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Simplified methods for evaluating the degradation of photovoltaic module and modeling considering partial shading
Measurement 138 (2019) 217–224
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Simplified methods for evaluating the degradation of photovoltaic module and modeling considering partial shading Arar Hemza a,⇑, Haouam Abdeslam a, Chenni Rachid a, Nouar Aoun b a b
MoDERNa Laboratory, Faculty of Science and Technology, Mentouri University of Constantine 1, Algeria Unité de Recherche en Energies Renouvelables en Milieu Saharien (URERMS), Adrar, Algeria
a r t i c l e
i n f o
Article history: Received 3 August 2017 Received in revised form 10 October 2018 Accepted 31 January 2019 Available online 2 February 2019 Keywords: Solar cell LabVIEW software Mathematical PV model Partial shading Visual inspection
a b s t r a c t In this paper, an accurate modeling procedure of a photovoltaic (PV) cell or module is proposed. The simulation behavior of the solar module is presented under different operation conditions, considering the effect of mismatch conditions due to the shadow patterns. The model is flexible in accurately predicting the current-voltage (I-V) and power-voltage (P-V) curves and maximum power point under partial shading of different solar module types. In this paper, a single STP080S PV module was experimentally tested for more than eight years of exposure on the roof of the University of Constantine (Mediterranean climate). For the first time, the evaluation of ageing due to the failure of the PV module in the Mediterranean climate was tested using visual inspection and I-V output. These two inspections show a decrease in the conversion efficiency of the STP080S PV module over time. Finally, the experimental and simulated I-V and P-V curves of the STP080S PV module are compared and demonstrate the effectiveness of the proposed modeling. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Electrical power is currently a global requirement. The renewable energy resources will be an increasingly important component for the production of electricity. In this context, photovoltaic (PV) systems are the most widely used resources worldwide—for example, solar electric power systems have grown gradually over the past 10–15 years [1,2]. In a photovoltaic field, the semiconductor cell’s P-N junction directly converts sunlight energy into electricity. Solar cells are connected in series in a module and in a PV panel. The modules are wired with each other in series and in parallel to achieve the necessary voltage and current to meet our needs. The output energy generated by a PV array will be significantly reduced due to the mismatch loss created by the effect of partial shading, temperature variations, and nonuniform irradiation [3]. The impact of partial shading is the main problem that researchers have been studying [4–6]. This partial shading is caused by many things (e.g., snow, sand, tree, or bird dung covering the surface of PV modules) and can lead to hot spot phenomena and consequently to permanent damage and ageing of modules [7]. Bypassing the shaded solar cells by introducing a bypass diode is an alternative solution to decreasing the dissipa⇑ Corresponding author. E-mail addresses: [email protected] (A. Hemza), [email protected] (C. Rachid). https://doi.org/10.1016/j.measurement.2019.01.098 0263-2241/Ó 2019 Elsevier Ltd. All rights reserved.
tion power [8,9]. The number and the state of bypass diodes in PV modules depend on the number of solar cells connected in series. Accurate and reliable prediction modeling of PV system output helps designers to develop efficient PV modules. Several mathematical models have been proposed to represent the behaviors of solar cells, but two are predominant: the two-diode model [10,11] and the five-parameters model [12–15]. The two-diode model is known to be more accurate at lower levels of irradiation but has a large number of electrical parameters that complicate the algorithm and increase the computation time. The five-parameters model is used by researchers because of its simplicity and low number of electrical parameters. Ishaque [16] reduced the sevenparameters model (double diode model) to only four parameters to achieve the output performance of the model based on the Newton-Raphson method. The same author [17] presented modeling and simulation current-voltage of a large PV array using a modified two-diode model with reduced computational time. He used [18] Newton-Raphson method to solve the I-V relationship equation of a PV system based on the two-diode model. A photovoltaic array simulator is presented to extract the I-V and P-V characteristics under partial shading and a mismatch condition. Jung [19] proposed a new mathematical equation from the one-diode model to reflect the present output characteristics of the PV module under a reverse bias condition; this model is used to analyze the electrical loss of photovoltaic module due to the presence of a shading con-
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dition. Bai [4] used a mechanism analysis method to describe the electrical output of a photovoltaic panel in the case of partial shading or a mismatch condition. A judgment algorithm using the fiveparameters model is also presented to study the state of bypass diode in a PV array under partial shading. Tian [20] presented a modified current-voltage equation based on the work of Ref. [13] to simulate the behavior of a PV module or array for a more complex connection of a PV module at only normal environmental conditions. This paper presents a procedural modeling of a PV system by the resolution of a system of the nonlinear equations (five equations) using the Levenberg–Marquardt (LM) algorithm. Hence, the extraction of the necessary parameters is more accurate and enhances the prediction of the I-V and P-V characteristics of a PV module for different types. The simulation is achieved using the Matlab/Simulink environment and LabVIEW software. In addition, the presence of aging due to failures of the cells in a PV module has an impact in a reduction of the energy production [21]. So, in order to validate the proposed modeling experimentally, it is fundamental to firstly investigate the state of the PV module after being exposed for a long time on the roof laboratory at the University of Constantine under the effect of Mediterranean environment. This work is organized as follows. Section 2 describes the mathematical model of the solar cell and the method to extract the reference parameters. In Section 3, the output characteristic of a PV module and array are simulated for different patterns of shadow using Matlab/Simulink. Finally, a series of experimental measurements are presented in Section 4. 2. Mathematical model of PV cell To analyze the output current (I) and voltage (V) of PV system, the solar cell is traditionally represented by the well-known five parameters model. In [22], the model is simplified into four parameters by assuming that the parallel resistance is infinite. As shown in Fig. 1, the model used in this work consists of five parameters that must be known to describe the I-V relationship of solar cell. Using the node law of Kirchhoff:
I ¼ IL Id ISh
ð1Þ
where IL is the photocurrent (A) generated under sunlight irradiance, Id is the diode current (A) through the P-N junction diode, Ish is the leakage current (A) due to the shunt resistance Rsh . By substitution of the relevant expressions of Id and Ish, the equation relating the current and the voltage delivered by an individual PV solar cell [20] is obtained as follows
ðV þ IRS Þq V þ IRS I ¼ IL I0 exp NkT C RSh
ð2Þ
of solar cell (K). Based on (2), if N S solar cells are connected in series in PV module, the nonlinear Im -V m relationship is given in (3).
ðV M þ IM NS RS Þ V M þ I M N S RS 1 IM ¼ IL I0 exp NS V t NS RSh
The output current Ip and voltage V P of PV array containing N P strings in parallel and N m modules connected in series and N C cells in series for each module, is given by:
"
ðV P þ IP NNPS RS Þ
IP ¼ NP IL NP I0 exp
NS V t
!
#
1
V P þ IP NNPS RS NS R N P Sh
ð4Þ
where N S ¼ N m Nc 2.1. Parameters extraction method To solve the nonlinear behavior of the current-voltage relationship of PV system presented in (4), at least five algebraic equations containing IL , I0 , RS , Rsh , and n parameters are needed with the measured data provided by the manufacturer in three principal points as shown in Fig. 2; the short circuit current ISC , the open circuit voltage V OC , the MPP voltage V m and current Im , which are all at Standard Reference Condition SRC conditions to rate PV modules. The SRC refers to 1000 W/m2 solar irradiance, 25 °C PV module temperatures and air mass AM 1.5. At the open circuit point: I = 0, V = V OC . Substituting these values into (4) yields:
V OC;ref NP V OC;ref 1 0 ¼ NP IL;ref NP I0;ref exp NS V t;ref NS RP;ref
ð5Þ
where V t;ref = nref K T ref /q. At the short circuit point: V = 0,I ¼ ISC . Eq. (4) can thus be represented as follows:
ISC;ref RS;ref ISC;ref RS;ref 1 ISC;ref ¼ NP IL;ref NP I0;ref exp NP V t;ref RP;ref
ð6Þ
At maximum power point under SRC; I = Im and V =V m ,
"
Im ¼ N P IL;ref NP I0;ref exp
V m;ref þ Im;ref NS NP
NS NP
V m;ref þ NNPS RS;ref NP V t;ref
!
#
1
RS;ref
RP;ref
ð7Þ
At the maximum power point, the derivative of power with respect to voltage is equal to zero. If at SRC,
@P dI ¼IþV ¼0 @V P¼Pmax;STC dV
where I0 is the diode saturation current (A); RS is the series resistance (Ohm); Rsh is the shunt/parallel resistance (Ohm); V t ¼ nKT=q is the diode thermal voltage; n is the diode ideality factor; q is the charge of the electron (1:602 1019 C); K is the Bolzmann’s constant (1:381 1023 J=K) and T is the temperature
Fig. 1. Solar cell equivalent circuit.
ð3Þ
Fig. 2. Typical I-V and P-V curves of PV module.
ð8Þ
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The Eq. (4) will be
Im;ref ¼ V m;ref
NP I exp N S V t;ref 0;ref
1þ
V m;ref þIm;ref
NS R N P S;ref
! þ NS 1
N S V t;ref
RS;ref I exp V t;ref 0;ref
V m;ref þIm;ref
NS R N P S;ref
! NP þ
NS V t;ref
RP;ref
ð9Þ
RS;ref RP;ref
The shunt resistance affects the slope of I-V characteristic at the short circuit current as shown in Fig. 2. Thus, the fifth and final equation could be determined as follows: V¼0
dI 1 ¼ dV I¼ISC RP;ref
NP I exp N S V t;ref 0;ref
ð10Þ
NS R NP S;ref N S V t;ref
ISC
0I
R 1 þ VS;ref I0;ref exp@ t;ref
!
NS R NP S;ref A NS V t;ref
SC
RP;ref R
þ RS;ref
G IL ðG; TÞ ¼ IL;ref 1 þ aIsc T T ref Gref
¼
1 RP;ref
ð11Þ
P;ref
Using Eqs. (5)–(7), (9), and (11), the five parameters of the model can be determined if the values of V OC , ISC , Im , V m at reference conditions are available. To solve the system of non linear equations mentioned above, we need an iterative method. In this work, the ‘Levenberg–Marquardt (LM)’ algorithm [23] is used in Matlab based on the nonlinear equation solver ‘fsolve’ as shown in the flowchart in the Fig. 3. Once the values of the five parameters are obtained in standard reference conditions, the model can predict the output performance of the photovoltaic cell/module/panel under SRC. Otherwise, this model could be generalized at different environmental
ð12Þ
where: IL;ref and aIsC are the photocurrent and relative temperature coefficient of the short-circuit current under SRC. The solar irradiance and cell temperature at SRC are respectively: 1000 W/m2 and T ref = 25 °C. The diode saturation current is primarily dependent on the temperature of the cell as:
NS 1 1 NP
conditions thanks to the solar irradiance and operating temperature dependence of IL , I0 , RS , Rsh and n in Eqs. (12)–(18) below. The photocurrent generated IL increases slightly with temperature because the greater diffusion lengths of the minority carriers, whereas, the solar irradiance have an impact on photocurrent as described in Eq. (12).
I0 ¼ I0;ref
T T ref
3
Eg;ref Eg exp KT ref KT 4
Eg ¼ 1:16 7:02 10
! T2 T 1108
ð13Þ
ð14Þ
where: I0;ref and Eg;ref are the diode saturation current and band gap energy at SRC. The solar cell temperature T depends on the ambient temperature and the insulation [19].
T ¼ T amb þ
NOCT 20 C G 0:8
ð15Þ
where (T amb ) is the ambient temperature and NOCT is the nominal operation cell temperature. The value of the ideality factor is 1 n 2, the author in [24] assumed that n = 1.3 for silicon. In this study n is compared to the value of nref at Standard Reference Conditions (SRC).
n ¼ nref
ð16Þ
The series resistance RS is assumed to be constant with the variation of the solar irradiation and operation temperature.
RS ¼ RS;ref
ð17Þ
The shunt resistance Rsh represents the leakage of current due mainly to the recombination of the carriers in the p-n interface of the diode. The shunt resistance (Rsh ) is proportional to solar irradiance as given in Eq. (18) [19].
Gref Rsh ¼ Rsh;ref G
ð18Þ
3. Results and discussions
Fig. 3. Calculation procedure algorithm.
In the present work, the one-diode model and its parameters have been employed to simulate the output performance of a PV module for several cell temperatures and irradiance values using Matlab/Simulink. The specification of the module—ETM572190BB and Siemens SM55 (mono crystalline), Kyocera KC200GT and BP 3series 220 W (multi crystalline), and Shell ST40 (CIS thin film)—is summarized in Table 1. The simulation results under SRC (irradiance of 1000 W/m2, temperature of 25 °C) and the reference parameters of the PV modules mentioned above are detailed in Table 2. The output performance of the model is compared with the measured data provided by the manufacturer and the results from LabVIEW software, which are recently used in the literature [25] as a tool to model a PV system. The comparison at short-circuit current, open-circuit voltage, and the maximum operating point reveals
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Table 1 Standard Test Conditions manufacturer data of modules. Parameters
ET-M572190 BB
Siemens SM55
Kyocera KC200GT
BP3 series-220 W
Shell ST40
P m (W) V OC (V) ISC (A) V m (V) Im (A)
190 45.21 5.56 36.68 5.18
55 21.7 3.45 17.40 3.15
200 32.9 8.21 26.30 7.61
220 36.6 8.20 28.91 7.6
40 23.3 2.68 16.60 2.41
Table 2 Reference and simulation parameters results for ET-M572190BB, Siemens SM55, Kyocera KC200GT and Shell ST40 modules. parameter
P m (W) V OC (V) ISC (A) V m (V) Im (A) IL;ref I0;ref RS;ref Rsh;ref n
ET-M 190 W
Siemens SM55
KyoceraKC200
Shell ST40
LabVIEW
Matlab
LabVIEW
Matlab
LabVIEW
Matlab
LabVIEW
Matlab
189.91 45.05 5.55 36.62 5.18 5.56 3.65*109 0.0065 8.48 1.156
190.08 45.17 5.55 36.53 5.20
54.81 21.67 3.45 17.36 3.15 3.45 2.7*108 0.0099 6.00 1.25
54.94 21.69 3.45 17.52 3.13
200.14 32.99 8.21 26.32 7.60 8.21 4.31*108 0.0046 7.35 1.24
199.98 32.83 8.21 26.42 7.56
40.16 23.3 2.68 16.66 2.41 2.69 6.16*109 0.034 6.72 1.014
40.12 23.3 2.68 16.66 2.41
that the prediction values of the proposed model using Matlab/ simulink and LabVIEW closely match the published values in the module’s datasheet. 4. Experimental test and results
URERMS, Adrar, Algeria (Latitude 27.88N, Longitude 0.27E). The MP-160-I-V tracer instrument from EKO was used to achieve the I-V characteristics of the PV module. The CM11 Kipp & Zonen Pyranometer and Type-T thermocouple were employed to measure the solar irradiance and module temperature. 4.1. Evaluating of STP080S PV module degradation
In this study, a series of outdoor measurements were conducted using a PV module installed on the roof of the north laboratory building at the University of Constantine for more of eight years. A STP080S PV module was selected as the experimental module (Fig. 4) to validate the simulation results obtained with the proposed model. All measurements presented in this work were carried out in the field of the renewable energy research unit,
This section seeks to identify the degradation of the performance of the STP080S PV module after a long period of exposure. This module has been installed on the roof of a building at the
Fig. 4. STP080S PV module.
Fig. 5. Solar cells discoloration.
A. Hemza et al. / Measurement 138 (2019) 217–224
221
Fig. 6. Solar cells hot spot.
Table 3 Degradation percentage of STP080S module. Parameters
Experimental data
Manufacturer data
Degradation rate (%)
P m (W) V OC (V) ISC (A) V m (V) Im (A)
69.64 19.93 5.00 15.48 4.49
80 21.6 5.00 17.2 4.65
12.95 7.73 0 10 3.44
Table 4 Reference parameters results for STP080S PV module. Parameters
Experimental data
IL;ref I0;ref RS;ref Rsh;ref n
5.074 3.58*109 0.0036 6 1.81
University of Constantine (Latitude 36.32N, Longitude 6.61E), situated in northeastern Algeria, for more than eight years. Currently, there is more than one method to characterize PV module degradation [26–28]. In this test, two methods are used: - Visual inspections; this represents the quickest method to identify degradation due to failure. - I-V characteristic measurements at STC; this was used as a diagnostic tool to verify the degradation performance of the PV module. 4.1.1. Visual inspections 4.1.1.1. Anti-reflective coating (ARC) degradation. To improve the performance of the PV module, a silicon dioxide and silicon nitride layer (ARC) was formed on all PV cells within the PV module for deferent technologies [29,30]. The anti-reflective coating maximizes the light that reaches the cells, and this increases the conversion efficiency of PV module. After a long exposure of the STP080S PV module under sunlight on the roof of the laboratory building at the University of Constantine, the discoloration mode of degradation
Fig. 7. I-V characteristic for STP080S module.
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is observed on the anti-reflective coating of the cells. As shown in Fig. 5, there are some cells in the same module that have different colors of ARC, which probably induce changes in their properties. Consequently, the conversion efficiency of the PV module will be lower than expected. 4.1.1.2. Hot spot defects. A second visual inspection defect was observed in our PV module, that is, a hot spot appeared at the edge in some cells of the STP080S PV module (Fig. 6). This defect due to the high temperature of cell could be due to various causes, including partial shadowing, inappropriate bypass diode, or mismatch conditions. The solar cells that exhibited this hotspot effect operate as charge in the photovoltaic module, which significantly reduces the conversion efficiency of the entire PV panel.
4.1.2. I-V characteristic measurements The Measuring I-V and P-V characteristics constitute the best method to determine the electric parameters of the PV module. To evaluate the degradation of the STP080S PV module after a long period of exposure, the measured I-V and P-V curves under normal operation conditions are normalized at a standard test condition (STC) using a MP-160-I-V tracer. Then, the measured data are collected and compared with experimental data provided by the manufacturer regarding some key parameters: maximum power (Pmax ), open circuit voltage (V OC ), short circuit current (ISC ), maximum current (Imax ), and maximum voltage (V max ). Table 3 illustrates the experimental results and the data provided by the manufacturer of the STP080S PV module under STC (1000 W/m, 25 °C). The comparison between the outdoor experiments and the data provided
Table 5 Partial shading scheme and environmental data. Testing scheme
Shading condition of No. 1 cell string
Shading condition of No. 2 cell string
Solar irradiance (W/m2)
Temperature (°C)
1 2
Three cells 50% shading Three cells 50% shading
No shading Three cells 75% shading
837 820
53.5 60
Fig. 8. (a) I-V curve, (b) P-V curve for STP080S module for shading condition (1).
A. Hemza et al. / Measurement 138 (2019) 217–224
by the manufacturer revealed that the electric parameters (Pmax , V max , Imax , ISC , V OC ) of the STP080S PV module are degraded. The maximum power output is decreased from 80 W to 69.64 W (1.61%/year). A possible reason for this could be the ageing PV module and the discoloration of the anti-reflective coating of the PV module. Additionally, the hotspot defect reduces the active area of the PV cell, and the PV cell will be unable to produce its rated power, which reduces the conversion efficiency of the entire PV module. 4.2. Normal operation conditions Table 4 presents the reference parameters of the STP080S PV module with its degradation defects. Fig. 7 shows the I-V curve for a single STP080S PV module with a temperature of 55 °C and irradiance of 873 W/m2. The output performance calculated from the proposed model in Matlab/simulink was evaluated against the measured data. The model has a good prediction of maximum power point (MPP) under general conditions compared to the values of the manufacturer, which prove that the extracted reference parameters with the used mentioned method are valid.
223
4.3. Effect of partial shading on PV module To test the effectiveness of the modeling to predict the behavior of the PV module in the case of partial shading, the mono crystalline STP080S module has been selected as a tested module to study its I-V and P-V characteristics. The manufacturer’s datasheet provides only the performance of the module under similar irradiance and temperature values on entire solar cells in the module. Therefore, we studied the effect of the bypass diode in the circuit. Table 5 presents various schemes of partially shaded conditions used to study the output performance of the model. The STP080S module contains two bypass diodes for each of the two solar cell strings, in which 18 cells are serially connected. Figs. 7 and 8 show the I-V and P-V characteristic curves for the tested PV module under two partial shading schemes. The shaded cells generate less photocurrent than the other non-shaded cells; they behave like a charge, which significantly reduces the generated current of the module. However, the cell string containing the shaded cells is bypassed through the bypass diode, which explains the two peaks in the P-V characteristics. The simulation results are compared with the experimental data. The comparison reveals a good consis-
Fig. 9. (a) I-V curve, (b) P-V curve for STP080S module for shading condition (2).
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tency at the location of the peaks in the P-V characteristic shape. Nevertheless, there are some disagreements, especially at the location of the peaks in the P-V curve, which is probably due to the employed temperature sensor and the used solar cell model (See Fig. 9). 5. Conclusion In this paper, an accurate procedure modeling of solar module under partial shading conditions is presented. Based on equivalent circuit of the five parameters model, an efficient iterative method based on Levenberg-Marquardt (LM) algorithm is used to extract the five references parameters. Firstly, the investigation of the ageing due to the defect failure of STP080S PV module proven that the degradation affects the rated power of PV module from 80 W to 69.64 W (1.61%/year). Secondly, the five parameters’ of the tested PV module was extracted according to its new maximum power after long time (more than eight years) of exposure. Finally, the model was validated by comparing the I-V and P-V characteristics of STP080S PV module with the measured data acquired in given partial shading conditions. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.measurement.2019.01.098. References [1] Rakesh Pal, Dr. V.K. Sethi, Anurag Gour., 2014. Assessing the Performance of 100 kW Solar PV Power-plants Through I-V Characterization & Validation of Tilted Irradiance Calculation Compared to an Hourly Model. (2014, Jan) 2322082. [2] E.F. Camacho, M. Berenguel, A.J. Gallego, Control of thermal solar energy plants, J. Process Control 24 (2014) 332–340. [3] Y. Kouhlane, D. Bouhafs, N. Khelifati, S. Belhousse, H. Menari, A. Guenda, A. Khelfane, Effect of rapid thermal processing on light-induced degradation of carrier lifetime in czochralski p-type silicon bare wafers, J. Electron. Mater. 45 (2016) 5621–5625. [4] J. Bai, Y. Cao, Y. Hao, Z. Zhang, S. Liu, F. Cao, Characteristic output of PV systems under partial shading or mismatch conditions, Sol. Energy 112 (2015) 41–54. [5] S.R. Potnuru, D. Pattabiraman, S.I. Ganesan, N. Chilakapati, Positioning of PV panels for reduction in line losses and mismatch losses in PV array, Renew. Energy 78 (2015) 264–275. [6] H. Patel, V. Agarwal, MATLAB-based modeling to study the effects of partial shading on PV array characteristics, IEEE Trans. Energy Convers. 23 (2008) 302–310. [7] D. Rossi, M. Omaña, D. Giaffreda, C. Metra, Modeling and detection of hotspot in shaded photovoltaic cells, IEEE Trans. Very Large Scale Integr. VLSI Syst. 23 (2015) 1031–1039. [8] S. Silvestre, A. Boronat, A. Chouder, Study of bypass diodes configuration on PV modules, Appl. Energy 86 (2009) 1632–1640.
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Measurement journal homepage: www.elsevier.com/locate/measurement
Simplified methods for evaluating the degradation of photovoltaic module and modeling considering partial shading Arar Hemza a,⇑, Haouam Abdeslam a, Chenni Rachid a, Nouar Aoun b a b
MoDERNa Laboratory, Faculty of Science and Technology, Mentouri University of Constantine 1, Algeria Unité de Recherche en Energies Renouvelables en Milieu Saharien (URERMS), Adrar, Algeria
a r t i c l e
i n f o
Article history: Received 3 August 2017 Received in revised form 10 October 2018 Accepted 31 January 2019 Available online 2 February 2019 Keywords: Solar cell LabVIEW software Mathematical PV model Partial shading Visual inspection
a b s t r a c t In this paper, an accurate modeling procedure of a photovoltaic (PV) cell or module is proposed. The simulation behavior of the solar module is presented under different operation conditions, considering the effect of mismatch conditions due to the shadow patterns. The model is flexible in accurately predicting the current-voltage (I-V) and power-voltage (P-V) curves and maximum power point under partial shading of different solar module types. In this paper, a single STP080S PV module was experimentally tested for more than eight years of exposure on the roof of the University of Constantine (Mediterranean climate). For the first time, the evaluation of ageing due to the failure of the PV module in the Mediterranean climate was tested using visual inspection and I-V output. These two inspections show a decrease in the conversion efficiency of the STP080S PV module over time. Finally, the experimental and simulated I-V and P-V curves of the STP080S PV module are compared and demonstrate the effectiveness of the proposed modeling. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Electrical power is currently a global requirement. The renewable energy resources will be an increasingly important component for the production of electricity. In this context, photovoltaic (PV) systems are the most widely used resources worldwide—for example, solar electric power systems have grown gradually over the past 10–15 years [1,2]. In a photovoltaic field, the semiconductor cell’s P-N junction directly converts sunlight energy into electricity. Solar cells are connected in series in a module and in a PV panel. The modules are wired with each other in series and in parallel to achieve the necessary voltage and current to meet our needs. The output energy generated by a PV array will be significantly reduced due to the mismatch loss created by the effect of partial shading, temperature variations, and nonuniform irradiation [3]. The impact of partial shading is the main problem that researchers have been studying [4–6]. This partial shading is caused by many things (e.g., snow, sand, tree, or bird dung covering the surface of PV modules) and can lead to hot spot phenomena and consequently to permanent damage and ageing of modules [7]. Bypassing the shaded solar cells by introducing a bypass diode is an alternative solution to decreasing the dissipa⇑ Corresponding author. E-mail addresses: [email protected] (A. Hemza), [email protected] (C. Rachid). https://doi.org/10.1016/j.measurement.2019.01.098 0263-2241/Ó 2019 Elsevier Ltd. All rights reserved.
tion power [8,9]. The number and the state of bypass diodes in PV modules depend on the number of solar cells connected in series. Accurate and reliable prediction modeling of PV system output helps designers to develop efficient PV modules. Several mathematical models have been proposed to represent the behaviors of solar cells, but two are predominant: the two-diode model [10,11] and the five-parameters model [12–15]. The two-diode model is known to be more accurate at lower levels of irradiation but has a large number of electrical parameters that complicate the algorithm and increase the computation time. The five-parameters model is used by researchers because of its simplicity and low number of electrical parameters. Ishaque [16] reduced the sevenparameters model (double diode model) to only four parameters to achieve the output performance of the model based on the Newton-Raphson method. The same author [17] presented modeling and simulation current-voltage of a large PV array using a modified two-diode model with reduced computational time. He used [18] Newton-Raphson method to solve the I-V relationship equation of a PV system based on the two-diode model. A photovoltaic array simulator is presented to extract the I-V and P-V characteristics under partial shading and a mismatch condition. Jung [19] proposed a new mathematical equation from the one-diode model to reflect the present output characteristics of the PV module under a reverse bias condition; this model is used to analyze the electrical loss of photovoltaic module due to the presence of a shading con-
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dition. Bai [4] used a mechanism analysis method to describe the electrical output of a photovoltaic panel in the case of partial shading or a mismatch condition. A judgment algorithm using the fiveparameters model is also presented to study the state of bypass diode in a PV array under partial shading. Tian [20] presented a modified current-voltage equation based on the work of Ref. [13] to simulate the behavior of a PV module or array for a more complex connection of a PV module at only normal environmental conditions. This paper presents a procedural modeling of a PV system by the resolution of a system of the nonlinear equations (five equations) using the Levenberg–Marquardt (LM) algorithm. Hence, the extraction of the necessary parameters is more accurate and enhances the prediction of the I-V and P-V characteristics of a PV module for different types. The simulation is achieved using the Matlab/Simulink environment and LabVIEW software. In addition, the presence of aging due to failures of the cells in a PV module has an impact in a reduction of the energy production [21]. So, in order to validate the proposed modeling experimentally, it is fundamental to firstly investigate the state of the PV module after being exposed for a long time on the roof laboratory at the University of Constantine under the effect of Mediterranean environment. This work is organized as follows. Section 2 describes the mathematical model of the solar cell and the method to extract the reference parameters. In Section 3, the output characteristic of a PV module and array are simulated for different patterns of shadow using Matlab/Simulink. Finally, a series of experimental measurements are presented in Section 4. 2. Mathematical model of PV cell To analyze the output current (I) and voltage (V) of PV system, the solar cell is traditionally represented by the well-known five parameters model. In [22], the model is simplified into four parameters by assuming that the parallel resistance is infinite. As shown in Fig. 1, the model used in this work consists of five parameters that must be known to describe the I-V relationship of solar cell. Using the node law of Kirchhoff:
I ¼ IL Id ISh
ð1Þ
where IL is the photocurrent (A) generated under sunlight irradiance, Id is the diode current (A) through the P-N junction diode, Ish is the leakage current (A) due to the shunt resistance Rsh . By substitution of the relevant expressions of Id and Ish, the equation relating the current and the voltage delivered by an individual PV solar cell [20] is obtained as follows
ðV þ IRS Þq V þ IRS I ¼ IL I0 exp NkT C RSh
ð2Þ
of solar cell (K). Based on (2), if N S solar cells are connected in series in PV module, the nonlinear Im -V m relationship is given in (3).
ðV M þ IM NS RS Þ V M þ I M N S RS 1 IM ¼ IL I0 exp NS V t NS RSh
The output current Ip and voltage V P of PV array containing N P strings in parallel and N m modules connected in series and N C cells in series for each module, is given by:
"
ðV P þ IP NNPS RS Þ
IP ¼ NP IL NP I0 exp
NS V t
!
#
1
V P þ IP NNPS RS NS R N P Sh
ð4Þ
where N S ¼ N m Nc 2.1. Parameters extraction method To solve the nonlinear behavior of the current-voltage relationship of PV system presented in (4), at least five algebraic equations containing IL , I0 , RS , Rsh , and n parameters are needed with the measured data provided by the manufacturer in three principal points as shown in Fig. 2; the short circuit current ISC , the open circuit voltage V OC , the MPP voltage V m and current Im , which are all at Standard Reference Condition SRC conditions to rate PV modules. The SRC refers to 1000 W/m2 solar irradiance, 25 °C PV module temperatures and air mass AM 1.5. At the open circuit point: I = 0, V = V OC . Substituting these values into (4) yields:
V OC;ref NP V OC;ref 1 0 ¼ NP IL;ref NP I0;ref exp NS V t;ref NS RP;ref
ð5Þ
where V t;ref = nref K T ref /q. At the short circuit point: V = 0,I ¼ ISC . Eq. (4) can thus be represented as follows:
ISC;ref RS;ref ISC;ref RS;ref 1 ISC;ref ¼ NP IL;ref NP I0;ref exp NP V t;ref RP;ref
ð6Þ
At maximum power point under SRC; I = Im and V =V m ,
"
Im ¼ N P IL;ref NP I0;ref exp
V m;ref þ Im;ref NS NP
NS NP
V m;ref þ NNPS RS;ref NP V t;ref
!
#
1
RS;ref
RP;ref
ð7Þ
At the maximum power point, the derivative of power with respect to voltage is equal to zero. If at SRC,
@P dI ¼IþV ¼0 @V P¼Pmax;STC dV
where I0 is the diode saturation current (A); RS is the series resistance (Ohm); Rsh is the shunt/parallel resistance (Ohm); V t ¼ nKT=q is the diode thermal voltage; n is the diode ideality factor; q is the charge of the electron (1:602 1019 C); K is the Bolzmann’s constant (1:381 1023 J=K) and T is the temperature
Fig. 1. Solar cell equivalent circuit.
ð3Þ
Fig. 2. Typical I-V and P-V curves of PV module.
ð8Þ
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The Eq. (4) will be
Im;ref ¼ V m;ref
NP I exp N S V t;ref 0;ref
1þ
V m;ref þIm;ref
NS R N P S;ref
! þ NS 1
N S V t;ref
RS;ref I exp V t;ref 0;ref
V m;ref þIm;ref
NS R N P S;ref
! NP þ
NS V t;ref
RP;ref
ð9Þ
RS;ref RP;ref
The shunt resistance affects the slope of I-V characteristic at the short circuit current as shown in Fig. 2. Thus, the fifth and final equation could be determined as follows: V¼0
dI 1 ¼ dV I¼ISC RP;ref
NP I exp N S V t;ref 0;ref
ð10Þ
NS R NP S;ref N S V t;ref
ISC
0I
R 1 þ VS;ref I0;ref exp@ t;ref
!
NS R NP S;ref A NS V t;ref
SC
RP;ref R
þ RS;ref
G IL ðG; TÞ ¼ IL;ref 1 þ aIsc T T ref Gref
¼
1 RP;ref
ð11Þ
P;ref
Using Eqs. (5)–(7), (9), and (11), the five parameters of the model can be determined if the values of V OC , ISC , Im , V m at reference conditions are available. To solve the system of non linear equations mentioned above, we need an iterative method. In this work, the ‘Levenberg–Marquardt (LM)’ algorithm [23] is used in Matlab based on the nonlinear equation solver ‘fsolve’ as shown in the flowchart in the Fig. 3. Once the values of the five parameters are obtained in standard reference conditions, the model can predict the output performance of the photovoltaic cell/module/panel under SRC. Otherwise, this model could be generalized at different environmental
ð12Þ
where: IL;ref and aIsC are the photocurrent and relative temperature coefficient of the short-circuit current under SRC. The solar irradiance and cell temperature at SRC are respectively: 1000 W/m2 and T ref = 25 °C. The diode saturation current is primarily dependent on the temperature of the cell as:
NS 1 1 NP
conditions thanks to the solar irradiance and operating temperature dependence of IL , I0 , RS , Rsh and n in Eqs. (12)–(18) below. The photocurrent generated IL increases slightly with temperature because the greater diffusion lengths of the minority carriers, whereas, the solar irradiance have an impact on photocurrent as described in Eq. (12).
I0 ¼ I0;ref
T T ref
3
Eg;ref Eg exp KT ref KT 4
Eg ¼ 1:16 7:02 10
! T2 T 1108
ð13Þ
ð14Þ
where: I0;ref and Eg;ref are the diode saturation current and band gap energy at SRC. The solar cell temperature T depends on the ambient temperature and the insulation [19].
T ¼ T amb þ
NOCT 20 C G 0:8
ð15Þ
where (T amb ) is the ambient temperature and NOCT is the nominal operation cell temperature. The value of the ideality factor is 1 n 2, the author in [24] assumed that n = 1.3 for silicon. In this study n is compared to the value of nref at Standard Reference Conditions (SRC).
n ¼ nref
ð16Þ
The series resistance RS is assumed to be constant with the variation of the solar irradiation and operation temperature.
RS ¼ RS;ref
ð17Þ
The shunt resistance Rsh represents the leakage of current due mainly to the recombination of the carriers in the p-n interface of the diode. The shunt resistance (Rsh ) is proportional to solar irradiance as given in Eq. (18) [19].
Gref Rsh ¼ Rsh;ref G
ð18Þ
3. Results and discussions
Fig. 3. Calculation procedure algorithm.
In the present work, the one-diode model and its parameters have been employed to simulate the output performance of a PV module for several cell temperatures and irradiance values using Matlab/Simulink. The specification of the module—ETM572190BB and Siemens SM55 (mono crystalline), Kyocera KC200GT and BP 3series 220 W (multi crystalline), and Shell ST40 (CIS thin film)—is summarized in Table 1. The simulation results under SRC (irradiance of 1000 W/m2, temperature of 25 °C) and the reference parameters of the PV modules mentioned above are detailed in Table 2. The output performance of the model is compared with the measured data provided by the manufacturer and the results from LabVIEW software, which are recently used in the literature [25] as a tool to model a PV system. The comparison at short-circuit current, open-circuit voltage, and the maximum operating point reveals
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Table 1 Standard Test Conditions manufacturer data of modules. Parameters
ET-M572190 BB
Siemens SM55
Kyocera KC200GT
BP3 series-220 W
Shell ST40
P m (W) V OC (V) ISC (A) V m (V) Im (A)
190 45.21 5.56 36.68 5.18
55 21.7 3.45 17.40 3.15
200 32.9 8.21 26.30 7.61
220 36.6 8.20 28.91 7.6
40 23.3 2.68 16.60 2.41
Table 2 Reference and simulation parameters results for ET-M572190BB, Siemens SM55, Kyocera KC200GT and Shell ST40 modules. parameter
P m (W) V OC (V) ISC (A) V m (V) Im (A) IL;ref I0;ref RS;ref Rsh;ref n
ET-M 190 W
Siemens SM55
KyoceraKC200
Shell ST40
LabVIEW
Matlab
LabVIEW
Matlab
LabVIEW
Matlab
LabVIEW
Matlab
189.91 45.05 5.55 36.62 5.18 5.56 3.65*109 0.0065 8.48 1.156
190.08 45.17 5.55 36.53 5.20
54.81 21.67 3.45 17.36 3.15 3.45 2.7*108 0.0099 6.00 1.25
54.94 21.69 3.45 17.52 3.13
200.14 32.99 8.21 26.32 7.60 8.21 4.31*108 0.0046 7.35 1.24
199.98 32.83 8.21 26.42 7.56
40.16 23.3 2.68 16.66 2.41 2.69 6.16*109 0.034 6.72 1.014
40.12 23.3 2.68 16.66 2.41
that the prediction values of the proposed model using Matlab/ simulink and LabVIEW closely match the published values in the module’s datasheet. 4. Experimental test and results
URERMS, Adrar, Algeria (Latitude 27.88N, Longitude 0.27E). The MP-160-I-V tracer instrument from EKO was used to achieve the I-V characteristics of the PV module. The CM11 Kipp & Zonen Pyranometer and Type-T thermocouple were employed to measure the solar irradiance and module temperature. 4.1. Evaluating of STP080S PV module degradation
In this study, a series of outdoor measurements were conducted using a PV module installed on the roof of the north laboratory building at the University of Constantine for more of eight years. A STP080S PV module was selected as the experimental module (Fig. 4) to validate the simulation results obtained with the proposed model. All measurements presented in this work were carried out in the field of the renewable energy research unit,
This section seeks to identify the degradation of the performance of the STP080S PV module after a long period of exposure. This module has been installed on the roof of a building at the
Fig. 4. STP080S PV module.
Fig. 5. Solar cells discoloration.
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Fig. 6. Solar cells hot spot.
Table 3 Degradation percentage of STP080S module. Parameters
Experimental data
Manufacturer data
Degradation rate (%)
P m (W) V OC (V) ISC (A) V m (V) Im (A)
69.64 19.93 5.00 15.48 4.49
80 21.6 5.00 17.2 4.65
12.95 7.73 0 10 3.44
Table 4 Reference parameters results for STP080S PV module. Parameters
Experimental data
IL;ref I0;ref RS;ref Rsh;ref n
5.074 3.58*109 0.0036 6 1.81
University of Constantine (Latitude 36.32N, Longitude 6.61E), situated in northeastern Algeria, for more than eight years. Currently, there is more than one method to characterize PV module degradation [26–28]. In this test, two methods are used: - Visual inspections; this represents the quickest method to identify degradation due to failure. - I-V characteristic measurements at STC; this was used as a diagnostic tool to verify the degradation performance of the PV module. 4.1.1. Visual inspections 4.1.1.1. Anti-reflective coating (ARC) degradation. To improve the performance of the PV module, a silicon dioxide and silicon nitride layer (ARC) was formed on all PV cells within the PV module for deferent technologies [29,30]. The anti-reflective coating maximizes the light that reaches the cells, and this increases the conversion efficiency of PV module. After a long exposure of the STP080S PV module under sunlight on the roof of the laboratory building at the University of Constantine, the discoloration mode of degradation
Fig. 7. I-V characteristic for STP080S module.
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is observed on the anti-reflective coating of the cells. As shown in Fig. 5, there are some cells in the same module that have different colors of ARC, which probably induce changes in their properties. Consequently, the conversion efficiency of the PV module will be lower than expected. 4.1.1.2. Hot spot defects. A second visual inspection defect was observed in our PV module, that is, a hot spot appeared at the edge in some cells of the STP080S PV module (Fig. 6). This defect due to the high temperature of cell could be due to various causes, including partial shadowing, inappropriate bypass diode, or mismatch conditions. The solar cells that exhibited this hotspot effect operate as charge in the photovoltaic module, which significantly reduces the conversion efficiency of the entire PV panel.
4.1.2. I-V characteristic measurements The Measuring I-V and P-V characteristics constitute the best method to determine the electric parameters of the PV module. To evaluate the degradation of the STP080S PV module after a long period of exposure, the measured I-V and P-V curves under normal operation conditions are normalized at a standard test condition (STC) using a MP-160-I-V tracer. Then, the measured data are collected and compared with experimental data provided by the manufacturer regarding some key parameters: maximum power (Pmax ), open circuit voltage (V OC ), short circuit current (ISC ), maximum current (Imax ), and maximum voltage (V max ). Table 3 illustrates the experimental results and the data provided by the manufacturer of the STP080S PV module under STC (1000 W/m, 25 °C). The comparison between the outdoor experiments and the data provided
Table 5 Partial shading scheme and environmental data. Testing scheme
Shading condition of No. 1 cell string
Shading condition of No. 2 cell string
Solar irradiance (W/m2)
Temperature (°C)
1 2
Three cells 50% shading Three cells 50% shading
No shading Three cells 75% shading
837 820
53.5 60
Fig. 8. (a) I-V curve, (b) P-V curve for STP080S module for shading condition (1).
A. Hemza et al. / Measurement 138 (2019) 217–224
by the manufacturer revealed that the electric parameters (Pmax , V max , Imax , ISC , V OC ) of the STP080S PV module are degraded. The maximum power output is decreased from 80 W to 69.64 W (1.61%/year). A possible reason for this could be the ageing PV module and the discoloration of the anti-reflective coating of the PV module. Additionally, the hotspot defect reduces the active area of the PV cell, and the PV cell will be unable to produce its rated power, which reduces the conversion efficiency of the entire PV module. 4.2. Normal operation conditions Table 4 presents the reference parameters of the STP080S PV module with its degradation defects. Fig. 7 shows the I-V curve for a single STP080S PV module with a temperature of 55 °C and irradiance of 873 W/m2. The output performance calculated from the proposed model in Matlab/simulink was evaluated against the measured data. The model has a good prediction of maximum power point (MPP) under general conditions compared to the values of the manufacturer, which prove that the extracted reference parameters with the used mentioned method are valid.
223
4.3. Effect of partial shading on PV module To test the effectiveness of the modeling to predict the behavior of the PV module in the case of partial shading, the mono crystalline STP080S module has been selected as a tested module to study its I-V and P-V characteristics. The manufacturer’s datasheet provides only the performance of the module under similar irradiance and temperature values on entire solar cells in the module. Therefore, we studied the effect of the bypass diode in the circuit. Table 5 presents various schemes of partially shaded conditions used to study the output performance of the model. The STP080S module contains two bypass diodes for each of the two solar cell strings, in which 18 cells are serially connected. Figs. 7 and 8 show the I-V and P-V characteristic curves for the tested PV module under two partial shading schemes. The shaded cells generate less photocurrent than the other non-shaded cells; they behave like a charge, which significantly reduces the generated current of the module. However, the cell string containing the shaded cells is bypassed through the bypass diode, which explains the two peaks in the P-V characteristics. The simulation results are compared with the experimental data. The comparison reveals a good consis-
Fig. 9. (a) I-V curve, (b) P-V curve for STP080S module for shading condition (2).
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tency at the location of the peaks in the P-V characteristic shape. Nevertheless, there are some disagreements, especially at the location of the peaks in the P-V curve, which is probably due to the employed temperature sensor and the used solar cell model (See Fig. 9). 5. Conclusion In this paper, an accurate procedure modeling of solar module under partial shading conditions is presented. Based on equivalent circuit of the five parameters model, an efficient iterative method based on Levenberg-Marquardt (LM) algorithm is used to extract the five references parameters. Firstly, the investigation of the ageing due to the defect failure of STP080S PV module proven that the degradation affects the rated power of PV module from 80 W to 69.64 W (1.61%/year). Secondly, the five parameters’ of the tested PV module was extracted according to its new maximum power after long time (more than eight years) of exposure. Finally, the model was validated by comparing the I-V and P-V characteristics of STP080S PV module with the measured data acquired in given partial shading conditions. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.measurement.2019.01.098. References [1] Rakesh Pal, Dr. V.K. Sethi, Anurag Gour., 2014. Assessing the Performance of 100 kW Solar PV Power-plants Through I-V Characterization & Validation of Tilted Irradiance Calculation Compared to an Hourly Model. (2014, Jan) 2322082. [2] E.F. Camacho, M. Berenguel, A.J. Gallego, Control of thermal solar energy plants, J. Process Control 24 (2014) 332–340. [3] Y. Kouhlane, D. Bouhafs, N. Khelifati, S. Belhousse, H. Menari, A. Guenda, A. Khelfane, Effect of rapid thermal processing on light-induced degradation of carrier lifetime in czochralski p-type silicon bare wafers, J. Electron. Mater. 45 (2016) 5621–5625. [4] J. Bai, Y. Cao, Y. Hao, Z. Zhang, S. Liu, F. Cao, Characteristic output of PV systems under partial shading or mismatch conditions, Sol. Energy 112 (2015) 41–54. [5] S.R. Potnuru, D. Pattabiraman, S.I. Ganesan, N. Chilakapati, Positioning of PV panels for reduction in line losses and mismatch losses in PV array, Renew. Energy 78 (2015) 264–275. [6] H. Patel, V. Agarwal, MATLAB-based modeling to study the effects of partial shading on PV array characteristics, IEEE Trans. Energy Convers. 23 (2008) 302–310. [7] D. Rossi, M. Omaña, D. Giaffreda, C. Metra, Modeling and detection of hotspot in shaded photovoltaic cells, IEEE Trans. Very Large Scale Integr. VLSI Syst. 23 (2015) 1031–1039. [8] S. Silvestre, A. Boronat, A. Chouder, Study of bypass diodes configuration on PV modules, Appl. Energy 86 (2009) 1632–1640.
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