# Minimizing the Utilized Area of PV Systems by Generating the Optimal Inter-Row Spacing Factor

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

- Generating the optimal inter-row spacing factor for minimizing the installation area and maximizing the energy output of the PV system for flat and non-flat terrains.
- A detailed method of estimating the needed angles of the sun’s path, which play an essential role in systems design.
- A comprehensive description of inter-row spacing estimation is given to establish the most appropriate spacing that avoids the worst-case scenario of the shading effect.
- Generating an inter-row spacing factor formula and validating it through a case study that was conducted in the Kingdom of Saudi Arabia (KSA), which has high solar radiation and solar energy potential but insufficient studies in this regard.

## 2. Definitions and Methodology

#### 2.1. Sun Angles Calculation

#### 2.2. Multiplier Factor Estimation

#### 2.3. Inter-Row Spacing Considered for Non-Flat Terrain

## 3. Methodology of Optimum Area Estimation

## 4. Objective Function

_{S}is the surface area of the PV panel, r is the solar panel efficiency, G

_{R}is the tilted surface mean solar radiation, and PR is the performance ratio. Knowing this, the energy density is the ratio between the generated energy and the installation area:

_{d}is the energy density in (kWh/m

^{2}), E

_{out}is the energy output in (kWh), and A is the total area of the system in (m

^{2}). If we substitute Equation (8) into Equation (10), then E

_{d}can be written as follows:

_{worst}is the inter-row spacing under the worst-case scenario (21 December).

## 5. Case Studies and Validation Process

#### 5.1. Saudi Arabia Case Study

^{2}due to the proposed approach of estimating the area, based on optimal inter-row spacing using the generated multiplier factor.

^{2}less than the standardized case, and, inevitably, the energy yield is maximized when setting the tilt angle of row 1 to 22°, the optimal angle.

#### 5.2. Yemen Case Study

^{2}, as illustrated in Table 4. However, since this value is sufficient to prevent shading in this case study, it cannot be employed in limited-area applications. Therefore, the mathematical model developed in this paper is used to provide the optimal inter-row spacing factor for limited area applications.

^{2}. As shown in Table 2, there are two different inter-row spacing distances between arrays in this case study. The first one is the inter-row spacing between the distant arrays A1 and A2, and A2 and A3. The second inter-row spacing is between A3 and A4. The former is less than the latter because its height difference is less than the latter, being 20 cm for the former, vs. 30 cm for the latter, as illustrated in Table 5. The optimal inter-row spacing factor is estimated for this case study, using Equation (4). Then, the spacing is decided, considering the non-flat terrain, using Equation (6). Considering these differences in terrain, the minimum spacing area is calculated using Equation (8) and is found to be less than the actual spacing area by around 16%.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

PV | photovoltaic |

MENA | Middle East and South Africa (MENA) |

MPPT | maximum power point tracking |

2-D | 2-dimensional |

ΔH | PV panel height from the ground |

θ_{az} | Azimuth angle |

θ_{elev} | Elevation angle |

θ_{tilt} | Tilt angle |

X | Shading length |

D | Spacing between rows |

L | PV panel length |

w | PV panel width |

F | Inter row spacing factor |

h1 | Height difference with positive slope |

h2 | Height difference with negative slope |

A | PV system area |

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**Figure 1.**Example of a two-dimensional sun path, with angles estimated [33].

**Figure 4.**Effect of changing the azimuth angle on the distance (D) and the inter-row spacing factor.

**Figure 7.**Geometry of the essential factors to estimate the area of the PV system for non-flat terrain.

Province Name | Latitude | Longitude | Elevation Angle (Degree) | Azimuth Angle (Degree) | Factor Multiplier |
---|---|---|---|---|---|

Riyadh | 24.774265 | 46.738586 | 25 | 46 | 1.49 |

Makkah | 21.422510 | 39.826168 | 27.5 | 48 | 1.29 |

Dammam | 26.551680 | 49.957581 | 24 | 45 | 1.59 |

Abha | 18.216797 | 42.503765 | 29 | 49 | 1.18 |

Jazan | 16.909683 | 42.567902 | 31 | 50 | 1.07 |

Madinah | 24.470901 | 39.612236 | 26 | 46 | 1.42 |

Buraidah | 26.32599 | 43.97497 | 24 | 45 | 1.59 |

Tabuk | 28.390393 | 36.57151 | 23 | 45 | 1.67 |

Ha’il | 27.523647 | 41.696632 | 23.5 | 45 | 1.63 |

Najran | 17.49326 | 44.12766 | 30 | 49 | 1.14 |

Sakaka | 29.953894 | 40.197044 | 22 | 44 | 1.78 |

Al-Baha | 20.01288 | 41.46767 | 28 | 48 | 1.26 |

Arar | 30.983334 | 41.016666 | 21 | 44 | 1.87 |

Jeddah | 21.543333 | 39.172779 | 28 | 45 | 1.33 |

**Table 2.**Installation area of the case study and the optimal area of scenario 1 (with a 15° tilt angle).

Roof Number | Tilt Angle | Number of Modules | Installation Area (m^{2}) | Optimal Area (m^{2}) |
---|---|---|---|---|

A1 | 15° | 316 | 786.11 | 752 |

A2 | 15° | 292 | 786.11 | 694 |

A3 | 15° | 50 | 113.19 | 119 |

A4 | 15° | 48 | 172.59 | 114 |

A5 | 15° | 44 | 126.43 | 98 |

Total | 15° | 750 | 1984.43 | 1777 |

Roof Number | Tilt Angle | Number of Modules | Installation Area (m^{2}) at Tilt 15° | Optimal Area (m^{2}) with 15° and 22° Row-1 |
---|---|---|---|---|

A1 | 15° and 22°, row 1 | 316 | 786.11 | 747 |

A2 | 15° and 22°, row 1 | 292 | 786.11 | 690 |

A3 | 15° and 22°, row 1 | 50 | 113.19 | 118 |

A4 | 15° and 22°, row 1 | 48 | 172.59 | 113 |

A5 | 15° and 22°, row 1 | 44 | 126.43 | 98 |

Total | 15° and 22°, row 1 | 750 | 1984.43 | 1766 |

Parameter | Value |
---|---|

Module width | 1.134 m |

Module length | 2.274 m |

Tilt angle | 13° |

Installed inter-row spacing | 1.8 m |

Actual Total area | 370 m^{2} |

Parameter | Value |
---|---|

h between (A1 and A2, A2 and A3) | 20 cm |

h between (A3 and A4) | 30 cm |

Azimuth angle | 50° |

Elevation angle | 32° |

Inter-row spacing factor | 1.03, (4) |

Inter-row spacing between (A1 and A2, A2 and A3) | 1.26 m, (6) |

Inter-row spacing between (A3 and A4) | 1.36 m, (6) |

Required area | 310.17 m^{2}, (8) |

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**MDPI and ACS Style**

Al-Quraan, A.; Al-Mahmodi, M.; Alzaareer, K.; El-Bayeh, C.; Eicker, U.
Minimizing the Utilized Area of PV Systems by Generating the Optimal Inter-Row Spacing Factor. *Sustainability* **2022**, *14*, 6077.
https://doi.org/10.3390/su14106077

**AMA Style**

Al-Quraan A, Al-Mahmodi M, Alzaareer K, El-Bayeh C, Eicker U.
Minimizing the Utilized Area of PV Systems by Generating the Optimal Inter-Row Spacing Factor. *Sustainability*. 2022; 14(10):6077.
https://doi.org/10.3390/su14106077

**Chicago/Turabian Style**

Al-Quraan, Ayman, Mohammed Al-Mahmodi, Khaled Alzaareer, Claude El-Bayeh, and Ursula Eicker.
2022. "Minimizing the Utilized Area of PV Systems by Generating the Optimal Inter-Row Spacing Factor" *Sustainability* 14, no. 10: 6077.
https://doi.org/10.3390/su14106077