# Performance Evaluation of Analytical Methods for Parameters Extraction of Photovoltaic Generators

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## Abstract

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## 1. Introduction

## 2. Mathematical Grounds for the Analytical Methods

## 3. Parameters Extraction Methods

#### 3.1. Method One

#### 3.1.1. Extraction of the Photocurrent

#### 3.1.2. Extraction of the Shunt Resistance

#### 3.1.3. Extraction of the Series Resistance

#### 3.1.4. Extraction of the Reverse Saturation Current

#### 3.1.5. Extraction of the Ideality Factor n

#### 3.2. Method Two

#### 3.3. Method Three

#### 3.3.1. Extraction of the Photocurrent

#### 3.3.2. Extraction of the Saturation Current

#### 3.3.3. Extraction of the Series Resistance

#### 3.3.4. Extraction of the Ideality Factor

#### 3.4. Method Four

#### 3.5. Method Five

#### 3.6. Method Six

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

$a$ | Modified ideality factor ($a=n{N}_{s}{V}_{th}$) |

${\alpha}_{{I}_{sc}}$ | Temperature coefficient of the short-circuit current $(\mathrm{A}/\xb0\mathrm{C})$ |

${\beta}_{{V}_{oc}}$ | Temperature coefficient of the open-circuit voltage ($\mathrm{V}/\xb0\mathrm{C})$ |

$\delta $ | Coefficient for the single-diode model defined as $a/{V}_{oc}$. |

$G$ | Insolation (W/m^{2}) |

${G}_{STC}$ | Insolation at standard test conditions ($\mathrm{W}/{\mathrm{m}}^{2}$) |

I | Terminal current of a photovoltaic cell or module (A) |

${I}_{mp}$ | Current at the maximum power point (A) |

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

${I}_{sat}$ | Reverse saturation current (A) |

${I}_{ph}$ | Photocurrent (A) |

${I}_{ph,STC}$ | Photocurrent at standard test conditions (A) |

k | Boltzmann’s constant ($1.38065\times {10}^{-23}\text{}\mathrm{J}/\mathrm{K}$) |

MPP | Maximum power point |

n | ideality factor of a PV cell/diode |

${N}_{s}$ | Number of series-connected cells in a PV module |

P | Power (W) |

${P}_{mp}$ | Power at maximum power point (W) |

PV | Photovoltaic |

q | Electronic charge 1.602 × 10^{−19} (C) |

${R}_{s}$ | Series resistance of a photovoltaic module ($\mathsf{\Omega}$) |

${R}_{so}$ | The negative of the reciprocal of the slope of the I–V curve at the open-circuit voltage point |

${R}_{sh}$ | Shunt resistance of a PV module ($\mathsf{\Omega}$) |

${R}_{sho}$ | The negative of the reciprocal of the slope of the I–V curve at the short-circuit current point |

SDM | Single-diode model |

STC | Standard test conditions (Insolation = 1000 $\mathrm{W}/{\mathrm{m}}^{2}$, air mass AM = 1.5, T = 25 $\xb0\mathrm{C}$) |

T | Temperature (k) |

${T}_{STC}$ | Temperature at standard test conditions ($\xb0\mathrm{C}$) |

V | Terminal voltage of a PV module (V) |

${V}_{th}$ | Thermal voltage (V) |

${V}_{oc}$ | Open-circuit voltage of a PV module (V) |

${V}_{mp}$ | Voltage at maximum power point (V) |

${V}_{oc,STC}$ | Open-circuit voltage of a PV module at STC (V) |

$\mathrm{W}$ | Lambert-W function |

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**Figure 1.**Normalised experimental current–voltage (I–V) and power–voltage (P–V) characteristics of a generic PV generator.

**Figure 5.**Comparison between the I–V (

**left**) and P–V (

**right**) curves obtained using Methods two and three with those obtained using numerical method for the KC200GT module.

**Figure 6.**Comparison between the I–V (

**left**) and P–V (

**right**) curves obtained using Methods one and five with those obtained using numerical method for the KC200GT module.

**Figure 7.**Comparison between the I–V (

**left**) and P–V (

**right**) curves obtained using Method four with those obtained using numerical method for the KC200GT module.

**Figure 8.**Comparison between the I–V (

**left**) and P–V (

**right**) curves obtained using Method six with those obtained using numerical method for the KC200GT module.

Datasheet | KC200GT | LC50-12M | 180BA19 |
---|---|---|---|

Parameters | Multi-Crystalline | Mono-Crystalline | Thin Film |

${I}_{sc}\left(\mathrm{A}\right)$ | 8.21 A | 3.2 A | 3.65 A |

${V}_{oc}\left(\mathrm{V}\right)$ | 32.9 V | 22.5 V | 66.4 V |

${I}_{mp}\left(\mathrm{A}\right)$ | 7.61 A | 2.9 A | 3.33 A |

${V}_{mp}\left(\mathrm{V}\right)$ | 26.3 V | 17.2 V | 54 V |

${\mathsf{\mu}}_{{V}_{oc}}$$(\mathrm{V}/\xb0\mathrm{C})$ | −1.23 × 10^{−1} | −7.88 × 10^{−2} | −173 × 10^{−3} |

${\mathsf{\mu}}_{{I}_{sc}}$$(\mathrm{A}/\xb0\mathrm{C})$ | 3.18 × 10^{−3} | 2.88 × 10^{−3} | 1.01 × 10^{−3} |

${N}_{s}$ | 54 | 36 | 96 |

Method | Parameter | ||||
---|---|---|---|---|---|

n | ${\mathit{R}}_{\mathit{s}}$ | ${\mathit{R}}_{\mathit{s}\mathit{h}}$ | ${\mathit{I}}_{\mathit{s}\mathit{a}\mathit{t}}$ | ${\mathit{I}}_{\mathit{p}\mathit{h}}$ | |

Method 1 | 1.08317 | 0.27077 | 124 | 2.4885 × 10^{−9} | 8.22793 |

Method 2 | 1.81764 | 0 | infinite | 1.78074 × 10^{−5} | 8.21 |

Method 3 | 1.40991 | 0.19455 | infinite | 4.09919 × 10^{−7} | 8.21 |

Method 4 | 0.65008 | 0.39999 | 82.5508 | 1.14541 × 10^{−15} | 8.24978 |

Method 5 | 0.88423 | 0.38033 | 123.62 | 1.81544 × 10^{−11} | 8.23526 |

Method 6 | 1.00258 | 0.30567 | 130.466 | 4.43777 × 10^{−10} | 8.22924 |

Iterative [14] | 1.3 | 0.2283 | 572.124 | 9.89443 × 10^{−8} | 8.21329 |

Numerical [34] | 1.3405 | 0.2172 | 951.327 | 1.7097 × 10^{−7} | 8.2119 |

Method | Parameter | ||||
---|---|---|---|---|---|

n | ${\mathit{R}}_{\mathit{s}}$ | ${\mathit{R}}_{\mathit{s}\mathit{h}}$ | ${\mathit{I}}_{\mathit{s}\mathit{a}\mathit{t}}$ | ${\mathit{I}}_{\mathit{p}\mathit{h}}$ | |

Method 1 | 2.0361 | 0.10045 | 206 | 2.0109 × 10^{−5} | 3.20156 |

Method 2 | 2.41979 | 0 | ∞ | 1.3832 × 10^{−4} | 3.2 |

Method 3 | 1.76187 | 0.4969 | ∞ | 3.24464 × 10^{−6} | 3.2 |

Method 4 | 0.79342 | 0.93255 | 105.70414 | 1.47618 × 10^{−13} | 3.22823 |

Method 5 | 1.24254 | 0.77359 | 205.22641 | 9.82922 × 10^{−9} | 3.21206 |

Method 6 | 0.99693 | 0.84024 | 125.53699 | 8.22168 × 10^{−11} | 3.22142 |

Iterative method [14] | 1.2 | 0.784 | 186.40574 | 5.06574 × 10^{−9} | 3.21352 |

Numerical method [19] | No convergence |

Method | Parameter | ||||
---|---|---|---|---|---|

n | ${\mathit{R}}_{\mathit{s}}$ | ${\mathit{R}}_{\mathit{s}\mathit{h}}$ | ${\mathit{I}}_{\mathit{s}\mathit{a}\mathit{t}}$ | ${\mathit{I}}_{\mathit{p}\mathit{h}}$ | |

Method 1 | 0.55767 | 2.69004 | 2329 | 3.99938 × 10^{−21} | 3.65422 |

Method 2 | 2.06455 | 0 | ∞ | 7.9701 × 10^{−6} | 3.65 |

Method 3 | 2.11483 | −0.09068 | ∞ | 1.08651 × 10^{−5} | 3.65 |

Method 4 | 0.95729 | 1.13544 | 313.85129 | 2.13594 × 10^{−12} | 3.6632 |

Method 5 | 1.95145 | 0.10657 | 2328.8934 | 3.71538 × 10^{−6} | 3.65017 |

Method 6 | 0.95589 | 1.41883 | 327.95525 | 2.1766 × 10^{−12} | 3.66579 |

Iterative [14] | 1.8 | 0.27300 | 1181.56509 | 1.17348 × 10^{−12} | 3.65084 |

Numerical method [19] | No convergence |

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**MDPI and ACS Style**

Anani, N.; Ibrahim, H.
Performance Evaluation of Analytical Methods for Parameters Extraction of Photovoltaic Generators. *Energies* **2020**, *13*, 4825.
https://doi.org/10.3390/en13184825

**AMA Style**

Anani N, Ibrahim H.
Performance Evaluation of Analytical Methods for Parameters Extraction of Photovoltaic Generators. *Energies*. 2020; 13(18):4825.
https://doi.org/10.3390/en13184825

**Chicago/Turabian Style**

Anani, Nader, and Haider Ibrahim.
2020. "Performance Evaluation of Analytical Methods for Parameters Extraction of Photovoltaic Generators" *Energies* 13, no. 18: 4825.
https://doi.org/10.3390/en13184825