# Influence of Solar Position Calculation Methods Applied to Horizontal Single-Axis Solar Trackers on Energy Generation

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## Abstract

**:**

## 1. Introduction

## 2. Solar Position Calculation Algorithms

#### 2.1. Solar Position Algorithm (SPA)

#### 2.2. Grena

## 3. Materials and Methods

#### 3.1. Pvlib Tool and Simulations

#### 3.2. PV Model

#### 3.3. Methodology

## 4. Results

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AA | Astronomical Almanac |

CPU | Central Process Unit |

CSP | Concentrated Solar Power |

DHI | Diffuse Horizontal Irradiance |

DNI | Direct Normal Irradiance |

GHI | Global Horizontal Irradiance |

MPPT | Maximum Power Point Tracking |

NOAA | National Oceanic and Atmospheric Administration |

PV | Photovoltaic |

PVPMC | Photovoltaic Performance and Modeling Collaboration |

SPA | Solar Position Algorithm |

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**Figure 5.**Error in relation to ideal scenario for: (

**a**) Araçariguama, Brazil; (

**b**) Cape Town, South Africa; (

**c**) Kiruna, Sweden.

Equipment | Brand | Model | Power | Amount |
---|---|---|---|---|

Photovoltaic module | Talesun Solar^{®} | TP762M-310 | 310 Wp | 6 |

Inverter | Fronius International^{®} | IG Plus 55 V-1 | 5 kW | 1 |

Scenario | Algorithm Used to Calculate the Real Sun Position | Algorithm Used by Solar Trackers |
---|---|---|

1 | NOAA | NOAA |

2 | NOAA | SPA |

3 | NOAA | GRENA 1 |

4 | NOAA | GRENA 2 |

5 | NOAA | GRENA 3 |

6 | NOAA | GRENA 4 |

7 | NOAA | GRENA 5 |

**Table 3.**Result of energy generation estimation using different algorithms for Sun tracking in Araçariguama, Brazil.

Scenario | Algorithm Used by Sinle-Axis Solar Trackers | Energy Generation Estimation (MWh) | ||||
---|---|---|---|---|---|---|

Isotropic | Reindl | Klucher | Hay | Perez | ||

1 | NOAA | 6.012594 | 6.338760 | 6.325719 | 6.305979 | 6.543707 |

2 | SPA | 6.012589 | 6.338758 | 6.325716 | 6.305976 | 6.543706 |

3 | GRENA 1 | 6.012265 | 6.338174 | 6.325364 | 6.305391 | 6.543678 |

4 | GRENA 2 | 6.012222 | 6.338105 | 6.325319 | 6.305324 | 6.543659 |

5 | GRENA 3 | 6.012219 | 6.338104 | 6.325317 | 6.305321 | 6.543657 |

6 | GRENA 4 | 6.012219 | 6.338103 | 6.325317 | 6.305321 | 6.543657 |

7 | GRENA 5 | 6.012218 | 6.338103 | 6.325316 | 6.305321 | 6.543657 |

**Table 4.**Result of energy generation estimation using different algorithms for Sun tracking in Cape Town, South Africa.

Scenario | Algorithm Used by Sinle-Axis Solar Trackers | Energy Generation Estimation (MWh) | ||||
---|---|---|---|---|---|---|

Isotropic | Reindl | Klucher | Hay | Perez | ||

1 | NOAA | 8.069870 | 8.564122 | 8.405154 | 8.538255 | 8.549887 |

2 | SPA | 8.069754 | 8.563903 | 8.405026 | 8.538035 | 8.549813 |

3 | GRENA 1 | 8.068618 | 8.561675 | 8.403759 | 8.535820 | 8.549020 |

4 | GRENA 2 | 8.068471 | 8.561373 | 8.403594 | 8.535521 | 8.548916 |

5 | GRENA 3 | 8.067663 | 8.559537 | 8.402732 | 8.533688 | 8.548169 |

6 | GRENA 4 | 8.067663 | 8.559538 | 8.402732 | 8.533688 | 8.548170 |

7 | GRENA 5 | 8.067663 | 8.559538 | 8.402733 | 8.533689 | 8.548171 |

**Table 5.**Result of energy generation estimation using different algorithms for Sun tracking in Kiruna, Sweden.

Scenario | Algorithm Used by Sinle-Axis Solar Trackers | Energy Generation Estimation (MWh) | ||||
---|---|---|---|---|---|---|

Isotropic | Reindl | Klucher | Hay | Perez | ||

1 | NOAA | 3.393033 | 3.637877 | 3.548495 | 3.623429 | 3.841570 |

2 | SPA | 3.393026 | 3.637872 | 3.548489 | 3.623424 | 3.841570 |

3 | GRENA 1 | 3.392167 | 3.636253 | 3.547614 | 3.621843 | 3.840457 |

4 | GRENA 2 | 3.392249 | 3.636323 | 3.547680 | 3.621917 | 3.840865 |

5 | GRENA 3 | 3.392271 | 3.636339 | 3.547702 | 3.621935 | 3.840877 |

6 | GRENA 4 | 3.392268 | 3.636337 | 3.547698 | 3.621932 | 3.840876 |

7 | GRENA 5 | 3.392269 | 3.636339 | 3.547700 | 3.621933 | 3.840877 |

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**MDPI and ACS Style**

Melo, K.B.d.; Moreira, H.S.; Villalva, M.G.
Influence of Solar Position Calculation Methods Applied to Horizontal Single-Axis Solar Trackers on Energy Generation. *Energies* **2020**, *13*, 3826.
https://doi.org/10.3390/en13153826

**AMA Style**

Melo KBd, Moreira HS, Villalva MG.
Influence of Solar Position Calculation Methods Applied to Horizontal Single-Axis Solar Trackers on Energy Generation. *Energies*. 2020; 13(15):3826.
https://doi.org/10.3390/en13153826

**Chicago/Turabian Style**

Melo, Karen Barbosa de, Hugo Soeiro Moreira, and Marcelo Gradella Villalva.
2020. "Influence of Solar Position Calculation Methods Applied to Horizontal Single-Axis Solar Trackers on Energy Generation" *Energies* 13, no. 15: 3826.
https://doi.org/10.3390/en13153826