# A Practical Approach for Estimating the Optimum Tilt Angle of a Photovoltaic Panel for a Long Period—Experimental Recorded Data

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## Abstract

**:**

## 1. Introduction

#### 1.1. Solar Energy

^{15}TW, and the energy from the latter’s radiation that reaches the earth every day is 100,000 times the amount of the energy produced by all power plants in the world. Therefore, given the sun, there will be no potential energy shortage globally, and solar energy is equivalent to 20,000 times the current human consumption. This amount seems to be an excellent source to meet human needs, especially because its use does not cause any environmental damage or pollution [1,2,3].

#### 1.2. Literature Review of the Existing Studies

#### 1.3. Empirical Approach Background

#### 1.4. Aim of Current Study

## 2. Methods

#### 2.1. Theory

#### 2.2. Calculation of Daily Solar Radiation on Horizontal Surfaces Outside the Atmosphere

## 3. Results

#### 3.1. Monthly Tilt Angle

^{2}and the lowest amount of radiation in July was 18.07 MJ/m

^{2}. As evidenced in Figure 4, the highest amount of radiation was received in November.

^{2}and by increasing the tilt, the amount of radiation increases to 22.52 MJ/m

^{2}at an angle of 62 degrees—this tilt angle is optimal. For January and following months, by increasing the tilt, the amount of radiation on the photovoltaic panel decreases and reaches 21 MJ/m

^{2}for the vertical plate.

#### 3.2. Seasonal Tilt Angle

#### 3.3. Six-Month Tilt Angle

## 4. Discussion

_{2}emission, and sustainable energy are significant considerations; this paper shows it is necessary to focus on the optimum tilt angle, based on maximum sustainable energy absorption. Previous studies say that the annual tilt angle, or changing the angle bi-annually, is suitable, and it is without significant change to the monthly tilt angle set up [1,2,22]. It seems this statement was focused on minimizing inclined surface setup, but with the current experimental study in a specified city, there is about 6–7% distinction for changing the angle two or four times per year. This difference mentions how much energy will be lost during decades. Although, based on the capacity of the solar power plant, this 6–7% could be a significant amount of energy. With a consideration of the monthly tilt angle, for summer months, there is about 20% more energy received with a monthly tilt angle than an annual tilt angle. Usually, in places with high solar energy potential—the subject of this study—such as Middle Eastern countries, the summer months have warm weather, such that power consumption goes up because of air conditioning and cooling systems. Therefore, the base power grid will need more production to support the electricity demand. It is possible to have a monthly tilt angle that produces 20% more power than the annual tilt angle.

## 5. Conclusions

- -
- In the summer, the inclined surface is adjusted with a monthly tilt angle.
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- For the rest of the year, an annual tilt angle is set up.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Changes in daily average monthly radiation on the solar panel facing south for different slope angles in Tehran during the year’s first six months.

**Figure 4.**Changes in daily average monthly radiation on the solar panel facing south for different slope angles in Tehran during the second half of the year.

**Figure 6.**Monthly total radiation gained for inclined surface with tilt angle set up monthly, seasonally, bi-annually, and annually, respectively.

**Figure 7.**Annual total radiation gained for inclined surface with tilt angle set up monthly, seasonally, bi-annually, and annually.

**Figure 9.**Optimal tilt angle changes and changes in the maximum amount of incoming radiation in the months of the year.

Month | $\mathbf{n}$ | $\overline{\mathbf{H}}$ $(\mathbf{M}\mathbf{j}/{\mathbf{m}}^{2})$ | ${\overline{\mathbf{H}}}_{\mathbf{d}}$ $(\mathbf{M}\mathbf{j}/{\mathbf{m}}^{2})$ | ${\overline{\mathbf{H}}}_{\mathbf{b}}$ $(\mathbf{M}\mathbf{j}/{\mathbf{m}}^{2})$ | ${\mathbf{H}}_{0}$ $(\mathbf{M}\mathbf{j}/{\mathbf{m}}^{2})$ | ${\overline{\mathbf{K}}}_{\mathbf{T}}$ |
---|---|---|---|---|---|---|

January | 17 | 11.92 | 2.92 | 8.99 | 17.85 | 0.66 |

February | 47 | 14.85 | 3.89 | 10.95 | 22.93 | 0.64 |

March | 75 | 16.82 | 6.07 | 10.74 | 29.30 | 0.57 |

April | 105 | 17.98 | 7.64 | 10.33 | 35.67 | 0.50 |

May | 135 | 18.47 | 8.61 | 9.85 | 39.94 | 0.46 |

June | 162 | 18.65 | 8.96 | 9.68 | 41.60 | 0.44 |

July | 198 | 18.07 | 8.77 | 9.29 | 40.72 | 0.44 |

August | 228 | 18.51 | 8.01 | 10.49 | 37.31 | 0.49 |

September | 258 | 18.34 | 6.53 | 11.80 | 31.65 | 0.57 |

October | 288 | 15.81 | 4.85 | 10.95 | 24.86 | 0.63 |

November | 318 | 12.60 | 3.17 | 4.42 | 19.09 | 0.66 |

December | 344 | 10.77 | 2.76 | 8.00 | 16.45 | 0.65 |

**Table 2.**Daily average monthly radiation incident on an inclined surface under various settings $\frac{\mathrm{MJ}}{{\mathrm{m}}^{2}}.$

Monthly Period | ${\mathsf{\beta}}_{\mathbf{o}\mathbf{p}\mathbf{t}}$ (Degree) | $\overline{{\mathbf{H}}_{\mathbf{t}}}$$(\mathbf{M}\mathbf{j}/{\mathbf{m}}^{2})$ | Seasonal Period | ${\mathsf{\beta}}_{\mathbf{o}\mathbf{p}\mathbf{t}}$ (Degree) | $\overline{{\mathbf{H}}_{\mathbf{t}}}$$(\mathbf{M}\mathbf{j}/{\mathbf{m}}^{2})$ | Bi-Annual Period | ${\mathsf{\beta}}_{\mathbf{o}\mathbf{p}\mathbf{t}}$ (Degree) | $\overline{{\mathbf{H}}_{\mathbf{t}}}$$(\mathbf{M}\mathbf{j}/{\mathbf{m}}^{2})$ | Annual Period | ${\mathsf{\beta}}_{\mathbf{o}\mathbf{p}\mathbf{t}}$ (Degree) | $\overline{{\mathbf{H}}_{\mathbf{t}}}$$(\mathbf{M}\mathbf{j}/{\mathbf{m}}^{2})$ |
---|---|---|---|---|---|---|---|---|---|---|---|

January | 62 | 22.52 | Winter | 51 | 22.14 | Cold Months | 54 | 23.13 | Annually | 40 | 21.04 |

February | 53 | 22.29 | 22.28 | 22.29 | 21.83 | ||||||

March | 36 | 19.71 | 19.22 | 19.00 | 19.68 | ||||||

April | 18 | 18.56 | Spring | 6 | 18.30 | Hot Months | 11 | 18.48 | 17.60 | ||

May | 3 | 18.48 | 18.47 | 18.38 | 16.26 | ||||||

June | −3 | 18.67 | 18.51 | 18.32 | 15.75 | ||||||

July | −1 | 18.07 | Summer | 15 | 17.67 | 17.85 | 15.54 | ||||

August | 11 | 18.74 | 18.71 | 18.74 | 17.24 | ||||||

September | 33 | 20.25 | 19.79 | 19.50 | 19.98 | ||||||

October | 47 | 21.40 | Fall | 57 | 21.16 | Cold Months | 54 | 21.28 | 21.26 | ||

November | 60 | 22.23 | 22.21 | 22.13 | 21.08 | ||||||

December | 64 | 21.56 | 21.40 | 21.25 | 19.87 |

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**MDPI and ACS Style**

Hassanian, R.; Riedel, M.; Yeganeh, N.; Unnthorsson, R. A Practical Approach for Estimating the Optimum Tilt Angle of a Photovoltaic Panel for a Long Period—Experimental Recorded Data. *Solar* **2021**, *1*, 41-51.
https://doi.org/10.3390/solar1010005

**AMA Style**

Hassanian R, Riedel M, Yeganeh N, Unnthorsson R. A Practical Approach for Estimating the Optimum Tilt Angle of a Photovoltaic Panel for a Long Period—Experimental Recorded Data. *Solar*. 2021; 1(1):41-51.
https://doi.org/10.3390/solar1010005

**Chicago/Turabian Style**

Hassanian, Reza, Morris Riedel, Nashmin Yeganeh, and Runar Unnthorsson. 2021. "A Practical Approach for Estimating the Optimum Tilt Angle of a Photovoltaic Panel for a Long Period—Experimental Recorded Data" *Solar* 1, no. 1: 41-51.
https://doi.org/10.3390/solar1010005