# Prediction Model of Photovoltaic Module Temperature for Power Performance of Floating PVs

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## Abstract

**:**

## 1. Introduction

## 2. Floating PV System Introduction and Performance

#### 2.1. Site Information of Floating PV System

#### 2.2. Power Outputs of Floating PV Versus Rooftop-Based System

## 3. Methodology of Floating PV Temperature Model

## 4. FPV Temperature Model Results and Comparisons

#### 4.1. Model Results

#### 4.2. Comparison with Land-Based PV System

#### 4.3. Comparison with Selected Temperature Models

#### 4.4. Comparison of Models with Minitab Model

## 5. FPV Module Efficiency and Power Prediction

## 6. Conclusions

_{a}), solar irradiance (G

_{t}), and wind speeds (V

_{w}). When compared to the measured FPV module temperature over entire year, the error of model 1 is 2%. Model 2 includes the three aforementioned independent variables in addition to water temperature (T

_{w}). Although the error of Model 2 increases slightly to 4%, the results are within the reasonable range of error. Fitting of the experimental data is reproduced with a minor error.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Monthly daily average energy of the month (kWh) and corresponding normalized power comparisons for FPV systems vs. 1000 kW rooftop system.

**Figure 6.**Histograms comparison of FPV Model 1 (

**a**), Model 2 (

**b**), Minitab data fitting model (

**c**), and module field data (

**d**).

**Figure 8.**(

**a**) Time series plot of module efficiency (Model 1); (

**b**) efficiency over module temperature.

Sensor Type | Maker | Model | Accuracy | Range | Mounting |
---|---|---|---|---|---|

Solar Irradiance | Apogee | SP-110 | ±5% | 0–1750 Wm^{2} | Leveling fixture |

Anemometer (Wind Speed) | Jinyang | WM-IV-WS | ±0.15 m/s | 0–75 m/s | Pole mount |

Accelerometer | Das | MSENS-IN360 | 0.10° | 0–360° | Pole mount |

Humidity and Temperature Probe | Vaisala | HMP155 | ±0.176% | −80–60 °C | Protective housing |

PVM Temperature | Taeyeon | DY-HW-7NN | ±0.20% | −5–55 °C | PVM rear surface |

Water Temperature | Taeyeon | DY-HW-11NN | ±0.20% | −5–55 °C | Water submerged |

Project Type | Test Bed | Floating PV | Rooftop PV |
---|---|---|---|

Site Name | Hapcheon Dam | Hapcheon Dam | Haman |

Site Coordinates | N 35.5°33′06″ E 128°00′49″ | N 35.5°33′36″ E 128°02′ 26″ | N 35° 16′10″ E 128° 24′ 01″ |

Installation Capacity | 100 kW | 500 kW | 1 MW |

Installation Year | 2011 | 2012 | 2012 |

Module Slope | 33° | 33° | 30° |

Module Type | c-Silicon | c-Silicon | c-Silicon |

Mounting | Aluminum, steel | Aluminum | Aluminum |

Mounting Type | Fixed | Fixed | Fixed |

Water Depth | 20 m | 40 m | n/a |

Output Energy | Floating PV | Rooftop PV | ||||
---|---|---|---|---|---|---|

100 kW | 500 kW | 1000 kW | ||||

Annual Output (kWh/year) | 130,305 | 693,219 | 1,197,547 | |||

Daily Yearly Average (kWh/year/days of year) | 357 | 1859 | 3281 | |||

Normal Power | Yearly | kWh/year/kWp | (h/year) | 1303 | 1386 | 1198 |

Monthly | kWh/month/kWp | (h/month) | Monthly details in Figure 2 | |||

Daily | kWh/year/days/kWp | (h/d) | 3.58 | 3.80 | 3.28 |

Term | Predictor Variables | Symbol | Unit |
---|---|---|---|

x_{1} | Ambient Temperature | ${T}_{a}$ | °C |

x_{2} | Solar Irradiance | ${G}_{T}$ | W/m² |

x_{3} | Wind Speed | ${V}_{w}$ | m/s |

x_{4} | Water Temp. | ${T}_{w}$ | °C |

Model | Empirical Models |
---|---|

Ross (1976) [14] | ${T}_{c}={T}_{a}+k{G}_{T}$ where $k=\Delta \left({T}_{c}-{T}_{a}\right)/\Delta {G}_{T}$ |

Rauschenbach (1980) [15] | ${T}_{c}={T}_{a}+\left({G}_{T}/{G}_{T,NOCT}\right)\left({T}_{c,NOCT}-{T}_{c,NOCT}\right)\left(1-{n}_{m}/\gamma \right)$ |

Risser & Fuentes (1983) [16] | ${T}_{c}=3.81+0.0282\times {G}_{T}1.31\times {T}_{a}-165{V}_{w}$ |

Schott (1985) [17] | ${T}_{c}={T}_{a}+0.028\times {G}_{T}-1$ |

Ross & Smokler (1986) [14] | ${T}_{c}={T}_{a}+0.035\times {G}_{T}$ |

Mondol et al. (2005, 2007) | ${T}_{c}={T}_{a}+0.031{G}_{T}$ ${T}_{c}={T}_{a}+0.031{G}_{T}-0.058$ |

Lasnier & Ang (1990) [5] | ${T}_{c}=30.006+0.0175\left({G}_{T}-300\right)+1.14\left({T}_{a}-25\right)$ |

Servant (1985) | ${T}_{c}={T}_{a}+\alpha {G}_{T}\left(1+\beta Ta\right)\left(1-\gamma {V}_{w}\right)\left(1-1.053{n}_{m,ref}\right)$ |

Duffie & Beckman [3] | ${T}_{c}={T}_{a}+\left({G}_{T}/{G}_{NOCT}\right)\left(9.5/5.7\times 3.8{V}_{w}\right)\left({T}_{NOCT}-{T}_{a,NOCT}\right)\left(1-{n}_{m}\right)$ |

Koehl (2011) [6] | ${T}_{c}={T}_{a}+{G}_{T}/\left({U}_{0}+{U}_{1}\times {V}_{w}\right)$ |

Kurtz S (2009) [7] | ${T}_{c}={T}_{a}+{G}_{T}\times {e}^{-3.473-0.0594\times {V}_{w}}$ |

Skoplaki (2009) [8] | ${T}_{c}={T}_{a}+\left({G}_{T}/{G}_{NOCT}\right)\times \left({T}_{NOCT}-{T}_{a,NOCT}\right)\times {h}_{w,NOCT}/{h}_{w}\times \left[1-{\eta}_{STC}/\tau \times \alpha \left(-{\beta}_{STC}{T}_{STC}\right)\right]$ |

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**MDPI and ACS Style**

Charles Lawrence Kamuyu, W.; Lim, J.R.; Won, C.S.; Ahn, H.K.
Prediction Model of Photovoltaic Module Temperature for Power Performance of Floating PVs. *Energies* **2018**, *11*, 447.
https://doi.org/10.3390/en11020447

**AMA Style**

Charles Lawrence Kamuyu W, Lim JR, Won CS, Ahn HK.
Prediction Model of Photovoltaic Module Temperature for Power Performance of Floating PVs. *Energies*. 2018; 11(2):447.
https://doi.org/10.3390/en11020447

**Chicago/Turabian Style**

Charles Lawrence Kamuyu, Waithiru, Jong Rok Lim, Chang Sub Won, and Hyung Keun Ahn.
2018. "Prediction Model of Photovoltaic Module Temperature for Power Performance of Floating PVs" *Energies* 11, no. 2: 447.
https://doi.org/10.3390/en11020447