# 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

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**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