Capacitance Evolution of Photovoltaic Solar Modules ... - Science Direct

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ScienceDirect Energy Procedia 74 (2015) 1466 – 1475

CAPACITANCE EVOLUTION OF PHOTOVOLTAIC SOLAR MODULES UNDER THE INFLUENCE OF ELECTRICAL STRESS Jean ZARAKETa,b, Michel AILLERIEb and Chafic SALAMEa, d a

CEER, Faculty of Sciences II, Lebanese University, B.P 90656 Jdeidet El Mten, Lebanon b LMOPS-SUPELEC, Université de Lorraine, 2 rue Eduard Belin, 57070 Metz Cedex, France d

CNRSL, National Council for Scientific Research, Beirut, Lebanon [email protected]

Abstract The main purpose of this work was to study the effect of electric currents reverse stress on the capacitance and in general the performance of photovoltaic modules. Different levels of reverse stress current are injected into the solar cell structure and the C-V characteristic are measured in the dark and illuminated conditions, at room temperature for several common periods of time. A digital double exponential model was used to analyze the experimental measurements. The dramatic changes in capacitance characteristics are caused from the effect of a reverse current introduced for different stress levels, simulated the effect of accumulated extreme reverse currents that can occur in the solar cells and modules for different reasons. The paper contributes to research on the adverse effects of reverse currents on the capacitance and normal functioning of cells and solar modules. © Published by Elsevier Ltd. This © 2015 2015The TheAuthors. Authors. Published by Elsevier Ltd.is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD). Peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD) Keywords: Solar cell/module, Photovoltaic, capacitance–voltage characteristics , reverse stress current, double exponential model.

1. Introduction Solar energy such as photovoltaic cells energy (PV) is the most available energy source which is capable to provide most of the world’s energy needs. The conversion of sunlight into electricity using solar cells system is a worthwhile

1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4 .0/). Peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD) doi:10.1016/j.egypro.2015.07.795

Jean Zaraket et al. / Energy Procedia 74 (2015) 1466 – 1475

way of producing this alternative energy. The history of photovoltaic energy started in 1839 when AlexandreEdmond Becquerel discovered the photovoltaic effect [1, 2]. The photovoltaic system uses various materials and technologies such as crystalline Silicon (c-Si), Cadmium telluride (CdTe), Gallium arsenide (GaAs), chalcopyrite films of Copper-Indium-Selenite (CuInSe2), and other [2,3]. Now, silicon solar cells represent 40 % of the world solar cells production and yield efficiencies well higher than 25 % [4]. To simulate this capacitive behavior a Gaussian function has been employed, which is then multiplied by an asymmetric factor, replacing the exponential dependent free carrier capacitance used by others [5]. The reverse current is also referred to certain fault currents and environmental conditions in photovoltaic arrays with several strings connected in parallel to form a PV array with a direct-current output equal to the sum of the PV string outputs. The panel circuitry can be then referred to as the PV generator. Standards, such as the Australian Standard AS/NZ5033 “Installation of PV Arrays”, recommend fuses to protect both cabling and PV modules in case of the occurrence of these fault conditions. The relationship between acceptable reverse current levels and exposure durations of reverse currents on PV modules are compared with trip current of fuses and typical time delays experienced with fuse tripping [6]. Several research papers studied the effect of reverse currents as a result of electrical stresses in solar cells and modules where I-V characteristics has shown to be strongly affected by these currents [7, 8]. These studies however tackled the problem in the dark conditions. Another study contributed to the effect of heat on the performance of photovoltaic cells and modules, where the heat resulted in the occurrence of reverse currents affecting the I-V characteristics [9]. Experimental investigate to fulfill the above mentioned, extensive analysis of characteristic C-V in dark and illuminated conditions of solar cells. This work focuses on the experimental quantitative measurement of the effect of an induced reverse current on C-V dark and illuminated current characteristics due, by applying a high level of electric stress in the opposite electron flow direction of collected solar cell/ module to simulate a damaging reverse bias affecting the module over a certain current. The results and discussion offered aimed to contribute to material, performance and efficiency of photovoltaic solar cell/ module research. 2. Fundamentals General mathematical description of I-V and C-V output characteristics for a PV cell has been studied for over the past four decades. Such equivalent circuit-based models are mainly used for the MPPT (Maximum Power Point Tracking) technologies. The equivalent circuit of the general model consists of a photo current, a diode, a parallel resistor expressing a leakage current, and a series resistor describing an internal resistance to the current flow [10]. A more precise explanation of a mathematical description of a solar cell is called the double exponential model as shown in Figure 1, which is derived from the physical behavior of the solar cells based on polycrystalline silicon technology. This model is composed of a two ideal diodes, D1 and D2, a parallel shunt resistance Rsh and a series resistance Rs. It considers the calculation of both series and shunt resistances along with the junction ideality factor A and the diode diffusion I01, recombination I02 saturation currents, Cd is the diffusion capacitance and Cj is the depletion layer (barrier) capacitance. .

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Fig. 1. Idealized equivalent circuit of a double exponential model [10] The fundamental equation describing the double exponential model of a p-n junction is formulated by the following equation [11]: ‫ܫ = ܫ‬01 ൜exp ൬

ܸ െ ܴ௦ . ‫ܫ‬ ܸ െ ܴ௦ . ‫ܫ‬ ܸ െ ܴ௦ . ‫ܫ‬ ൰ െ 1ൠ + ‫ܫ‬02 ൜exp ൬ ൰ െ 1ൠ + ்ܸ ‫்ܸܣ‬ ܴ௦௛

where: I: intensity of the total cell; IO1 is the reverse saturation current corresponding to the diffusion and recombination of electrons and holes in the p- and n-side; IO2 is the reverse saturation current corresponding to generation and recombination of electrons and holes in the depletion region; V is the applied voltage, VT=KT/q is the thermal voltage, q is the elementary electron charge = 1.6 × 10í19 C, k is the Boltzmann constant =1.38 ×10-23 J/K, T is the absolute cell temperature, A is the ideality factor that can be evaluated and always found above 1. [12] The capacitance has two equations one for each type of capacitance as follows: ୯

Cd, the diffusion capacitance [13]: Cd = ୏୘ȉ),',6 Cj, the depletion layer (barrier) capacitance [13]: Cj =

፴బ፴౧ొఽ ౏ మ౒ౠ ౑ (ଵି )భ/మ ౒ౠ

ට

Where S is the diode area, ‫ܭ‬o‫ܭ‬q is the electrical permittivity of a semiconductor, q is the elementary charge, and Vj is the built-in potential. A diffusion capacitance can be expressed by the diode current ID and the time constant TF, the saturation current IS, the acceptor concentration NA, and the biasing voltage U [14]. The total capacitance of a photovoltaic cell is related to junction and to the free carrier capacitances. Junction capacitance represents the charge storage in the depletion layer. Free carrier capacitance combines the capacitances due to the minority carrier storage in the quasi-neutral regions of the junction (diffusion capacitance) and the capacitance attributed to defects and interface states (transient carrier capacitance). Typically, capacitance is dominated by junction capacitances at low voltages (~0-0.3V) increasing linearly, then diffusion capacitance (~0.30.7V) takes over so that, the total capacitance increases exponentially. Finally for voltages above 0.7V total capacitance shows a rapid decrease attributed to the interface states [15]. In addition, the determination of the capacitance-voltage properties of the cell is useful for the determination of its I-V characteristics. Depending on the type of PV cell, the AC capacitance can be used to derive such parameters as doping concentration and the built-in voltage of the junction [16].


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3. Experimental A set of commercial photovoltaic modules 6x6 (36 cells) 3.8 v and 85 mA were collected from the local consumer market. These photovoltaic modules are usually used to power small appliances such as lamps, mobile phones and small calculators. In this experiment, the photovoltaic modules were placed under stress in the dark and light in order to study their behavior under dark and illuminated conditions. To simulate the reverse current that occurs in the solar module when partially shaded, modules underwent several quantities of reverse current induced by the laboratory through the p-n junction. The reverse stress current values ranged from 10 mA up to 70 mA, adjusting a 10 min time intervals for each reverse current level. Data was collected for each procedure and presented in this paper. The procedures and method of work are illustrated in Fig. 2. C-V characteristics of a solar cell are measured and then plotted into graphs.

Fig. 2. Main diagram

During experiments, the CV curves were measured at a frequency of 1 MHz, for stress currents of 10 mA up to 70 mA, respectively for a variation of capacity voltage varying from -35V to 20V. The setting time of 10 min was given for each stressing level.

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4. Result and Discussion Capacitance Measurements The C-V characteristics in dark as function of the reverse currents induced in the cells are represented in Fig. 3. We observe that the capacitance variation is more significant at higher voltages. It can be explain as the leakage current flowing over into the module increases at this voltage levels and thus induces a reducing of the capacity. In dark, as shown in Fig.3, the threshold voltage where the capacitance values began to increase is shown to be around 10V. Then from this threshold value of the voltage, the capacitance remains constant, corresponding to the state of the cell with the current flowing in the forward direction. .

T=10min caracteristic in dark

1.20E-008

capacitance (F)

1.00E-008

8.00E-009

without stress 10mA 20mA 30mA 40mA 50mA 60mA 70mA

6.00E-009

4.00E-009

2.00E-009 -40

-30

-20

-10

0

10

20

30

V(v) reverse stress current Fig. 3. Capacitance vs V in dark

In a similar manner, the C-V characteristics under illumination as function of the reverse currents induced in the cells are represented in Fig. 4. In this case, as shown in Fig.4, the above mentioned threshold voltage decreases down to 0V. In this case, i.e. under illumination, the capacitance values at the beginning of the experiment have a relatively constant behavior up to the threshold voltage values, then increase between this threshold and a voltage equal to around 10V and finally remain constant above 10V corresponding to the state of the cell with the current flowing in the forward direction.


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2.00E-008

T=10min caracteristic in Light

1.95E-008 1.90E-008

Capacitance(F)

1.85E-008 1.80E-008 1.75E-008 1.70E-008 1.65E-008

without stress 20mA 30mA 40mA 50mA 60mA

1.60E-008 1.55E-008 1.50E-008 1.45E-008 -40

-30

-20

-10

0

10

20

30

V(v) reverse stress current

Fig. 4. Capacitance vs V in Light (87klux)

For the sake of comparison and clearing the effect of stressing currents in light and in the dark conditions of operation, a graph was constructed in Fig. 5, to show the C-V characteristics in terms of the change in the photo current Ph , without the influence of the stress currents, in light and the dark conditions. The photo current was calculated as follows: Ph (photo current) = [(without stress) Light - (without stress) Dark]. Another graph is shown in Fig. 5 which represents the change in the C-V characteristics, before and after applying a certain stress current, in the light and dark conditions. The so named L – D is referred to as follows: L - D = [(without stress - stress 10mA) Light - (without stress - stress 10mA) Dark]. It will be also wise to compare both curves in the same figure for the sake of clearing the effect of stressing currents on the C-V behaviour of photovoltaic modules.

1.40E-008

capacitane(F)

1.20E-008 1.00E-008 8.00E-009 6.00E-009

L-D ph

4.00E-009 2.00E-009 0.00E+000 -40

-30

-20

-10

0

10

voltage (v)

Fig. 5. Comparison of the (L-D) and Ph under the influence of a 10mA stressing current

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The (L-D) is more important than the photocurrent because Ph > (L-D), i.e. the reverse stress current causes the photocurrent to decrease by time. This issue raises the fact that defect are active in the Ph more than in the (L-D) as a result of stressing currents being applied inducing more defects in the materials by creating recombination centers. In a second measurement, the C-V curves were measured at a frequency of 1 MHz, for stress currents of values from 10 mA up to 30 mA, respectively and a voltage ranged between -35V and 20V. The setting time of 10 min was given for each stressing level. The variation in capacitance is more significant at higher voltages because there is a leakage current flowing over into the module, thus reducing the capacity. In both dark and light cases, shown in Fig.6 and 7respectively, the capacitance monotony slightly increases with voltage below 0V and a sharp increase of the capacitance is observed for positive voltage between 0 and 10V, and finally remains constant due to the forward current.

1.20E-007

T=10min C-V in dark

1.00E-007

1.00E-007

T=10min C-V in dark

capacitance (F)

6.00E-008

without stress 10mA 20mA 30mA

4.00E-008

2.00E-008

6.00E-008


4.00E-008

2.00E-008

0.00E+000

0.00E+000 -40

-30

-20

-10

0

10

20

30

voltage (v) reverse stress current in light (10klux)

-40

-30

-20

T=10min C-V in dark

8.00E-008

6.00E-008


4.00E-008

2.00E-008

0.00E+000

-40

-30

-20

-10

0

10

20

Voltage (V) reverse stress current in light (20klux)

1.00E-007

capacitance (F)

capacitance (F)

8.00E-008 8.00E-008

-10

0

10

20


Fig. 6. Capacitance vs V in dark condition

30

30

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1.35E-007

T=10min C-V in light (30klux)

1.50E-007


1.30E-007


1.40E-007

capacitance (F)

capacitance (F)

1.25E-007 1.20E-007 1.15E-007 1.10E-007

1.30E-007

1.20E-007

1.10E-007

1.05E-007 1.00E-007

1.00E-007


9.50E-008

9.00E-008 -40

9.00E-008 -40

-30

-20

-10

0

10

20

30

volltage (v) reverse stress current in light (10klux)

1.50E-007


capacitance (F)

1.40E-007


1.30E-007

1.20E-007

1.10E-007

1.00E-007

9.00E-008 -40

-30

-20

-10

0

10

20

30


Fig. 7. Capacitance vs V in light

-30

-20

-10

0

10

Voltage (v) reverse stress current in light (20klux)

20

30

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Once more, the comparison of both the Ph and the L – D, presented in Fig. 8, shows to be of great importance. The reverse stress current caused the photocurrent to decrease a bit, which indicates that the defect caused by the reverse current are more active in the Ph rather than in the (L-D). On the other hand, as the quantity of light increased the L-D (10klux) showed a higher value than the other two L-D (20klux ) and L-D (30klux) which seemed to be of approximately the same value. The deviation did not show a considerable value as expected. This may be explained by the fact that the defected areas in the cells are of no more of importance because of the leakage of current avoiding the defected ares.

8.00E-008

capacitance(F)

6.00E-008

ph L-D(10klux) L-D(20klux) L-D (30klux)

4.00E-008

2.00E-008

0.00E+000

-40

-35

-30

-25

-20

-15

-10

-5

0

5

voltage (V) Fig. 8. Comparison the (L-D) and Ph in light

Conclusions In this paper, considerable amount of information regarding the effect of reverse currents, due to electrical stresses, on the capacitance – voltage characteristics has been furnished. The reverse current showed to have remarkable and degrading effects on the performance of photovoltaic solar modules in the dark as well as in the illuminated conditions. The effect of reverse currents is also a degrading factor when considering power and efficiency in solar cells and modules. These results maybe applicable for solar cells, modules, arrays, or even a farm of arrays creating a photovoltaic solar generator. It is strongly recommended to take these results into consideration in future research projects, for the sake of producing and offering safe, cheaper and sound photovoltaic solar systems operating under the effect of severe conditions Funds This project has been funded by the Lebanese National Council for Scientific Research References [1] Sze, S.M., (1981): “Physics of semiconductors devices”; 2nd Edition, Wiley Interscience, Editor: John Wiley and Sons (WIE). ISBN-10 0471 0566 18. New York 11 p. 802. [2] Shockley, W., Bardeen, J. and Brattain, W., 91949, “The Theory of P-N Junctions in Semiconductors and P-N Junction Transistors” Bell System Technical Journal, Semiconductive Materials Transistor. ISSN: 0005-8580, Vol 28: 1949, p. 435.


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