# New Omnidirectional Sensor Based on Open-Source Software and Hardware for Tracking and Backtracking of Dual-Axis Solar Trackers in Photovoltaic Plants

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## Abstract

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## 1. Introduction

#### 1.1. Literature Review on Solar Tracking

#### 1.2. Literature Review on Free and Open-Source Hardware and Software Applied to PV Energy

## 2. Proposed Design

#### 2.1. Algorithm for the Detection of Inter-Shading between Collectors

- The width $\left(\mathit{a}\right)$ and height $\left(\mathit{b}\right)$ of the solar collectors.
- The set of Cartesian coordinates$\left(\mathit{x},\mathit{y},\mathit{z}\right)$ of the base of each solar tracker, using as a reference system a local coordinate system in which the Ox axis goes to the West, the Oy to the South and the Oz to the point Zenith. This information is structured by three arrays$\mathit{x}\left. [\mathit{i}\right],\mathit{y}\left. [\mathit{i}\right],\mathit{z}\left. [\mathit{i}\right]$ in which $\mathit{i}$ is the index assigned to each solar tracker (Figure 1), so that$1\mathit{i}\mathit{N}$ is verified, where $\mathit{N}$ is the number of trackers in the installation.
- The solar vector or unit vector that points to the solar disk at each instant of time that, in the reference system considered, is given by the Equation (1):$$\begin{array}{c}\overrightarrow{\mathit{s}}={\mathit{s}}_{\mathit{x}}\overrightarrow{\mathit{i}}+{\mathit{s}}_{\mathit{y}}\overrightarrow{\mathit{j}}+{\mathit{s}}_{\mathit{z}}\overrightarrow{\mathit{k}}=\\ =\mathrm{sin}\Omega \mathit{t}\mathrm{cos}\delta \overrightarrow{\mathit{i}}+\\ +\left(\mathrm{cos}\Omega \mathit{t}\mathrm{cos}\delta \mathrm{sin}\phi -\mathrm{sin}\delta \mathrm{cos}\phi \right)\overrightarrow{\mathit{j}}+\\ +\left(\mathrm{cos}\Omega \mathit{t}\mathrm{cos}\delta \mathrm{cos}\phi +\mathrm{sin}\delta \mathrm{sin}\phi \right)\overrightarrow{\mathit{k}},\end{array}$$$$\begin{array}{c}\delta \left(\mathit{r}\mathit{a}\mathit{d}\right)=[0.006918-0.399912\mathrm{cos}\left(\Gamma \right)+\\ +0.070257\mathrm{sin}\left(\Gamma \right)-0.006758\mathrm{cos}\left(2\Gamma \right)+\\ +0.000907\mathrm{sin}\left(2\Gamma \right)-0.002697\mathrm{cos}\left(3\Gamma \right)+\\ +0.00148\mathrm{sin}\left(3\Gamma \right)],\end{array}$$$$\Gamma \left(\mathit{r}\mathit{a}\mathit{d}\right)=\frac{2\pi ({\mathit{d}}_{\mathit{j}}-1)}{365}.$$
- The unit vector $\overrightarrow{\mathit{n}}$, which indicates the direction towards which the solar trackers are oriented, being perpendicular to the collectors, and which is given by the Equation (4).$$\overrightarrow{\mathit{n}}=\mathrm{cos}\alpha \xb7\mathrm{sin}\gamma \overrightarrow{i}+\mathrm{cos}\alpha \xb7\mathrm{cos}\gamma \overrightarrow{\mathit{j}}+\mathrm{sin}\alpha \overrightarrow{\mathit{k}},$$
- The unit vectors $\overrightarrow{\mathit{u}}$ y $\overrightarrow{\mathit{v}}$ included in the collector plane, where $\overrightarrow{\mathit{u}}$ is horizontal (Equation (5)) and $\overrightarrow{\mathit{v}}$ (Equation (6)) perpendicular to $\overrightarrow{\mathit{u}}$.$$\overrightarrow{\mathit{u}}=-\mathrm{cos}\gamma \overrightarrow{\mathit{i}}+\mathrm{sin}\gamma \overrightarrow{\mathit{j}},$$$$\overrightarrow{\mathit{v}}=\mathrm{sin}\alpha \xb7\mathrm{cos}\gamma \overrightarrow{\mathit{i}}-\mathrm{sin}\alpha \xb7\mathrm{cos}\gamma \overrightarrow{\mathit{j}}+\mathrm{cos}\alpha \overrightarrow{\mathit{k}}.$$

#### 2.2. Design of the Proposed Technological Solution

- Sensors: On the one hand, the system includes a sensor system whose purpose is to know the solar time corresponding to orientations that are not allowed because they cause inter-shading between the collectors. For this, among the different options to obtain the time (internal clock of the microcontroller, time server or external RTC module), in this prototype, a DS1307 real-time clock has been chosen, with autonomous power supply by means of a CR2025 battery. Likewise, for the irradiance measurement, a calibrated photovoltaic cell of the Fadisol C-0121 type has been used that provides a linear current output with respect to irradiance, comprised between 36 mA for 125 W/m
^{2}and 288 mA for 1000 W/m^{2}. The measurement of the intensity of the electric current provided by these short-circuited photovoltaic cells is measured by means of an INA219 module, consisting of a shunt equipped with a 12-bit analog-digital converter and I2C output. In this way, adjusting the gain in the module configuration, an accuracy of 0.1 mA and a maximum intensity of 400 mA are obtained. Finally, an initialisation of the azimuth and elevation position has been provided, using two mechanical micro-switches that indicate the zero relative position to the microcontroller. - Processing: In the philosophy of this work, several alternatives for processing have been evaluated, opting for a TTGO ESP32 Lora development board. The ESP32 microcontroller integrates analog and digital inputs and outputs, as well as various communication interfaces, both wireless (Wi-Fi and Bluetooth Low Energy) and wired (I2C, SPI, UART). The selected board also has a LoRa communication module, model SEMTECH SX1276 that enables communication at a frequency of 868 MHz.
- Drive: Two 28BYJ-48 stepper motors, powered at 5 V, with 4096 steps per revolution that provide a maximum precision of 0.001534 radians, have been used to drive the two axes of movement of the omnidirectional server presented. The management of the stepper motors requires a controller, for which two units of the type LM298 have been used.
- Communications: Finally, it has been considered that the communications between the position server and the solar trackers require a range according to the typical dimensions of photovoltaic installations. The receiving devices of the orientation command can be arranged in a radius of up to 15 km around the server [61], which is achieved with direct vision between antennas, in optimal conditions, while in unfavourable conditions, such as suburban areas, 3 km are reached [62].

## 3. Results

^{2}) measurements are made, which are represented by the corresponding iso-level curves (grey lines).

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Glossary

$\mathit{a}$ | solar collector width |

$\mathit{b}$ | solar collector height |

${\mathit{d}}_{\mathit{j}}$ | Julian day |

$\mathit{i}$ | index assigned to each solar tracker |

$\mathit{j}$ | secondary index assigned to each solar tracker ($\mathit{i}\ne \mathit{j})$ |

$\mathit{N}$ | number of solar trackers in the installation |

$\overrightarrow{\mathit{i}},\overrightarrow{\mathit{j}},\overrightarrow{\mathit{k}}$ | unit vectors associated to a local Cartesian system |

$\overrightarrow{\mathit{s}}$ | solar vector |

${\mathit{s}}_{\mathit{x}},{\mathit{s}}_{\mathit{y}},{\mathit{s}}_{\mathit{z}}$ | components of solar vector |

$\overrightarrow{\mathit{n}}$ | unit vector perpendicular to the collector surface that indicates the direction towardsthe tracker is oriented |

$\overrightarrow{\mathit{u}}$ | unit horizontal vector included in the collector plane |

$\overrightarrow{\mathit{v}}$ | unit vector included in the collector plane and perpendicular to $\overrightarrow{\mathit{u}}$ |

$\mathit{t}$ | specific solar hour |

$\mathit{x},\mathit{y},\mathit{z}$ | Cartesian coordinates of the base of each solar tracker |

$\mathit{x}\left. [\mathit{i}\right],\mathit{y}\left. [\mathit{i}\right],\mathit{z}\left. [\mathit{i}\right]$ | arrays containing information about coordinates of each solar tracker |

Greek Letters | |

$\alpha $ | elevation angle of the collector |

$\gamma $ | azimuth angle of the collector rotation axis |

$\phi $ | latitude |

$\Omega $ | Earth’s rotation speed |

$\delta $ | solar declination |

$\theta $ | angle of incidence of sunbeams on the inclined plane |

$\Gamma $ | auxiliary angular magnitude dependent on the Julian day |

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**Figure 3.**(

**a**) Design of the system, (

**b**) electronical components, and (

**c**) photography of the prototype.

**Figure 6.**Simulation of the irradiance (W/m

^{2}) values registered by the proposed device and the fragmentation of the celestial sphere at different moments of time: (

**a**) 21 December at 8:24 a.m. in True Solar Time, (

**b**) 21 December at 15:24 p.m. in True Solar Time, (

**c**) 21 June at 7:30 a.m. in True Solar Time, and (

**d**) 21 June at 15:48 p.m. in True Solar Time.

Tracker | x (m) | y (m) | z (m) |
---|---|---|---|

1 | 18.50 | 22.70 | 0.00 |

2 | 22.29 | 40.70 | 0.00 |

3 | 26.08 | 58.71 | 0.00 |

4 | 29.88 | 76.71 | 0.00 |

5 | 33.67 | 94.72 | 0.00 |

6 | 37.46 | 112.72 | 0.00 |

7 | 41.50 | 17.86 | 0.00 |

8 | 45.29 | 35.86 | 0.00 |

9 | 49.08 | 53.87 | 0.00 |

10 | 52.87 | 71.87 | 0.00 |

11 | 56.66 | 89.88 | 0.00 |

12 | 60.46 | 107.88 | 0.00 |

13 | 64.49 | 13.01 | 0.00 |

14 | 68.28 | 31.02 | 0.00 |

15 | 72.08 | 49.02 | 0.00 |

16 | 75.87 | 67.03 | 0.00 |

17 | 79.66 | 85.03 | 0.00 |

18 | 83.45 | 103.04 | 0.00 |

19 | 87.49 | 8.17 | 0.00 |

20 | 91.28 | 26.17 | 0.00 |

21 | 95.07 | 44.18 | 0.00 |

22 | 98.86 | 62.18 | 0.00 |

23 | 102.66 | 80.19 | 0.00 |

24 | 106.45 | 98.19 | 0.00 |

25 | 114.27 | 21.33 | 0.00 |

26 | 118.07 | 39.34 | 0.00 |

27 | 121.86 | 57.34 | 0.00 |

28 | 125.65 | 75.35 | 0.00 |

29 | 129.44 | 93.35 | 0.00 |

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**MDPI and ACS Style**

Gómez-Uceda, F.J.; Ramirez-Faz, J.; Varo-Martinez, M.; Fernández-Ahumada, L.M.
New Omnidirectional Sensor Based on Open-Source Software and Hardware for Tracking and Backtracking of Dual-Axis Solar Trackers in Photovoltaic Plants. *Sensors* **2021**, *21*, 726.
https://doi.org/10.3390/s21030726

**AMA Style**

Gómez-Uceda FJ, Ramirez-Faz J, Varo-Martinez M, Fernández-Ahumada LM.
New Omnidirectional Sensor Based on Open-Source Software and Hardware for Tracking and Backtracking of Dual-Axis Solar Trackers in Photovoltaic Plants. *Sensors*. 2021; 21(3):726.
https://doi.org/10.3390/s21030726

**Chicago/Turabian Style**

Gómez-Uceda, Francisco J., José Ramirez-Faz, Marta Varo-Martinez, and Luis Manuel Fernández-Ahumada.
2021. "New Omnidirectional Sensor Based on Open-Source Software and Hardware for Tracking and Backtracking of Dual-Axis Solar Trackers in Photovoltaic Plants" *Sensors* 21, no. 3: 726.
https://doi.org/10.3390/s21030726