# Series Connected Photovoltaic Cells—Modelling and Analysis

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{m}), voltage (V

_{m}) at maximum-power point, open-circuit voltage (V

_{oc}), short-circuit current (I

_{sc}), fill factor (FF), and efficiency (η). Figure 1 shows the current/voltage (I/V) characteristics of a PV module whose electrical parameters are depicted on the same figure.

## 2. Modified Standard Equivalent-Circuit (MSEC)

_{p}) reflects the leakage occurrence through the PN-junction of the PV cell [24], whereas R

_{s}represents the electrical losses of the cell’s surface and bulk. The current/voltage (I/V) characteristics can then be written as given in Equation (1) [25,26,27]:

_{sx}shown in Figure 3a is not linear since it depends on the current, as will be shown in the upcoming systems of equations.

_{phx}= I

_{ph}, we find the voltage across the PV cell as:

_{s}is temperature dependent and is expressed as:

_{ph}is also temperature- and illumination-dependent and can be expressed as:

_{0}= 25 °C, AM = 1.5, and radiation G

_{0}= 1000 W/m

^{2}. The band gap E

_{g}also decreases as the temperature increases [30,31] as follows:

## 3. Discussion and Results

^{2}.

^{2}. Figure 6 shows the comparison between the calculated I/V characteristics of a PV module using the SEC model (solid line) and the MSEC model (dashed line). Our modified model very well fit the measurement of the I/V characteristics of the tested PV module.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Babaa, S.; Armstrong, M.; Pickert, V. Overview of Maximum Power Point Tracking Control Methods for PV Systems. J. Power Energy Eng.
**2014**, 2, 59–72. [Google Scholar] [CrossRef] - Khalifa, M.; Saied, K.; SBitro, M.; Anwar, M.; Nizam, M. PV Power System Using Maximum Power Point Tracking (Increment Conductance Algorithm). Int. J. Innov. Res. Sci. Eng. Technol.
**2014**, 3, 5. [Google Scholar] - Vergura, S. A Complete and Simplified Datasheet-Based Model of PV Cells in Variable Environmental Conditions for Circuit Simulation. Energies
**2016**, 9, 326. [Google Scholar] [CrossRef] - Yatimi, H.; Aroudam, E. Mathematical Modeling and Simulation of Photovoltaic Power Source using Matlab/Simulink. Int. J. Innov. Appl. Stud.
**2016**, 16, 322–330. [Google Scholar] - Xiao, W.B.; Hu, F.Y.; Zhang, H.M.; Wu, H.M. Experimental Investigation of the Effects of Partial Shading on Photovoltaic Cells’ Electrical Parameters. Int. J. Photoenergy
**2015**, 2015. [Google Scholar] [CrossRef] - Mazouchi, M.; Jia, J.; Huo, Y. Analysis of luminescent coupling effects in n series-connected multijunction solar cells. Phys. Status Solidi A
**2016**, 213, 941–946. [Google Scholar] [CrossRef] - Bauer, A.; Hanisch, J.; Ahlswede, E. An Effective Single Solar Cell Equivalent Circuit Model for Two or More Solar Cells Connected in Series. IEEE J. Photovolt.
**2014**, 4, 340–347. [Google Scholar] [CrossRef] - Kumar, A.; Parimi, A.; Rao, K. A Comparative Study of Model Based Design of PV cell in MATLAB/Simulink/Simscape. Int. J. Adv. Trends Comput. Sci. Eng.
**2014**, 3, 37–42. [Google Scholar] - Sinha, D.; Das, A.; Dhak, D.; Sadhu, P. Equivalent circuit configuration for solar PV cell. In Proceedings of the 1st International Conference on Non-Conventional Energy, Kalyani, India, 16–17 January 2014.
- Bay, L.; West, K. An equivalent circuit approach to the modelling of the dynamics of dye sensitized solar cells. Sol. Energy Mater. Sol. Cells
**2005**, 87, 613–628. [Google Scholar] [CrossRef] - Castañer, L.; Silvestre, S. Modeling of Photovoltaic Cell Using Free Software Application for Training and Design Circuit in Photovoltaic Solar Energy; John Wiley and Sons Ltd.: Chichester, UK, 2002. [Google Scholar]
- Altas, I.H.; Sharaf, A.M.I. Array Simulation Model for Matlab-Simulink GUI Environment. In Proceedings of the European Photovoltaic Solar Energy Conference, Glasgow, UK, May 2000.
- Gray, J.L. The Physics of the Solar Cell. In Handbook of Photovoltaic Science and Engineering; Luque, A., Hegedus, S., Eds.; John Wiley and Sons: Chichester, UK, 2011. [Google Scholar]
- Romero, B.; del Pozo, G.; Arredondo, B. Exact analytical solution of a two diode circuit model for organic solar cells showing S-shape using Lambert W-functions. Sol. Energy
**2012**, 86, 3026–3029. [Google Scholar] [CrossRef] - Del Pozo, G.; Romero, B.; Arredondo, B. Evolution with annealing of solar cell parameters modelling the S-shape of the current–voltage characteristic. Sol. Energy Mater. Sol. Cells
**2012**, 104, 81–86. [Google Scholar] [CrossRef] - Ding, K.; Zhang, J.; Bian, X.; Xu, J. A simplified model for photovoltaic modules based on improved translation equations. Sol. Energy
**2014**, 101, 40–52. [Google Scholar] [CrossRef] - Anku, N.; Adu-Gyamfi, D.; Kankam, A.; Takyi, A.; Amponsah, R. A Model for Photovoltaic Module Optimisation. J. Mech. Eng. Autom.
**2015**, 5, 72–79. [Google Scholar] - Jazayeri, M.; Uysal, S.; Jazayeri, K. A simple MATLAB/Simulink simulation for PV modules based on one-diode model. In Proceedings of the International Conference on 10th IEEE High Capacity Optical Networks and Enabling Technologies (HONET-CNS), Magosa, Cyprus, 11–13 December 2013.
- Bikaneria, J.; Joshi, S.; Joshi, A.R. Modeling and Simulation of PV Cell using One-diode model. Int. J. Sci. Res. Publ.
**2013**, 3, 1–4. [Google Scholar] - Edouard, M.; Njomo, D. Mathematical Modeling and Digital Simulation of PV Solar Panel using MATLAB Software. Int. J. Emerg. Technol. Adv. Eng.
**2013**, 3, 24–32. [Google Scholar] - Santos, R.; Gaspar, P.D. Computational tool for simulating the performance of photovoltaic panels. In Proceedings of the International Conference on Engineering UBI—University of Beira Interior, Covilhã, Portugal, 28–30 November 2011.
- Wang, Y.; Sheu, R. A New Piecewise Linear Circuit Model for Photovoltaic Cells and Modules. Int. J. Electr. Eng.
**2015**, 22, 181–188. [Google Scholar] - Hsu, P.-C. Modelling of solar cells and modules using piecewise linear parallel branches. Renew. Power Gener.
**2011**, 5, 215–222. [Google Scholar] - Al Tarabsheh, A.; Etier, I.; Widyan, M. Investigating the Shunting Effects of Parallel-Connected A-Si:H Solar Cells. Int. J. Sustain. Energy
**2011**, 32, 71–77. [Google Scholar] [CrossRef] - Chander, S.; Purohit, A.; Sharma, A.; Arvindc, S.P.; Nehra, M.S.D. A study on photovoltaic parameters of mono-crystalline silicon solar cell with cell temperature. Energy Rep.
**2015**, 1, 104–109. [Google Scholar] [CrossRef] - Sharma, V.; Chandel, S.S. Performance and degradation analysis for long term reliability of solar photovoltaic systems: A review. Renew. Sustain. Energy Rev.
**2013**, 27, 753–767. [Google Scholar] [CrossRef] - Wuerfel, U.; Neher, D.; Spies, A.; Albrecht, S. Impact of charge transport on current–voltage characteristics and power-conversion efficiency of organic solar cells. Nat. Commun.
**2015**, 6, 6951. [Google Scholar] [CrossRef] [PubMed] - De Soto, W.; Klein, S.A. Improvement and validation of a model for photovoltaic array performance. Sol. Energy
**2006**, 80, 78–88. [Google Scholar] [CrossRef] - Al Tarabsheh, A. Description of the Ideality Factor of a-Si:H Photovoltaic Cells Under Different Illumination Intensity Levels. J. Renew. Sustain. Energy
**2015**, 7. [Google Scholar] [CrossRef] - Kim, S.; Jeon, J.H.; Cho, C.H.; Kim, E.S.; Ahn, J.B. Modeling and simulation of a grid-connected PV generation system for electromagnetic transient analysis. Sol. Energy
**2009**, 83, 664–678. [Google Scholar] [CrossRef] - Singh, P.; Ravindra, N.M. Temperature dependence of solar cell performance—An analysis. Sol. Energy Mater. Sol. Cells
**2012**, 101, 36–45. [Google Scholar] [CrossRef]

**Figure 1.**Current/voltage (I/V) characteristics of a PV module highlighting the key electrical parameters.

**Figure 3.**Modified standard equivalent-circuit models of (

**a**) one PV cell and (

**b**) N-series connected PV cells.

**Figure 4.**Calculated I/V characteristics of a PV module using the standard model expressed by Equation (7) (circles) and the modified model expressed by (Equation (6)) (line).

**Figure 5.**Calculated of I/V characteristics via SEC and MSEC. The difference between the line (slope = 1) and the circles is 0.05%.

**Figure 6.**Measured (circles) and modeled I/V characteristics of a PV module using the SEC model (solid line) and the MSEC model (dashed line).

**Figure 7.**Contour plot of the difference Δ (%) as a function of operating temperature T and radiation levels G.

**Figure 8.**Difference Δ versus series resistance (R

_{s}), parallel resistance (R

_{p}), ideality factor (n), and reverse saturation current (I

_{0}). The resulting difference in all cases is very small.

**Table 1.**Parameters of N identical series-connected PV cells used to calculate the I/V characteristics.

Cells 1-N | |
---|---|

Number of series-connected cells | 36 |

Absolute operating Temperature (K) | 300 |

Area of a PV cell (cm^{2}) | 10 × 10 |

Series resistance $Rs$ ($\Omega $) | 0.01 |

Shunt resistance $Rp$ ($\Omega $) | 100 |

Ideality factor $n$ | 1.5 |

Reverse saturation current ${I}_{s0}$ (A) | $1\times {10}^{-8}$ |

Short-circuit current ${I}_{ph0}$ (A) | 2.7 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Al Tarabsheh, A.; Akmal, M.; Ghazal, M.
Series Connected Photovoltaic Cells—Modelling and Analysis. *Sustainability* **2017**, *9*, 371.
https://doi.org/10.3390/su9030371

**AMA Style**

Al Tarabsheh A, Akmal M, Ghazal M.
Series Connected Photovoltaic Cells—Modelling and Analysis. *Sustainability*. 2017; 9(3):371.
https://doi.org/10.3390/su9030371

**Chicago/Turabian Style**

Al Tarabsheh, Anas, Muhammad Akmal, and Mohammed Ghazal.
2017. "Series Connected Photovoltaic Cells—Modelling and Analysis" *Sustainability* 9, no. 3: 371.
https://doi.org/10.3390/su9030371