# Adjusting the Single-Diode Model Parameters of a Photovoltaic Module with Irradiance and Temperature

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Analysis of the Single-Diode Model

## 3. Method of Adjusting the SDM Model Parameters

#### 3.1. Short-Circuit Current

#### 3.1.1. Method 1

#### 3.1.2. Method 2

#### 3.2. Open-Circuit Voltage

#### 3.2.1. Method 1

#### 3.2.2. Method 2

#### 3.2.3. Method 3

#### 3.2.4. Method 4

#### 3.2.5. Method 5

#### 3.3. Photocurrent ${I}_{ph}$

#### 3.3.1. Method 1

#### 3.3.2. Method 2

#### 3.3.3. Method 3

#### 3.3.4. Method 4

#### 3.4. Ideality Factor n

#### 3.5. Saturation Current ${I}_{sat}$

#### 3.5.1. Method 1

#### 3.5.2. Method 2

#### 3.5.3. Method 3

#### 3.5.4. Method 4

#### 3.5.5. Method 5

#### 3.6. Series and Shunt Resistances ${R}_{s},{R}_{sh}$

#### 3.6.1. Method 1

#### 3.6.2. Method 2

#### 3.6.3. Method 3

#### 3.6.4. Method 4

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Xiao, W.; Dunford, W.G.; Capel, A. A novel modeling method for photovoltaic cells. In Proceedings of the 2004 IEEE 35th Annual Power Electronics Specialists Conference (IEEE Cat. No.04CH37551), Aachen, Germany, 20–25 June 2004; pp. 1950–1956. [Google Scholar]
- Bellini, A.; Bifaretti, S.; Iacovone, V.; Cornaro, C. “Simplified Model of a Photovoltaic Module,” in Applied Electronics; IEEE: Piscataway, NJ, USA, 2009. [Google Scholar]
- Villalva, M.; Gazoli, J.R.; Filho, E. Comprehensive Approach to Modeling and Simulation of Photovoltaic Arrays. IEEE Trans. Power Electron.
**2009**, 24, 1198–1208. [Google Scholar] [CrossRef] - Femia, N.; Petrone, G.; Spagnuolo, G.; Vitelli, M. Power Electronics and Control Techniques for Maximum Energy Harvesting in Photovoltaic Systems; Informa UK Limited: Colchester, UK, 2017. [Google Scholar]
- Huang, P.-H.; Xiao, W.; Peng, J.C.-H.; Kirtley, J.L. Comprehensive Parameterization of Solar Cell: Improved Accuracy with Simulation Efficiency. IEEE Trans. Ind. Electron.
**2015**, 63, 1549–1560. [Google Scholar] [CrossRef] - Mahmoud, Y.; El-Saadany, E.F. A Photovoltaic Model with Reduced Computational Time. IEEE Trans. Ind. Electron.
**2014**, 62, 1. [Google Scholar] [CrossRef] - Tolić, I.; Primorac, M.; Milicevic, K. Measurement Uncertainty Propagation through Basic Photovoltaic Cell Models. Energies
**2019**, 12, 1029. [Google Scholar] [CrossRef] - Ibrahim, H.; Anani, N. Evaluation of Analytical Methods for Parameter Extraction of PV modules. Energy Procedia
**2017**, 134, 69–78. [Google Scholar] [CrossRef] - Chegaar, M.; Hamzaoui, A.; Namoda, A.; Petit, P.; Aillerie, M.; Herguth, A. Effect of Illumination Intensity on Solar Cells Parameters. Energy Procedia
**2013**, 36, 722–729. [Google Scholar] [CrossRef] - Singh, P.; Ravindra, N. Temperature dependence of solar cell performance—An analysis. Sol. Energy Mater. Sol. Cells
**2012**, 101, 36–45. [Google Scholar] [CrossRef] - Anani, N.; Shahid, M.; Al-Kharji, O.; Ponciano, J. A CAD Package for Modeling and Simulation of PV Arrays under Partial Shading Conditions. Energy Procedia
**2013**, 42, 397–405. [Google Scholar] [CrossRef][Green Version] - Silvestre, S.; Boronat, A.; Chouder, A. Study of bypass diodes configuration on PV modules. Appl. Energy
**2009**, 86, 1632–1640. [Google Scholar] [CrossRef] - Ibrahim, H.; Anani, N. Variation of the performance of a PV panel with the number of bypass diodes and partial shading patterns. In Proceedings of the 2019 International Conference on Power Generation Systems and Renewable Energy Technologies (PGSRET), Istanbul, Turkey, 26–27 August 2019; pp. 1–4. [Google Scholar]
- Ibrahim, H.; Anani, N. Study of the effect of different configurations of bypass diodes on the performance of a PV string. In Human Centred Intelligent Systems; Springer: Berlin, Germany, 2019; pp. 593–600. [Google Scholar]
- Brano, V.L.; Orioli, A.; Ciulla, G.; Di Gangi, A. An improved five-parameter model for photovoltaic modules. Sol. Energy Mater. Sol. Cells
**2010**, 94, 1358–1370. [Google Scholar] [CrossRef] - Chatterjee, A.; Keyhani, A.; Kapoor, D. Identification of Photovoltaic Source Models. IEEE Trans. Energy Convers.
**2011**, 26, 883–889. [Google Scholar] [CrossRef] - Sera, D.; Teodorescu, R.; Rodriguez, P. Photovoltaic module diagnostics by series resistance monitoring and temperature and rated power estimation. In Proceedings of the 2008 34th Annual Conference of IEEE Industrial Electronics, Orlando, FL, USA, 10–13 November 2008; pp. 2195–2199. [Google Scholar]
- Skoplaki, E.; Palyvos, J. On the temperature dependence of photovoltaic module electrical performance: A review of efficiency/power correlations. Sol. Energy
**2009**, 83, 614–624. [Google Scholar] [CrossRef] - Ibrahim, H.; Anani, N. Variations of PV module parameters with irradiance and temperature. Energy Procedia
**2017**, 134, 276–285. [Google Scholar] [CrossRef] - Kennerud, K. Analysis of Performance Degradation in CdS Solar Cells. In IEEE Trans. Aerosp. Electron. Syst.
**1969**, 5, 912–917. [Google Scholar] [CrossRef] - Siddique, H.A.B.; Xu, P.; De Doncker, R.W. Parameter extraction algorithm for one-diode model of PV panels based on datasheet values. In Proceedings of the 2013 International Conference on Clean Electrical Power (ICCEP), Alghero, Italy, 11–13 June 2013; pp. 7–13. [Google Scholar]
- Cubas, J.; Pindado, S.; Victoria, M. On the analytical approach for modeling photovoltaic systems behavior. J. Power Sources
**2014**, 247, 467–474. [Google Scholar] [CrossRef][Green Version] - Dongue, S.B.; Njomo, D.; Ebengai, L. An Improved Nonlinear Five-Point Model for Photovoltaic Modules. Int. J. Photoenergy
**2013**, 2013, 1–11. [Google Scholar] [CrossRef] - Ghani, F.; Duke, M. Numerical determination of parasitic resistances of a solar cell using the Lambert W-function. Sol. Energy
**2011**, 85, 2386–2394. [Google Scholar] [CrossRef] - Louzazni, M.; Khouya, A.; Crăciunescu, A.; Amechnoue, K.; Mussetta, M. Modelling and Parameters Extraction of Flexible Amorphous Silicon Solar Cell a-Si:H. Appl. Sol. Energy
**2020**, 56, 1–12. [Google Scholar] [CrossRef] - Luo, X.; Cao, L.; Wang, L.; Zhao, Z.; Huang, C. Parameter identification of the photovoltaic cell model with a hybrid Jaya-NM algorithm. Optik
**2018**, 171, 200–203. [Google Scholar] [CrossRef] - Saloux, E.; Teyssedou, A.; Sorin, M. Explicit model of photovoltaic panels to determine voltages and currents at the maximum power point. Sol. Energy
**2011**, 85, 713–722. [Google Scholar] [CrossRef] - Carrero, C.; Ramirez, D.; Rodriguez, J.; Platero, C. Accurate and fast convergence method for parameter estimation of PV generators based on three main points of the I–V curve. Renew. Energy
**2011**, 36, 2972–2977. [Google Scholar] [CrossRef] - Khezzar, R.; Zereg, M.; Khezzar, A. Modeling improvement of the four parameter model for photovoltaic modules. Sol. Energy
**2014**, 110, 452–462. [Google Scholar] [CrossRef] - Zhou, W.; Yang, H.; Fang, Z. A novel model for photovoltaic array performance prediction. Appl. Energy
**2007**, 84, 1187–1198. [Google Scholar] [CrossRef] - De Soto, W.; Klein, S.; Beckman, W. Improvement and validation of a model for photovoltaic array performance. Sol. Energy
**2006**, 80, 78–88. [Google Scholar] [CrossRef] - Mahmoud, Y.; Xiao, W.; Zeineldin, H.H. A Parameterization Approach for Enhancing PV Model Accuracy. IEEE Trans. Ind. Electron.
**2012**, 60, 5708–5716. [Google Scholar] [CrossRef] - Orioli, A.; Di Gangi, A. A procedure to calculate the five-parameter model of crystalline silicon photovoltaic modules on the basis of the tabular performance data. Appl. Energy
**2013**, 102, 1160–1177. [Google Scholar] [CrossRef] - da Luz, C.M.A.; Tofoli, F.L.; Vicente, P.D.S.; Vicente, E.M. Assessment of the ideality factor on the performance of photovoltaic modules. Energy Convers. Manag.
**2018**, 167, 63–69. [Google Scholar] [CrossRef] - Kim, W.; Choi, W. A novel parameter extraction method for the one-diode solar cell model. Sol. Energy
**2010**, 84, 1008–1019. [Google Scholar] [CrossRef] - Islam, M.H.; Djokic, S.Z.; Desmet, J.; Verhelst, B. Measurement-based modelling and validation of PV systems. In Proceedings of the 2013 IEEE Grenoble Conference, Grenoble, France, 16–20 June 2013; pp. 1–6. [Google Scholar]
- Can, H.; Ickilli, D.; Parlak, K. A New Numerical Solution Approach for the Real-Time Modeling of Photovoltaic Panels. In Proceedings of the 2012 Asia-Pacific Power and Energy Engineering Conference, Shanghai, China, 27–29 March 2012; pp. 1–4. [Google Scholar]
- Bai, J.; Liu, S.; Hao, Y.; Zhang, Z.; Jiang, M.; Zhang, Y. Development of a new compound method to extract the five parameters of PV modules. Energy Convers. Manag.
**2014**, 79, 294–303. [Google Scholar] [CrossRef] - Ghani, F.; Duke, M.; Carson, J. Numerical calculation of series and shunt resistance of a photovoltaic cell using the Lambert W-function: Experimental evaluation. Sol. Energy
**2013**, 87, 246–253. [Google Scholar] [CrossRef] - Mahmoud, Y.; Xiao, W.; Zeineldin, H.H. A Simple Approach to Modeling and Simulation of Photovoltaic Modules. IEEE Trans. Sustain. Energy
**2012**, 3, 185–186. [Google Scholar] [CrossRef] - Ma, J.; Man, K.L.; Ting, T.; Zhang, N.; Lim, E.G.; Guan, S.-U.; Wong, P.W.; Krilavičius, T.; Saulevicius, D.; Lei, C.-U. Simple Computational Method of Predicting Electrical Characteristics in Solar Cells. Elektron. Elektrotechnika
**2014**, 20, 41–44. [Google Scholar] [CrossRef][Green Version] - Virtuani, A.; Lotter, E.; Powalla, M. Performance of Cu(In,Ga)Se2 solar cells under low irradiance. Thin Solid Films
**2003**, 431, 443–447. [Google Scholar] [CrossRef] - POSHARP Inc. Shell SQ 150-PC Solar Panel from Shell Solar. Available online: http://www.posharp.com/shell-sq-150-pc-solar-panel-from-shell-solar_p1838324422d.aspx (accessed on 10 January 2020).
- KYOCERA North America. KC 175 GT. Available online: https://search.kyocera.co.jp/search?site=ZHS4H5NP&charset=UTF-8&group=62&design=69&query=KC175GT&_ga=2.256746382.462656309.1590188877-1511522101.1586353898 (accessed on 10 March 2020).
- POSHARP Inc. ST40 Solar Panel. Available online: http://www.posharp.com/st-40-solar-panel-from-shell-solar_p1208198951d.aspx (accessed on 1 May 2020).

**Figure 1.**The normalized I-V and P-V curves of a typical PV module (

**left**) and the single-diode model (

**right**).

Parameters | Shell SQ150 | KC175GT | Shell ST40 |
---|---|---|---|

${I}_{sc}$ | $4.8\text{\hspace{0.17em}}\mathrm{A}$ | $8.09\text{}\mathrm{A}$ | $2.68\text{}\mathrm{A}$ |

${V}_{oc}$ | $4.34\times 10\text{}\mathrm{V}$ | $2.92\times 10\text{}\mathrm{V}$ | $2.33\times 10\text{}\mathrm{V}$ |

${I}_{mp}$ | $4.4\text{\hspace{0.17em}}\mathrm{A}$ | $7.42\text{}\mathrm{A}$ | $2.41\text{}\mathrm{A}$ |

${V}_{mp}$ | $3.4\times 10\text{}\mathrm{V}$ | $2.36\times 10\text{}\mathrm{V}$ | $1.66\times 10\text{}\mathrm{V}$ |

${\mu}_{{V}_{oc}}\text{\hspace{0.17em}}{(\mathrm{V}/}^{\mathrm{o}}\mathrm{C})$ | −161 × 10^{−3} | −1.09 × 10^{−1} | −100 × 10^{−3} |

${\mu}_{{I}_{sc}}\text{\hspace{0.17em}}{(\mathrm{A}/}^{\mathrm{o}}\mathrm{C})$ | 1.4 × 10^{−3} | 3.18 × 10^{−3} | 0.35 × 10^{−3} |

${N}_{s}$ | 72 | 84 | 36 |

Constant | α | β | γ |
---|---|---|---|

Shell SQ150 | 0.998 | 0.055 | 1.0797 |

KC175GT | 0.977 | 0.053 | 1.32 |

Shell ST40 | 0.996 | 0.085 | 1.367 |

Parameters | Shell SQ150 | KC175GT | Shell ST40 |
---|---|---|---|

$n$ | $1.4397$ | $1.5036$ | $1.5028$ |

${R}_{s}$ | $5.906\times {10}^{-1}\text{}\Omega $ | $1.061\times {10}^{-1}\text{\hspace{0.17em}}\Omega $ | 1.4226 Ω |

${R}_{sh}$ | $1.1661\times {10}^{3}\text{\hspace{0.17em}}\Omega $ | $3.251018\times {10}^{2}\text{}\Omega $ | 952.405 Ω |

${I}_{sat}$ | $4.0163\times {10}^{-7}\text{}\mathrm{A}$ | $1.1662\times {10}^{-6\text{}}\mathrm{A}$ | $1.4057\times {10}^{-7}\text{}\mathrm{A}$ |

${I}_{ph}$ | 4.8024 A | 8.0926 A | 2.684 A |

**Table 4.**Measured and calculated values (by Methods 1 and 2, Section 3.1) of the short-circuit current ${I}_{sc}$ (A) and the relative error.

PV Module | ${\mathit{I}}_{\mathit{s}\mathit{c}}\left(\mathit{A}\right)$ | Irradiance W/m^{2} | ||||
---|---|---|---|---|---|---|

1000 | 800 | 600 | 400 | 200 | ||

Measured | 8.09 | 6.80889 | 4.91094 | 3.27396 | 1.56581 | |

KC175GT | Method 1 | 8.09 | 6.472 | 4.854 | 3.236 | 1.618 |

%error | 4.95478 | 1.1595 | 1.1595 | 3.331 | ||

Method 2 | 8.09 | 6.5053 | 4.9114 | 3.3049 | 1.679 | |

%error | 4.4587 | 0.0094 | 0.945 | 7.23 | ||

Measured | 4.8 | 3.84 | 2.88 | 1.90884 | 0.94884 | |

SQ150 | Method 1 | 4.8 | 3.84 | 2.88 | 1.92 | 0.96 |

%error | 0 | 0 | 0.5847 | 1.1762 | ||

Method 2 | 4.8 | 3.8417 | 2.8829 | 1.9235 | 0.9631 | |

%error | 0.0443 | 0.1007 | 0.768 | 1.5029 | ||

Measured | 2.68 | 2.14894 | 1.61171 | 1.07447 | 0.53724 | |

ST40 | Method 1 | 2.68 | 2.144 | 1.608 | 1.072 | 0.536 |

%error | 0.2299 | 0.2302 | 0.2299 | 0.2301 | ||

Method 2 | 2.68 | 2.1459 | 1.6113 | 1.0759 | 0.539 | |

%error | 0.1415 | 0.0254 | 0.1331 | 0.4207 |

PV Modules | Equation (30) | Method 1 | Method 2 | Method 3 | Method 4 |
---|---|---|---|---|---|

KC175GT | 8.0926406 | 8.09 | 8.09263991 | 8.09264031 | 8.0926406 |

SQ150 | 4.8024316 | 4.8 | 4.80243089 | 4.80243114 | 4.80243165 |

ST40 | 2.6840051 | 2.68 | 2.6840031 | 2.68400152 | 2.68400513 |

**Table 6.**Calculated and measured open-circuit voltage ${V}_{oc}$ (V) and relative error for the shell SQ150 module under different irradiance levels G (W/m

^{2}) and temperature of 25 $\mathbb{C}$.

G (W/m^{2}) | Measured | Method 1 | Method 2 | Method 3 | Method 4 | Method 5 |
---|---|---|---|---|---|---|

1000 | 43.4 | 43.4 | 43.4 | 43.4 | 43.4 | 43.4 |

%error | 0 | 0 | 0 | 0 | 0 | |

800 | 42.91547 | 43.4 | 42.823523 | 42.80548 | 43.38809 | 42.87381 |

%error | 1.1165 | 0.2143 | 0.2563 | 1.1013 | 0.0971 | |

600 | 42.22329 | 43.4 | 42.05706 | 42.03902 | 43.37352 | 42.21398 |

%error | 2.7869 | 0.3937 | 0.4364 | 2.7242 | 0.0221 | |

400 | 41.25423 | 43.4 | 40.97679 | 40.95875 | 43.35267 | 41.31775 |

%error | 5.2013 | 0.6725 | 0.7164 | 5.0866 | 0.154 | |

200 | 39.59298 | 43.4 | 39.13005 | 39.11201 | 43.32139 | 39.87068 |

%error | 8.7719 | 1.1692 | 1.2148 | 9.4169 | 0.70139 |

**Table 7.**Calculated and measured ${V}_{oc}$ (V) and relative error of the KC175GT module under different irradiance levels and a temperature of 25 $\mathbb{C}$.

Irradiance | ${\mathit{V}}_{\mathit{o}\mathit{c}}\text{}\left(\mathbf{V}\right)$ | |||||
---|---|---|---|---|---|---|

(W/m^{2}) | Measured | Method 1 | Method 2 | Method 3 | Method 4 | Method 5 |

1000 | 29.2 | 29.2 | 29.2 | 29.2 | 29.2 | 29.2 |

%error | 0 | 0 | 0 | 0 | 0 | |

800 | 28.81579 | 29.2 | 28.80708 | 28.78606 | 29.18809 | 28.8587 |

%error | 1.365 | 0.03023 | 0.1032 | 1.292 | 0.1489 | |

600 | 28.43158 | 29.2 | 28.27343 | 28.25241 | 29.17352 | 28.43029 |

%error | 2.7027 | 0.5563 | 0.6302 | 2.6096 | 0.4554 | |

400 | 27.81684 | 29.2 | 27.52128 | 27.50026 | 29.15432 | 27.8476 |

%error | 4.9724 | 1.0625 | 1.1381 | 4.8082 | 0.1107 | |

200 | 27.04842 | 29.2 | 26.23548 | 26.21446 | 29.12429 | 26.905 |

%error | 7.9546 | 3.0055 | 3.0832 | 7.6763 | 0.5302 |

**Table 8.**The calculated and measured ${V}_{oc}$ (V) and relative error of the shell ST40 module under different irradiance levels and a temperature of 25 °C.

Irradiance | ${\mathit{V}}_{\mathit{o}\mathit{c}}\text{}\left(\mathbf{V}\right)$ | |||||
---|---|---|---|---|---|---|

(W/m^{2}) | Measured | Method 1 | Method 2 | Method 3 | Method 4 | Method 5 |

1000 | 23.3 | 23.3 | 23.3 | 23.3 | 23.3 | 23.3 |

%error | 0 | 0 | 0 | 0 | 0 | |

800 | 22.79815 | 23.3 | 22.99962 | 22.98971 | 23.28809 | 22.86629 |

%error | 2.2013 | 0.8837 | 0.8402 | 2.149 | 0.2989 | |

600 | 22.29631 | 23.3 | 22.59959 | 22.58968 | 23.27352 | 22.33041 |

%error | 4.5016 | 1.3602 | 1.3158 | 4.3828 | 0.1529 | |

400 | 21.54354 | 23.3 | 22.03578 | 22.02587 | 23.25432 | 21.61641 |

%error | 8.1531 | 2.2849 | 2.2389 | 7.941 | 0.3383 | |

200 | 20.21723 | 23.3 | 21.07194 | 21.06204 | 23.22429 | 20.49609 |

%error | 15.248 | 4.2276 | 4.1787 | 14.8738 | 1.3793 |

**Table 9.**The calculated (Methods 1 and 5) and measured ${V}_{oc}$ (V) and relative error of the shell SQ150 module under different temperatures and an irradiance of 1000 W/m

^{2}.

Temperature | ${\mathit{V}}_{\mathit{o}\mathit{c}}\text{}\left(\mathbf{V}\right)$ | ||||
---|---|---|---|---|---|

(°C) | Measured | Method 1 | %Error | Method 5 | %Error |

20 | 44.205 | 44.205 | 0 | 44.2002 | 0.0109 |

25 | 43.4 | 43.4 | 0 | 43.4 | 0 |

30 | 42.7315 | 43.3195 | 1.376 | 42.6273 | 0.2439 |

40 | 41.258 | 40.985 | 0.6617 | 41.1587 | 0.2407 |

50 | 39.7845 | 39.375 | 1.0218 | 39.7846 | 0.00025 |

60 | 38.311 | 37.765 | 1.4252 | 38.4962 | 0.4834 |

**Table 10.**Calculated and measured ${V}_{oc}$ (V), and relative error of the KC175GT module under different temperatures and an irradiance of 1000 W/m

^{2}.

Temperature | ${\mathit{V}}_{\mathit{o}\mathit{c}}\text{}\left(\mathbf{V}\right)$ | ||||
---|---|---|---|---|---|

(°C) | Measured | Method 1 | %Error | Method 5 | %Error |

25 | 29.2 | 29.2 | 0 | 29.2 | 0 |

50 | 26.26533 | 26.475 | 0.7983 | 26.2649 | 0.00164 |

75 | 23.25729 | 23.75 | 2.1185 | 23.8122 | 2.386 |

**Table 11.**Calculated and measured ${V}_{oc}$ (V), and relative error of the shell ST40 module under different temperatures and an irradiance of 1000 W/m

^{2}.

Temperature | ${\mathit{V}}_{\mathit{o}\mathit{c}}\text{}\left(\mathbf{V}\right)$ | ||||
---|---|---|---|---|---|

(°C) | Measured | Method 1 | %Error | Method 5 | %Error |

20 | 23.8 | 23.8 | 0 | 23.8452 | 0.1899 |

25 | 23.3 | 23.3 | 0 | 23.3 | 0 |

30 | 22.81138 | 22.8 | 0.04989 | 22.776 | 0.1551 |

40 | 21.85938 | 21.8 | 0.2716 | 21.7872 | 0.3302 |

50 | 20.87077 | 20.8 | 0.3391 | 20.8703 | 0.0023 |

60 | 19.91877 | 19.8 | 0.5963 | 20.0184 | 0.5002 |

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## Share and Cite

**MDPI and ACS Style**

Anani, N.; Ibrahim, H.
Adjusting the Single-Diode Model Parameters of a Photovoltaic Module with Irradiance and Temperature. *Energies* **2020**, *13*, 3226.
https://doi.org/10.3390/en13123226

**AMA Style**

Anani N, Ibrahim H.
Adjusting the Single-Diode Model Parameters of a Photovoltaic Module with Irradiance and Temperature. *Energies*. 2020; 13(12):3226.
https://doi.org/10.3390/en13123226

**Chicago/Turabian Style**

Anani, Nader, and Haider Ibrahim.
2020. "Adjusting the Single-Diode Model Parameters of a Photovoltaic Module with Irradiance and Temperature" *Energies* 13, no. 12: 3226.
https://doi.org/10.3390/en13123226