations system, then the estimation of module parameters. The resolution approach was based on the modified least squares method applied to a non-linear model. The theoretical module model that is with one exponential, generally much used, is given by qðV þ I Rs Þ V þ I Rs I ¼ Iph I0 exp 1 , (1) AkT Rsh where Iph is the photocurrent generated by the module under radiation, I0 the reverse saturation current (A), Rs the series resistance (O), A the ideality factor, k the Boltzman’s constant, T the module temperature (K) and Rsh the shunt resistance (O). The expression of Eq. (1) is of implicit and non-linear type. It then requires knowledge of many parameters (Iph, Rs, A,y). In practice, these parameters should numerically be determined. As the application of the least squares method for this type of
Fig. 1. Modules of photovoltaic generator of the SAVPS.
equations is rather difficult, a program code based on a method found in the literature has been used [3,4]. This method has been validated using experimental data obtained in the case of the characterization of a group of photovoltaic modules connected together (Fig. 3). The comparison of measured and calculated values of voltage allows to see that they are approximately equal. The resultant computed error is about 0.21% and can then be fairly acceptable. This method of I– V curves fitting therefore appears to be suitable for the determination of module parameters.
5. Application of the model to I– V experimental characteristics The validation of the used numerical method has been checked for simple data and not for the case when the data are presented in the form of cloud points as those mentioned above. Running the program code several times has nevertheless allowed to reach the convergence of the equations system; then the determination of the main parameters of tested modules. The estimated errors fluctuate somewhere around 1%, a value which is relatively greater with regard to 0.21% value found with the I– V characteristics of Fig. 3. The values of the main parameters that have been found for some modules under test are presented in Table 2 (error values are also mentioned). The curves of Fig. 4 give a graphic representation of the I– V characteristics of some modules tested under different environmental conditions. These curves allowed to make comparison between the characteristics given by the numerical computation (fitted) and those obtained by outdoor measurement tests. The order of precision is not of the same magnitude as the one being obtained with the smoothing shown by Fig. 3. This can, however, be accepted owing to the fact that tests have been carried out in difficult conditions and the equipments used in the tests were lacking in some precision. It must also be mentioned that the shape of the distribution of I– V points obviously resulted in a reduction of the graphic fitting precision. A simple examination of the I– V curves presented by Fig. 4 lets to see that the maximum power points are localized on the left side of the characteristics. Consequently, this resulted in a reduction of the values of the maximum power and the fill factor as well.
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2.00
1.00
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0.00 4.00
0.00 8.00
12.00 Voltage (V)
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Fig. 2. Some modules I– V characteristics given by outdoor testing.
Table 2 Main parameters of some tested modules
12.00 model validation measured values computed values
Current (A)
8.00
Rsh (O)
Rs (O)
I0 (A)
Iph (A)
sexp (%)
X910317 X910346 X910356 X910315 X910309 X910306 X910308 X910351 X910312
429.6 500.0 349.4 499.4 500.0 500.0 443.8 423.8 500.0
0.903 0.481 0.648 1.045 0.376 1.86 1.292 1.59 1.193
0.0191 0.0523 0.0135 0.00275 0.0316 0.0031 0.0029 0.0095 0.0153
3.025 2.971 2.613 2.408 2.971 2.368 2.71 3.14 2.78
1.11 0.68 1.19 1.44 0.83 1.09 1.46 1.20 0.72
6. Comparison of fitted curves with those of Rauschenbach’s model
4.00
0.00 0.00
Module
10.00
20.00 Voltage (V)
30.00
Fig. 3. Validation of used numerical model.
40.00
The one exponential model is not the only one being proposed in the literature and which describes the I– V characteristic of a photovoltaic module. In effect, some references quote other explicit model simple to use and known as Rauschenbach’s model. It requires only three points of the I– V characteristic namely the short circuit current, the open circuit voltage and the maximum power point. Thus the current produced by the photovoltaic module is computed as a function of the voltage
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module: X891380 H=980 W/m2, Ta=31,7°C measured values computed values
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module: X910357 H=990 W/m2, Ta=23°C mesaured values computed values
0.00 0.00
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module: X910309 H=910 W/m2, Ta=31,5°C measured values computed values
16.00
20.00
0.00 0.00
4.00 8.00 Voltage (V)
12.00
Fig. 4. Some experimental and computed I– V characteristics modules.
7. Determination of maximum power points and fill factors
as follows [5,6]: V 1 . I ¼ Isc 1 C 1 Exp C 2 V oc
(2)
The coefficients C1 and C2 are given by the following expressions: C1 ¼
Im V m 1 , Exp Isc C 2 V oc
(3)
C2 ¼
ðV m =V oc Þ 1 . Lnð1 ðIm =Isc ÞÞ
(4)
The use of the previous expressions allowed to plot the I– V characteristics of the modules. For example, the curves of Fig. 5 present the I– V characteristics that were, respectively, obtained from the application of both models described above. Comparing between the resultant characteristics leads to draw the conclusion that these models present approximately a good agreement. The noted discrepancies are principally due to the approximations supposed in the Rauschenbach’s model.
Once the I– V characteristics were fitted and the principal parameters of modules were estimated, it would be possible to undertake the determination of the different maximum power points of the modules according to the environmental conditions of experiments. The implicit and non-linear model involved some difficulties in the estimation of the maximum power values of modules. As a result, this inevitably led to the use of the numerical methods in finding of maximums’ function. For this case, the chosen method is based on the research of functions maxima and also combined with successive iterations. The found values of the maximum power of some tested photovoltaic modules are given in Table 3. The corresponding values of solar irradiance and ambient temperature are also mentioned with the reference of the module. The values of the fill factor parameter have been computed by using the formula of Eq. (5). Table 4 gives values of such a parameter determined for some tested modules. FF ¼
Pm . V oc Icc
(5)
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0.00 0.00
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module: X910346 implicit model Rauschenbach's model
16.00
20.00
0.00 0.00
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8.00 12.00 Voltage (V)
Fig. 5. Comparison of fitted curves with those of Rauschenbach’s model.
8. Translation of I– V characteristics
Table 3 Maximum power values of some tested modules Module
H (W/m2)
Ta (1C)
Pmax (W)
X891380 X910360 X910357 X910342 X910365 X910305
980 1000 680 670 740 810
31.7 24.0 27.7 27.7 28.2 23.8
25.77 25.75 29.19 20.68 26.36 26.52
Table 4 Some values of fill factor Module
Fill factor
X910384 X910314 X910344 X910311 X910303 X910305
0.49 0.44 0.43 0.42 0.40 0.45
The fitted characteristics that were previously obtained seem to be not convenient for a subsequent use because they have been recorded for ambient conditions which are not necessarily identical. They must then be presented for the same ambient conditions in order to be able to make a comparison among them [7]. This task is called the translation of I– V characteristics for the standard test conditions (by abbreviation STC translation). With such a translation it would therefore be possible to compare between the I– V characteristics obtained by experiments and those mentioned by the constructor of modules. Moreover, the performances of new photovoltaic modules are generally given at standard rating conditions. The literature gives different reference conditions at which the I– V characteristics can be translated. However, the most used translation method corresponds to values of solar irradiance and cell junction temperature which are equal to values of 1000 W/m2 and 25 1C, respectively, with the reference air mass 1.5 solar spectral irradiance distribution.
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1.00 module: X910307 experimental characteristic STC translated characteristic
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16.00
Fig. 6. I– V characteristics translated to STC.
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In this case, the electric characteristics of modules have been translated to STC using the following formulas: [8,9] ISTC ¼ Imeas
HSTC Hmeas
þ a ðT c T STC Þ,
(6)
V STC ¼ V meas b : ðT STC T C Þ Rs ðImeas ISTC Þ HSTC þ V t Ln , Hmeas
(7)
with ISTC is the current module at STC (A), VSTC the voltage module at STC (V), HSTC the reference irradiance (W/m2), Hmeas the measured irradiance (W/m2), TSTC the reference module temperature (1C), Tc the measured (or computed) module temperature (1C), a the temperature coefficient of the current, b the temperature coefficient of the voltage, Rs the series resistance, Imeas the measured current, Vmeas the measured voltage, Vt the thermal module voltage. The module temperature is computed using the well-known cell temperature model found in Refs. [10,11]. The module is then assumed to have an equivalent temperature value. The formulas used for the STC translation have been applied for different tested modules characteristics and have then allowed to new ones as it is shown by Fig. 6. In Fig. 7, translated characteristics of some tested photovoltaic modules have been brought together in order to get a further illustration about the translation. The comparison can thus be made between the performances of modules. It can therefore be noted that the translated characteristics are relatively close to each other. This could be logical because all tested modules are of the same type and the translation of course refers to the same values of irradiance and temperature. The noted differences can nevertheless be ascribed to different factors:
both coefficients a and b were supposed to have the same
In order to study the time evolution of the performances of the modules one must know their outdoor I– V characteristics being given by the constructor. The modules characteristics translated for the standard test conditions should also be known. Since the characteristic of each module was not initially known, it has then been thought proper to suppose the characteristic of a module of the same type (UDTS-50). This characteristic will thus substitute for the one of each module of the system. The main parameters of a UDTS-50 module type, found in some bibliographical reference, are presented in Table 5. The values of the fill factor computed for some tested modules are presented in Table 6. On this point, it is necessary to note once again that these values have been determined after supposing that the fill factor initially has the same value given in Table 5. In the photovoltaic technology, it is clear that the modules do not necessarily maintain their initial performances throughout the periods of exposition. Some modules degrade or even fail
Table 5 Main parameters of used module type Open circuit voltage (Voc) Short circuit current (Isc) Voltage at maximum power point (Vm) Current at maximum power point (Im) Maximum power (Pm) Fill factor (FF) Output module (Z)
Module
Fill factor (%)
Degradation factor (%)
X910312 X910307 X910315 X910023 X910356
54 50 52 49 50
25 30 27 32 30
3.00
3.00
2.00
1.00
21.6 V 3.18 A 17.5 V 2.9 A 49.4 W 0.72 11.6%
Table 6 Degradation factor of some tested modules
Current (A)
Current (A)
values for all the modules under test, temperature model used in the estimation of equivalent temperature of module, others sources of errors due to experimentation.
9. Study of performances modules degradation
STC translated I-V characteristics module: X891380 module: X910023 module: X910303 module: X910308 module: X910314 module: X910356 module: X910357 module: X910384
0.00 0.00
5.00
10.00 15.00 Voltage (V)
2.00 STC translated I-V characteristics
1.00
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module: X910307 module: X910311 module: X910313 module: X910343 module: X910344 module: X910345 module: X910363 module: X910365
5.00
10.00 15.00 Voltage (V)
Fig. 7. STC translated I– V characteristics of some photovoltaic modules.
20.00
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when operating outdoors for extended periods [12–14]. Many factors could be the causes of such degradations and decreases of the modules’ performances. In order to thoroughly analyse and monitor a module degradation process, a complete set of techniques is necessary [12–15]. In the case of this paper, it has been difficult to do that. However, a simple factor has been used so as to quantify the degradation rate. This degradation factor is computed using the following formula: FF A¼ 1 100. (8) FFinitial
Like it was mentioned above, the technical information quoted by the manufacturer was not available and especially the values of the temperature range of electrical connections. Nevertheless, many manual references of modules constructors indicated that the electrical connections can support high values of temperature. In the present study, the type of PV modules is equipped with aluminium-based connections. It has been used in many installations in this Saharan region and has proved a good endurance. However, two major problems have been encountered with electrical connections:
The degradation factor is given in percentage ratio. It must theoretically be estimated in relation to its initial value given separately for each photovoltaic module. However, such data do not generally exist, so the value mentioned above in Table 5 has been used. In addition to values of the fill factor, Table 6 gives those of the degradation factor of some tested photovoltaic modules. The values of the degradation factors presented in Table 6 allow to draw the conclusion that the modules have lost nearly the third of their performances. This inference must, however, been reviewed owing to the suppositions made in computing the factor A. On the other hand, in determining the STC performances of the modules, the values of parameters such as a, b, NOCTy have been gotten from the bibliography. Information quoted by the constructor does not generally involve values of these parameters. It can, however, be considered that these values of the degradation rate remain logical by taking into account that the tested modules were installed and exposed to solar radiation since a long time (over ten years). In this paper a simple review of the degradation of modules has been given by comparing the actual performances to the initial ones. The study of module degradation still requires periodic monitoring and measurements of the principal parameters characterizing the functioning of this module. Without appropriate means, it was difficult to exactly know the factors which led to the modules being degraded. The visual inspections on photovoltaic modules did not provide the expected identification of the degradation mechanisms. In the case of this work, however, the degradation of the modules’ performance could be due to three major factors:
may slacken off. For this reason connections must be regularly inspected and tightened if necessary; the penetration of dust in the electrical connection boxes causes bad contacts between modules and cables, so they must be periodically cleaned and inspected.
discoloration of the EVA copolymer encapsulant: visual
inspection revealed the browning of the encapsulant in some areas on the inside of the modules. This browning often happens after long term exposure to UV sunlight with module operating temperature near 50 1C [12]. A previous study has reported that the module performance degradation cannot be fully attributed to the extent of encapsulant discoloration [13]. absorption of UV light: some research work concluded that the degradation is probably caused by UV sunlight absorption at or close to the top of Si surface [13]. hot spot formation: in a PV module, hot spot can occur by any combination of cell failure, interconnection failure, partial shading and variation in the photocurrent from cell to cell (mismatch). It also results from inadequate module bypass or from a cracked cell in the module. Depending on the severity of the crack, a cracked cell potentially produces less current than the cell in the string [15]. In this work, this factor can have a major consequence on the degradation of modules.
As for the temperature effect, it has been reported, in a previous work, that the causes of the degradation are not thermally activated [13].
due to the thermal differences, the module wiring connectors
10. Conclusion This paper was presented the results obtained by achieving the outdoor measurements of many photovoltaic modules forming the array of a stand alone photovoltaic system installed in a region of the Sahara which is characterized by high level of solar irradiance. The outdoor tests have allowed to carry out the I– V characteristics of tested modules. The use of the least squares method and its application for the implicit form of the I– V characteristic model led to the determination of the most representative parameters of modules. The difficulties encountered in the fitting of experimental data were principally lied in the cloud-points distribution of the current–voltage pairs of each characteristic. The graphic smoothing which allows the determination of module parameters has successfully been made with acceptable errors. Moreover, these fitted I– V curves are nearly close to those obtained when the Rauschenbach’s model has been applied. The use of the translation equations has resulted in an estimation of the module parameters such as the open circuit voltage, the short circuit current and the maximum power point for the same environmental operating conditions (1000 W/m2, 25 1C) The study has also included the degradation of the modules’ performances. The values of degradation factors have then revealed that the modules have lost nearly the third of their initial performances. Unfortunately, the lack of suitable instruments did not contribute to go deeply into the degradation phenomenon; nevertheless, this can be attributed to different factors like UV light absorption, encapsulant discoloration and hot spot formation. References [1] Capderou M. Atlas Solaire de l’Alge´rie, Tome 2. Alger: Office des Publications Universitaires; 1985. [2] Sadok M, Mehdaoui A, Hamek H. Photovoltaic rural electrification of a village in Algeria. In: World renewable energy congress VI. Brighton, UK; 2000. p. 1925–7. [3] Braunstein A, Bany J, Appelbaum J. Determination of solar cell equation parameters from empirical data. Energy Conversion 1977;17:1–6. [4] Hartley HO. The modified Gauss–Newton method for the fitting of non-linear regression functions by least squares. Technometrics 1961;3: 269–80. [5] Hart GW. Residential photovoltaic system simulation: electrical aspects. In: Proceedings of the 16th IEEE photovoltaic specialists conference (PVSC); 1982. p. 281–8. [6] Lasnier F, Sivoththaman. Photovoltaic system sizing and performance by the comparison of demand and expected radiations. Int J Solar Energy 1990;9: 65–76.
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[7] Blaesser G. The reduced current–voltage characteristics of PV arrays and its quasi-independence of ambient conditions. In: Proceedings of the 14th European photovoltaic solar energy conference. Barcelona, Spain, 1997. p. 1520–3. [8] Leboeuf C, Ossenbrink H. PV module power output: sensitivity and uncertainty in non-STC measurements. In: Proceedings of IEEE photovoltaic specialists conference (PVSC); 1991. p. 614–9. [9] Knaup W. Power rating of photovoltaic modules from outdoor measurements. In: Proceedings of IEEE photovoltaic specialists conference (PVSC); 1991. p. 620–4. [10] Coakley JM, Kallis JM, Jones IR. Cell temperatures in terrestrial photovoltaic modules effect of design factors. In: Proceedings of the 17th IEEE photovoltaic specialists conference (PVSC); 1984. p. 496–501.
[11] Buresch M. Photovoltaic energy systems, design and installation. Mc GrawHill Book Company; 1983. [12] King DL, Quintana MA, Kratochvil JA, Ellibee DE, Hansen BR. Photovoltaic module performance and durability following long-term field exposure. Sandia National Laboratories Report may be accessed at: /http://www. sandia.gov/pvS. [13] Osterwald CR, Anderberg A, Rummel S, Ottoson L. Degradation analysis of weathered crystalline-silicon PV modules. In: Proceedings of the 29th IEEE photovoltaic specialists conference (PVSC). New Orleans, LA, USA; 2002. p. 1392–5. [14] Meyer EL, van Dyk EE. Assessing the reliability and degradation of photovoltaic module performance parameters. IEEE Trans Reliab 2004;53:83–92. [15] van Dyk EE, Meyer EL, Foster FJ, Leitch AWR. Long-term monitoring of photovoltaic devices. Renewable Energy 2002;25:183–97.
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Outdoor testing of photovoltaic arrays in the Saharan region Mohammed Sadok , Ahmed Mehdaoui Research Unit of Renewable Energy in Saharan Middle (URER/MS), B.P. 478, Adrar 01000, Algeria
a r t i c l e in f o
a b s t r a c t
Article history: Received 17 April 2007 Accepted 10 February 2008 Available online 15 May 2008
This article presents the results obtained from the analysis of the I– V electrical characteristics of photovoltaic arrays that were tested in a region of the Sahara. Experiments were carried out at Adrar in the southern part of Algeria. The study includes the determination of the most representative parameters of the arrays by using numerical methods for the one exponential model. After having determined these parameters, they were numerically used in order to carry out the plotting of the theoretical I– V characteristics of modules for the considered environmental variables such as ambient temperature and solar irradiance. Other model (Rauschenbach’s model) has also been considered in this article to make a comparison with the previous one. The study has been completed by carrying out the translation of the experimental characteristics for the standard conditions. This translation allowed the comparison to be made between the performances of tested modules. In the last part of the paper, some elements related to the degradation of arrays performances have been presented. & 2008 Elsevier Ltd. All rights reserved.
Keywords: Photovoltaic array Numerical method Electrical characteristic Standard test conditions Degradation
1. Introduction In any photovoltaic system, the array plays a main role in the setting of its energy balance. Consequently, when analysing the functioning of a photovoltaic system, the array must be looked into. The study of a photovoltaic array particularly aims at determining the principal parameters of the equation governing its electrical characteristic. Once these parameters are known, they can more easily be used in evaluating the performances of the considered photovoltaic array (yield, maximum power, fill factor,y). However, it is important to note that a standardized presentation of the modules’ performances makes them more significant. This work intends to present and analyse some of the results obtained from the outdoor testing of a photovoltaic array of a nominal 1.6 kWp stand alone photovoltaic system. This task includes two parts. The first part is detailed in the present paper whereas the second one essentially deals with the performances of the modules when they are associated together. The photovoltaic modules forming the generator of the SAPVS have been tested in outdoor conditions. Measurements were taken at Adrar in the southern part of Algeria. This site of experiments is considered as a very important location since it is often exposed to high levels of solar radiation. The mean annual of the daily
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E-mail address: [email protected] (M. Sadok). 0960-1481/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2008.02.016
global irradiance measured on tilted surface exceeds the value of 7 kWh/m2 [1].
2. Performance of the system The tested photovoltaic modules were associated together to constitute a generator of a nominal 1.6 kWp stand alone photovoltaic system with battery storage. In previous studies, the performances of this SAPVS have been determined for a considered functioning period. Though not sufficiently long, this period gave important information on the behaviour of the system and allowed to make the determination of the system performances. Some values of yield and performance indices, determined for three months of operating of the SAPVS, are given in Table 1 [2]. The formulas used for the determination of these parameters have already been detailed in previous Ref. [2]. The study of the monthly evolution of the generator daily yield shows that its values have not exceeded the threshold of 10% [2]. So it was obvious that these array yield values influence the global performances of all the system. For this reason, it was projected to perform outdoor characterization testing of modules which form the photovoltaic generator of the SAPVS. Experimental electrical characteristics have been obtained for different values of solar irradiance and ambient temperature. After plotting these characteristics, a code program was implemented in order to analyse data files and fit the I– V curves. The determination of the principal parameters of modules has therefore been achieved as well as the translation of the characteristics for the standard test conditions.
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Table 1 Some values of yield and performance indices of the SAPVS Month
Z (%)
YA
YR
YF
PR (%)
November December January
8.74 9.36 10.64
4.50 4.58 4.50
5.95 5.68 4.95
3.73 3.77 3.20
65.87 69.17 69.48
3. Experimentation The photovoltaic array of the studied SAPVS is presented by Fig. 1. The experimental setup used for the outdoor measurements consists of the module to test, a capacitive electronic load and a scopemeter. The values of the solar radiation and the ambient temperature are given by a CM11 Kipp & Zonen Pyranometer and a digital thermometer, respectively. The total number of the modules under test is 32. They were facing towards the equator and mounted on a fixed structure which was tilted at an angle equalling the latitude of the site. All modules are of UDTS-50 type which utilizes single crystal silicon cells laminated to tempered glass with ethylene vinyl acetate (EVA). Each module consists of 36 solar cells wired in serial connection. The tests of modules were repeated for different values of solar radiation and ambient temperature. While undertaking a module test, the corresponding values of environmental parameters were recorded. All of this information was saved to files named according to the serial type reference of the module in question. The obtained data files have been treated to eliminate erroneous points. The plotting of the electrical I– V characteristic of the module was then carried out. Thus it can be seen in these characteristics that the current–voltage pairs are presented in the form of cloud points (see Fig. 2).
4. Numerical method and validation The determination of the tested module parameters has been quite difficult because of the above-mentioned shape of the obtained I– V curves and the distribution of current–voltage points. Then it was necessary to have recourse to numerical methods so as to result in a best graphical representation of curves and quite accurate values of the module parameters. This task required the use of a computer model having the ability to mathematically describe the I– V curve of the module. Such a model must be combined with the experimental data to make the resolution of the equations system, then the estimation of module parameters. The resolution approach was based on the modified least squares method applied to a non-linear model. The theoretical module model that is with one exponential, generally much used, is given by qðV þ I Rs Þ V þ I Rs I ¼ Iph I0 exp 1 , (1) AkT Rsh where Iph is the photocurrent generated by the module under radiation, I0 the reverse saturation current (A), Rs the series resistance (O), A the ideality factor, k the Boltzman’s constant, T the module temperature (K) and Rsh the shunt resistance (O). The expression of Eq. (1) is of implicit and non-linear type. It then requires knowledge of many parameters (Iph, Rs, A,y). In practice, these parameters should numerically be determined. As the application of the least squares method for this type of
Fig. 1. Modules of photovoltaic generator of the SAVPS.
equations is rather difficult, a program code based on a method found in the literature has been used [3,4]. This method has been validated using experimental data obtained in the case of the characterization of a group of photovoltaic modules connected together (Fig. 3). The comparison of measured and calculated values of voltage allows to see that they are approximately equal. The resultant computed error is about 0.21% and can then be fairly acceptable. This method of I– V curves fitting therefore appears to be suitable for the determination of module parameters.
5. Application of the model to I– V experimental characteristics The validation of the used numerical method has been checked for simple data and not for the case when the data are presented in the form of cloud points as those mentioned above. Running the program code several times has nevertheless allowed to reach the convergence of the equations system; then the determination of the main parameters of tested modules. The estimated errors fluctuate somewhere around 1%, a value which is relatively greater with regard to 0.21% value found with the I– V characteristics of Fig. 3. The values of the main parameters that have been found for some modules under test are presented in Table 2 (error values are also mentioned). The curves of Fig. 4 give a graphic representation of the I– V characteristics of some modules tested under different environmental conditions. These curves allowed to make comparison between the characteristics given by the numerical computation (fitted) and those obtained by outdoor measurement tests. The order of precision is not of the same magnitude as the one being obtained with the smoothing shown by Fig. 3. This can, however, be accepted owing to the fact that tests have been carried out in difficult conditions and the equipments used in the tests were lacking in some precision. It must also be mentioned that the shape of the distribution of I– V points obviously resulted in a reduction of the graphic fitting precision. A simple examination of the I– V curves presented by Fig. 4 lets to see that the maximum power points are localized on the left side of the characteristics. Consequently, this resulted in a reduction of the values of the maximum power and the fill factor as well.
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2.00
1.00
1.00
0.00 4.00
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12.00 Voltage (V)
16.00
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Fig. 2. Some modules I– V characteristics given by outdoor testing.
Table 2 Main parameters of some tested modules
12.00 model validation measured values computed values
Current (A)
8.00
Rsh (O)
Rs (O)
I0 (A)
Iph (A)
sexp (%)
X910317 X910346 X910356 X910315 X910309 X910306 X910308 X910351 X910312
429.6 500.0 349.4 499.4 500.0 500.0 443.8 423.8 500.0
0.903 0.481 0.648 1.045 0.376 1.86 1.292 1.59 1.193
0.0191 0.0523 0.0135 0.00275 0.0316 0.0031 0.0029 0.0095 0.0153
3.025 2.971 2.613 2.408 2.971 2.368 2.71 3.14 2.78
1.11 0.68 1.19 1.44 0.83 1.09 1.46 1.20 0.72
6. Comparison of fitted curves with those of Rauschenbach’s model
4.00
0.00 0.00
Module
10.00
20.00 Voltage (V)
30.00
Fig. 3. Validation of used numerical model.
40.00
The one exponential model is not the only one being proposed in the literature and which describes the I– V characteristic of a photovoltaic module. In effect, some references quote other explicit model simple to use and known as Rauschenbach’s model. It requires only three points of the I– V characteristic namely the short circuit current, the open circuit voltage and the maximum power point. Thus the current produced by the photovoltaic module is computed as a function of the voltage
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module: X891380 H=980 W/m2, Ta=31,7°C measured values computed values
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module: X910357 H=990 W/m2, Ta=23°C mesaured values computed values
0.00 0.00
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module: X910309 H=910 W/m2, Ta=31,5°C measured values computed values
16.00
20.00
0.00 0.00
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12.00
Fig. 4. Some experimental and computed I– V characteristics modules.
7. Determination of maximum power points and fill factors
as follows [5,6]: V 1 . I ¼ Isc 1 C 1 Exp C 2 V oc
(2)
The coefficients C1 and C2 are given by the following expressions: C1 ¼
Im V m 1 , Exp Isc C 2 V oc
(3)
C2 ¼
ðV m =V oc Þ 1 . Lnð1 ðIm =Isc ÞÞ
(4)
The use of the previous expressions allowed to plot the I– V characteristics of the modules. For example, the curves of Fig. 5 present the I– V characteristics that were, respectively, obtained from the application of both models described above. Comparing between the resultant characteristics leads to draw the conclusion that these models present approximately a good agreement. The noted discrepancies are principally due to the approximations supposed in the Rauschenbach’s model.
Once the I– V characteristics were fitted and the principal parameters of modules were estimated, it would be possible to undertake the determination of the different maximum power points of the modules according to the environmental conditions of experiments. The implicit and non-linear model involved some difficulties in the estimation of the maximum power values of modules. As a result, this inevitably led to the use of the numerical methods in finding of maximums’ function. For this case, the chosen method is based on the research of functions maxima and also combined with successive iterations. The found values of the maximum power of some tested photovoltaic modules are given in Table 3. The corresponding values of solar irradiance and ambient temperature are also mentioned with the reference of the module. The values of the fill factor parameter have been computed by using the formula of Eq. (5). Table 4 gives values of such a parameter determined for some tested modules. FF ¼
Pm . V oc Icc
(5)
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module: X910346 implicit model Rauschenbach's model
16.00
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Fig. 5. Comparison of fitted curves with those of Rauschenbach’s model.
8. Translation of I– V characteristics
Table 3 Maximum power values of some tested modules Module
H (W/m2)
Ta (1C)
Pmax (W)
X891380 X910360 X910357 X910342 X910365 X910305
980 1000 680 670 740 810
31.7 24.0 27.7 27.7 28.2 23.8
25.77 25.75 29.19 20.68 26.36 26.52
Table 4 Some values of fill factor Module
Fill factor
X910384 X910314 X910344 X910311 X910303 X910305
0.49 0.44 0.43 0.42 0.40 0.45
The fitted characteristics that were previously obtained seem to be not convenient for a subsequent use because they have been recorded for ambient conditions which are not necessarily identical. They must then be presented for the same ambient conditions in order to be able to make a comparison among them [7]. This task is called the translation of I– V characteristics for the standard test conditions (by abbreviation STC translation). With such a translation it would therefore be possible to compare between the I– V characteristics obtained by experiments and those mentioned by the constructor of modules. Moreover, the performances of new photovoltaic modules are generally given at standard rating conditions. The literature gives different reference conditions at which the I– V characteristics can be translated. However, the most used translation method corresponds to values of solar irradiance and cell junction temperature which are equal to values of 1000 W/m2 and 25 1C, respectively, with the reference air mass 1.5 solar spectral irradiance distribution.
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Fig. 6. I– V characteristics translated to STC.
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In this case, the electric characteristics of modules have been translated to STC using the following formulas: [8,9] ISTC ¼ Imeas
HSTC Hmeas
þ a ðT c T STC Þ,
(6)
V STC ¼ V meas b : ðT STC T C Þ Rs ðImeas ISTC Þ HSTC þ V t Ln , Hmeas
(7)
with ISTC is the current module at STC (A), VSTC the voltage module at STC (V), HSTC the reference irradiance (W/m2), Hmeas the measured irradiance (W/m2), TSTC the reference module temperature (1C), Tc the measured (or computed) module temperature (1C), a the temperature coefficient of the current, b the temperature coefficient of the voltage, Rs the series resistance, Imeas the measured current, Vmeas the measured voltage, Vt the thermal module voltage. The module temperature is computed using the well-known cell temperature model found in Refs. [10,11]. The module is then assumed to have an equivalent temperature value. The formulas used for the STC translation have been applied for different tested modules characteristics and have then allowed to new ones as it is shown by Fig. 6. In Fig. 7, translated characteristics of some tested photovoltaic modules have been brought together in order to get a further illustration about the translation. The comparison can thus be made between the performances of modules. It can therefore be noted that the translated characteristics are relatively close to each other. This could be logical because all tested modules are of the same type and the translation of course refers to the same values of irradiance and temperature. The noted differences can nevertheless be ascribed to different factors:
both coefficients a and b were supposed to have the same
In order to study the time evolution of the performances of the modules one must know their outdoor I– V characteristics being given by the constructor. The modules characteristics translated for the standard test conditions should also be known. Since the characteristic of each module was not initially known, it has then been thought proper to suppose the characteristic of a module of the same type (UDTS-50). This characteristic will thus substitute for the one of each module of the system. The main parameters of a UDTS-50 module type, found in some bibliographical reference, are presented in Table 5. The values of the fill factor computed for some tested modules are presented in Table 6. On this point, it is necessary to note once again that these values have been determined after supposing that the fill factor initially has the same value given in Table 5. In the photovoltaic technology, it is clear that the modules do not necessarily maintain their initial performances throughout the periods of exposition. Some modules degrade or even fail
Table 5 Main parameters of used module type Open circuit voltage (Voc) Short circuit current (Isc) Voltage at maximum power point (Vm) Current at maximum power point (Im) Maximum power (Pm) Fill factor (FF) Output module (Z)
Module
Fill factor (%)
Degradation factor (%)
X910312 X910307 X910315 X910023 X910356
54 50 52 49 50
25 30 27 32 30
3.00
3.00
2.00
1.00
21.6 V 3.18 A 17.5 V 2.9 A 49.4 W 0.72 11.6%
Table 6 Degradation factor of some tested modules
Current (A)
Current (A)
values for all the modules under test, temperature model used in the estimation of equivalent temperature of module, others sources of errors due to experimentation.
9. Study of performances modules degradation
STC translated I-V characteristics module: X891380 module: X910023 module: X910303 module: X910308 module: X910314 module: X910356 module: X910357 module: X910384
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module: X910307 module: X910311 module: X910313 module: X910343 module: X910344 module: X910345 module: X910363 module: X910365
5.00
10.00 15.00 Voltage (V)
Fig. 7. STC translated I– V characteristics of some photovoltaic modules.
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when operating outdoors for extended periods [12–14]. Many factors could be the causes of such degradations and decreases of the modules’ performances. In order to thoroughly analyse and monitor a module degradation process, a complete set of techniques is necessary [12–15]. In the case of this paper, it has been difficult to do that. However, a simple factor has been used so as to quantify the degradation rate. This degradation factor is computed using the following formula: FF A¼ 1 100. (8) FFinitial
Like it was mentioned above, the technical information quoted by the manufacturer was not available and especially the values of the temperature range of electrical connections. Nevertheless, many manual references of modules constructors indicated that the electrical connections can support high values of temperature. In the present study, the type of PV modules is equipped with aluminium-based connections. It has been used in many installations in this Saharan region and has proved a good endurance. However, two major problems have been encountered with electrical connections:
The degradation factor is given in percentage ratio. It must theoretically be estimated in relation to its initial value given separately for each photovoltaic module. However, such data do not generally exist, so the value mentioned above in Table 5 has been used. In addition to values of the fill factor, Table 6 gives those of the degradation factor of some tested photovoltaic modules. The values of the degradation factors presented in Table 6 allow to draw the conclusion that the modules have lost nearly the third of their performances. This inference must, however, been reviewed owing to the suppositions made in computing the factor A. On the other hand, in determining the STC performances of the modules, the values of parameters such as a, b, NOCTy have been gotten from the bibliography. Information quoted by the constructor does not generally involve values of these parameters. It can, however, be considered that these values of the degradation rate remain logical by taking into account that the tested modules were installed and exposed to solar radiation since a long time (over ten years). In this paper a simple review of the degradation of modules has been given by comparing the actual performances to the initial ones. The study of module degradation still requires periodic monitoring and measurements of the principal parameters characterizing the functioning of this module. Without appropriate means, it was difficult to exactly know the factors which led to the modules being degraded. The visual inspections on photovoltaic modules did not provide the expected identification of the degradation mechanisms. In the case of this work, however, the degradation of the modules’ performance could be due to three major factors:
may slacken off. For this reason connections must be regularly inspected and tightened if necessary; the penetration of dust in the electrical connection boxes causes bad contacts between modules and cables, so they must be periodically cleaned and inspected.
discoloration of the EVA copolymer encapsulant: visual
inspection revealed the browning of the encapsulant in some areas on the inside of the modules. This browning often happens after long term exposure to UV sunlight with module operating temperature near 50 1C [12]. A previous study has reported that the module performance degradation cannot be fully attributed to the extent of encapsulant discoloration [13]. absorption of UV light: some research work concluded that the degradation is probably caused by UV sunlight absorption at or close to the top of Si surface [13]. hot spot formation: in a PV module, hot spot can occur by any combination of cell failure, interconnection failure, partial shading and variation in the photocurrent from cell to cell (mismatch). It also results from inadequate module bypass or from a cracked cell in the module. Depending on the severity of the crack, a cracked cell potentially produces less current than the cell in the string [15]. In this work, this factor can have a major consequence on the degradation of modules.
As for the temperature effect, it has been reported, in a previous work, that the causes of the degradation are not thermally activated [13].
due to the thermal differences, the module wiring connectors
10. Conclusion This paper was presented the results obtained by achieving the outdoor measurements of many photovoltaic modules forming the array of a stand alone photovoltaic system installed in a region of the Sahara which is characterized by high level of solar irradiance. The outdoor tests have allowed to carry out the I– V characteristics of tested modules. The use of the least squares method and its application for the implicit form of the I– V characteristic model led to the determination of the most representative parameters of modules. The difficulties encountered in the fitting of experimental data were principally lied in the cloud-points distribution of the current–voltage pairs of each characteristic. The graphic smoothing which allows the determination of module parameters has successfully been made with acceptable errors. Moreover, these fitted I– V curves are nearly close to those obtained when the Rauschenbach’s model has been applied. The use of the translation equations has resulted in an estimation of the module parameters such as the open circuit voltage, the short circuit current and the maximum power point for the same environmental operating conditions (1000 W/m2, 25 1C) The study has also included the degradation of the modules’ performances. The values of degradation factors have then revealed that the modules have lost nearly the third of their initial performances. Unfortunately, the lack of suitable instruments did not contribute to go deeply into the degradation phenomenon; nevertheless, this can be attributed to different factors like UV light absorption, encapsulant discoloration and hot spot formation. References [1] Capderou M. Atlas Solaire de l’Alge´rie, Tome 2. Alger: Office des Publications Universitaires; 1985. [2] Sadok M, Mehdaoui A, Hamek H. Photovoltaic rural electrification of a village in Algeria. In: World renewable energy congress VI. Brighton, UK; 2000. p. 1925–7. [3] Braunstein A, Bany J, Appelbaum J. Determination of solar cell equation parameters from empirical data. Energy Conversion 1977;17:1–6. [4] Hartley HO. The modified Gauss–Newton method for the fitting of non-linear regression functions by least squares. Technometrics 1961;3: 269–80. [5] Hart GW. Residential photovoltaic system simulation: electrical aspects. In: Proceedings of the 16th IEEE photovoltaic specialists conference (PVSC); 1982. p. 281–8. [6] Lasnier F, Sivoththaman. Photovoltaic system sizing and performance by the comparison of demand and expected radiations. Int J Solar Energy 1990;9: 65–76.
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[7] Blaesser G. The reduced current–voltage characteristics of PV arrays and its quasi-independence of ambient conditions. In: Proceedings of the 14th European photovoltaic solar energy conference. Barcelona, Spain, 1997. p. 1520–3. [8] Leboeuf C, Ossenbrink H. PV module power output: sensitivity and uncertainty in non-STC measurements. In: Proceedings of IEEE photovoltaic specialists conference (PVSC); 1991. p. 614–9. [9] Knaup W. Power rating of photovoltaic modules from outdoor measurements. In: Proceedings of IEEE photovoltaic specialists conference (PVSC); 1991. p. 620–4. [10] Coakley JM, Kallis JM, Jones IR. Cell temperatures in terrestrial photovoltaic modules effect of design factors. In: Proceedings of the 17th IEEE photovoltaic specialists conference (PVSC); 1984. p. 496–501.
[11] Buresch M. Photovoltaic energy systems, design and installation. Mc GrawHill Book Company; 1983. [12] King DL, Quintana MA, Kratochvil JA, Ellibee DE, Hansen BR. Photovoltaic module performance and durability following long-term field exposure. Sandia National Laboratories Report may be accessed at: /http://www. sandia.gov/pvS. [13] Osterwald CR, Anderberg A, Rummel S, Ottoson L. Degradation analysis of weathered crystalline-silicon PV modules. In: Proceedings of the 29th IEEE photovoltaic specialists conference (PVSC). New Orleans, LA, USA; 2002. p. 1392–5. [14] Meyer EL, van Dyk EE. Assessing the reliability and degradation of photovoltaic module performance parameters. IEEE Trans Reliab 2004;53:83–92. [15] van Dyk EE, Meyer EL, Foster FJ, Leitch AWR. Long-term monitoring of photovoltaic devices. Renewable Energy 2002;25:183–97.