# Development of a Solar-Tracking System for Horizontal Single-Axis PV Arrays Using Spatial Projection Analysis

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## Abstract

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## 1. Introduction

## 2. Modeling of Automatic Tracking for Horizontal Single-Axis PV Arrays on Sloping Terrain

#### 2.1. Formulation of Solar Irradiance Intensity

_{h}is composed of direct irradiance intensity I

_{bh}and diffuse irradiance intensity I

_{dh}[21], which can be expressed as:

_{0}is the solar irradiance at the top of the vertical atmospheric boundary (W/m

^{2}).

_{t}is determined by the direct irradiance I

_{bt}, diffuse irradiance I

_{dt}and reflected irradiance I

_{rt}. Given the tilt angle β and the azimuth angle γ (0° for true south, 90° for true west and −90° for true east) of the tilted surface, the total solar irradiance on the tilted surface can be calculated by converting the irradiance components on the horizontal plane [22], which then can be determined by:

#### 2.2. Shadow Modelling for the Horizontal Single-Axis Tracker

#### 2.2.1. Shadow Model on the Horizontal Plane

_{y}, the width is a

_{y}and the shaded area is C. The horizontal spacing of the PV array is L, the inclination angle of the PV panel is β (positive facing west, negative facing east), the solar altitude angle is h, and the solar azimuth angle is α (with due south as 0°, positive westward and negative eastward). As demonstrated in the figure, the shading of the PV array would be affected by the position of the sun, as well as the array dimensions. The geometric relationship between the width of the shaded area and the width of the PV string, spacing and solar altitude angle can be presented as in Figure 1b,c. Thus, the shaded width a

_{y}can be determined via Equation (9).

_{y}can be expressed as:

#### 2.2.2. Shadow Model on the Sloping Terrain

_{y}′ (with a relative decrease amount of Δa

_{y}) compared to the scenario of arrays on the horizontal ground. According to the geometric relationships shown in Figure 3b,c, the formula for the width of the shadow a

_{y}′ can be obtained from:

_{y}′ is limited by the dimensions of the string, its value range should be [0, a], where a

_{y}′ < 0 means that the rear PV string would not be affected by the shadow; thus, a

_{y}′ can be set as 0. a

_{y}′ > a means the shadow width has exceeded the rear PV string, and a

_{y}′ needs to be set as a.

_{y}′. Based on Equation (10), the formula for b

_{y}′ calculation can be expressed as:

_{y}′ ≤ b. Similarly, when b

_{y}′ < 0, set b

_{y}′ as 0; when b

_{y}′ > b, set b

_{y}′ as b.

#### 2.3. Horizontal Single-Axis Tracking Strategy for Sloping Terrain

#### 2.4. PV Power Output Model

_{sh}connected in parallel, and then connected in series with a resistance R

_{s}. In this circuit, the photocurrent I

_{ph}from the current source flows out in three directions, the forward current I

_{d}of the diode, the shunt resistance current I

_{sh}, and the output current I flows through the series resistance R

_{s}to the load [23].

_{p}is the number of PV cells connected in parallel, while N

_{s}represents the number of PV cells connected in series, I

_{r}denotes reverse saturation current, R

_{s}is the equivalent series resistance (Ω) of the load, R

_{sh}is the equivalent parallel resistance (Ω) of the load, V is the output voltage (V), T refers to the PV module temperature (K), q represents electron charge (C), n is the diode ideality factor, and K is the Boltzmann constant. The photocurrent I

_{ph}is affected by the irradiance received by the PV module, which can be formulated as:

_{sc}represents the short-circuit current (A), k

_{i}is the temperature coefficient of the photocurrent and T

_{n}refers to the reference temperature (with a default value of 298 K).

_{ph}is substituted into Equation (20) to obtain the theoretical I–V characteristic curve and output power of the PV module. Finally, the experimental data are compared and analyzed.

## 3. Simulation of a Flat Uniaxial Tracking Strategy on Sloping Terrain

#### 3.1. Site Characteristic Parameters

#### 3.2. Development of Simulation Modules

#### 3.3. Winter Solstice Typical Moments Simulation

_{Gmax}can be obtained by solving for the maximum value of the function G(β).

#### 3.4. Simulation Analysis of Different Sloping Terrains on the Winter Solstice

_{t}(β); therefore, the optimal tracking angle β corresponds to the slope angle i where I

_{t}is maximum. However, as shown in Equations (4)–(8), the calculation value of I

_{t}is independent of the slope angle I; thus, the tracking angles of horizontal single-axis arrays on different slopes are the same.

_{max}obtained by the PV array is 60.90% of that on the 9° slope, indicating that the slope topography factor has a significant impact on the irradiance that a fixed-axis array can receive at a given time. (2) Given a tracking strategy without consideration of the slope topography factors, according to the G-β curve on the 0° slope, it can be seen that the tracking angles on each slope are 23.5°. Compared with the β

_{Gmax}on each slope, as the tracking angles of the array on −9°, −6° and −3° slopes are too large, the corresponding G values are reduced by 25.59%, 13.22% and 6.69%, respectively. The tracking angles of the array on 9°, 6° and 3° slopes are too small, resulting in a decrease in G values by 14.60%, 14.60% and 8.39%, respectively. (3) For a fixed-axis array on 6° and 9° slopes, S = 0 can be satisfied with any tracking angle β, since the G-β curve on the 6° slope coincides with that on the 9° slope.

_{Gmax}and the average solar irradiance intensity G

_{max}considering seven typical slope scenarios on a winter solstice day. According to the solar altitude and azimuth angles presented in Figure 6, it can be seen that the power generation period on the winter solstice day mainly concentrates from 8:00 to 17:30. With a time step of 5 min, the β

_{Gmax}and G

_{max}curves on each slope scenario can be obtained and shown as in Figure 9.

## 4. Comparative Study and On-Site Validation

#### 4.1. Comparison of Simulation Results

#### 4.2. On-Site Validations

## 5. Concluding Remarks

_{Gmax}can be obtained by solving the maximum value of the G(β) function, which then can be used in the automatic solar tracking of the PV arrays.

_{Gmax}on various sloping terrains, leading to a decrease in the harvesting of average solar irradiance and thus reducing the energy production of PV systems.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

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**Figure 1.**Shading of PV strings on the horizontal ground: (

**a**) Shading illustration, (

**b**) Sideview of cross-section, (

**c**) Geometric interactions.

**Figure 3.**Shading of PV strings on the sloping terrain: (

**a**) Shading illustration, (

**b**) Sideview of cross-section, (

**c**) Geometric interactions.

**Figure 9.**Comparison of tracking angles and average irradiance intensity over slope terrains, (

**a**) Tracking angles, (

**b**) Average irradiance intensity.

**Figure 10.**Comparison of simulation results: (

**a**) Tracking angles, and (

**b**) Average irradiance and PV power output.

**Figure 11.**Comparison of experimental results with the two tracking strategies: (

**a**) FTT (

**left**) and STT (

**right**) at 16:30, (

**b**) Shading area ratio and PV power output, (

**c**) Monitoring array power output and daily electricity production and (

**d**) Comparison of the array’s annual electricity yield.

Key Parameters | Values |
---|---|

Latitude φ | 38.67 °N |

Longitude e | 106.67 °E |

Slope angle i | −9°~+9° |

Width of PV string a | 1.984 m |

Length of PV string b | 26.784 m |

Number of strings in a PV array | 16 |

Number of PV panels in a string | 27 |

Horizontal array spacing L | 5.00 m |

Ground reflectance ρ | 0.20 |

Atmospheric transparency coefficient P | 0.703 |

Key Parameters | Values |
---|---|

Rated power | 365 W |

Short-circuit current | 9.84 A |

Open-circuit voltage | 47.85 V |

Operating temperature | −40 °C~+80 °C |

Module dimensions | 1984 × 992 × 30 mm |

Mass | 26 ± 0.5 kg |

N_{p} | 3 |

N_{s} | 24 |

Cell type | Monocrystalline silicon |

Tracking range * | −45°~+45° |

Sloping Angle i | Solar Irradiance (W·h/m^{2}) | Difference (Based on I = 0°) |
---|---|---|

−9° | 2735.83 | −3.1% |

−6° | 2778.20 | −1.6% |

−3° | 2811.77 | −0.4% |

0° | 2824.06 | 0.0% |

3° | 2813.54 | −0.4% |

6° | 2779.82 | −1.6% |

9° | 2736.09 | −3.1% |

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**MDPI and ACS Style**

Huang, B.; Huang, J.; Xing, K.; Liao, L.; Xie, P.; Xiao, M.; Zhao, W.
Development of a Solar-Tracking System for Horizontal Single-Axis PV Arrays Using Spatial Projection Analysis. *Energies* **2023**, *16*, 4008.
https://doi.org/10.3390/en16104008

**AMA Style**

Huang B, Huang J, Xing K, Liao L, Xie P, Xiao M, Zhao W.
Development of a Solar-Tracking System for Horizontal Single-Axis PV Arrays Using Spatial Projection Analysis. *Energies*. 2023; 16(10):4008.
https://doi.org/10.3390/en16104008

**Chicago/Turabian Style**

Huang, Bin, Jialiang Huang, Ke Xing, Lida Liao, Peiling Xie, Meng Xiao, and Wei Zhao.
2023. "Development of a Solar-Tracking System for Horizontal Single-Axis PV Arrays Using Spatial Projection Analysis" *Energies* 16, no. 10: 4008.
https://doi.org/10.3390/en16104008