# A Statistical Analysis of Long-Term Grid-Connected PV System Operation in Niš (Serbia) under Temperate Continental Climatic Conditions

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

#### Background

## 2. Materials and Methods

^{2}(or 1.659 m

^{2}/module). The minimum distance between the solar modules and the roof surface was 50 cm to ensure natural air circulation, i.e., a passive air-cooling method for the solar modules was used so that the system balance could take place naturally without any additional (mechanical) technique, as can be seen in Figure 1. It should also be noted that the solar modules were free from any shading.

_{STC}= (I

_{SC}·V

_{OC}·FF)/I

_{STC}

_{STC}is the reference solar irradiance at STC of 1 kW/m

^{2}, FF is a fill factor of the solar module, I

_{SC}is the short-circuit current of solar module, and V

_{OC}is the open-circuit voltage of solar module [9]. If it is taken into account that FF = 76%, I

_{SC}= 4.64 A, V

_{OC}= 57.12 V, and the inverter efficiency η

_{inv}= 96.3%, which is based on the specification of the modules and inverter given by the manufactory datasheet and presented in [10], the approximate PV system efficiency at STC (ideally, excluding cable losses) is around 19.4%.

- The relationship between two numerical variables (PV system electricity output and total POA irradiation data), obtained by 10-year measurements, was statistically analyzed using JMP Pro software. For that purpose, a regression analysis, analysis of variance (ANOVA), and post hoc Tukey test were applied. ANOVA is a technique for statistical analysis where datasets are compared to provide and determine their significance. ANOVA also describes complex relationships between variables; in this case, they are POA radiation and PV electricity. As results in ANOVA do not identify which specific differences between pairs of means are significant, it is common to use post hoc tests to investigate differences between multiple groups’ means. Based on obtained results, the conclusion of the grid-connected PV system application’s degradation, efficiency, profitability, and stability during its 10-year operation for a specific climate region was presented.

## 3. Results and Discussion

#### 3.1. Performance Parameters

_{syst}), which is determined as the ratio of the PV system output (AC output from the inverter and transmitted to the city grid) to the total POA radiation on the PV array [10,39]. The 10-year average values of PV system energy efficiency (η

_{syst}) by month are given in Figure 4.

_{syst}) by month range from 8.61% (July) to 12.61% (January), while the PV system efficiency at STC is 19%.

_{r}) represents the ratio between the total POA radiation (in kWh/m

^{2}) and the reference solar radiation of 1 kW/m

^{2}(reference solar radiation is radiation at STC) and is a function of the geographical location and orientation of the PV array. On the other hand, the specific yield factor (Y

_{f}) represents the ratio between the PV system output (in kWh) and the total installed power of the PV system (in kW

_{p}). The specific yield factor (or final yield) is usually utilized to normalize the produced system energy relative to the PV system size. It could be said that Y

_{f}is a good parameter for comparing the energy produced by different sized PV systems [10]. The ratio between the specific yield factor (Y

_{f}) and the reference yield (Y

_{r}) for 10-year measurements is given in Figure 5.

_{f}for the unit change of the independent variable Y

_{r}. Thus, the ratio between the specific yield factor (Y

_{f}) and the reference yield (Y

_{r}) represents Performance Ratio (PR). Hence, the PR defines the rate of effective produced energy with the energy the PV system would generate if it continually worked on its efficiency at standard test conditions. So, the PR comprises all PV optical and electric losses in a system without being directly dependent on input parameters such as meteodata (temperature, solar radiation, wind speed, cloudiness, snow, precipitation, presence of aerosols, etc.), module efficiency, and orientation of the PV array [10,29,30,31,32,33,34,35,36,37].

_{r}and Y

_{f}, and for the 10-year measurement period, it is 22.3%.

_{syst}) and the wind speed (v) for 10-year measurements is given in Figure 7.

_{syst}for the unit change of the independent variable v. Figure 7 also shows that, with increasing wind speed, PV system efficiency linearly increases. However, this type of PV cooling does not significantly increase the system efficiency. It should be noted that wind speed values for Niš were taken from the website of the Hydrometeorological Institute of the Republic of Serbia (https://www.hidmet.gov.rs/ciril/meteorologija/klimatologija_godisnjaci.php, accessed on 8 May 2023.). It was also observed that the ratio between the average monthly values of PR and the wind speed (v) follows the same trend over the 10-year measurements, as is the case with PV system efficiency.

#### 3.2. Statistical Analysis of PV System Electricity and Total POA Radiation Data during 10 Years of Measurements

## 4. Conclusions

- The yearly average values of POA radiation on a south-oriented and optimally inclined plane and total POA radiation on the PV array for a 10-year measurements level are 120.5931 kWh/m
^{2}and 1,999,512 kWh, respectively. - The total electricity production of the PV system for 10 years of its operations is 22,934.65 kWh.
- The yearly average value of PV system efficiency, for the 10-year measurements level, is 10.49%, which is almost two times less than the given efficiency at STC, and the relative error of yearly average values of PV system efficiency, observed from year to year, range from 0.34% to 6.16%.
- The yearly average value of specific yield factor (Y
_{f}) for the 10-year measurements level is 1178.51 kWh/kW_{p}. - The yearly average value of CF over the 10-year period is 13.45%.
- The yearly average value of PR for the 10-year measurements level is 0.87, and the relative error of yearly average values of PR, observed from year to year, range from 0.97% to 6.83%. On the other hand, the PV system, which uses highly efficient components and is designed appropriately, shows a PR near 90% (“good” performances are >84%). Thus, the experimental results indicate that the behavior of the given PV system over 10 years of operation does not change significantly.

- A high correlation coefficient value allows for the formation of regression model between PV electricity and POA radiation of the PV array. The obtained model is statistically significant and enables prediction better than the simple average.
- ANOVA shows that the mean values of PV electricity are not statistically significant changed over the 10 observed years.
- ANOVA and post hoc Tukey test show that there is a statistically significant difference of POA mean radiation during the months over 10 years and that the highest values of POA radiation are in July and on August. The Tukey test enables the months to be separated within the groups based on difference of POA radiation on PV array. The months within the groups are without statistically significant differences of POA radiation, while the months in various groups differ statistically significantly in terms of POA radiation.
- Based on the POA radiation values and by applying the obtained model, a prediction of the PV system output can be made for similar PV installations.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**PV array installed on the roof of the faculty [39].

**Figure 3.**The 10-year average values of energy yield (Ey) depending on the 10-year average values of total POA radiation reached on the total PV array area by month.

**Figure 5.**The ratio between the specific yield factor (Y

_{f}) and the reference yield (Y

_{r}) for 10-year measurements.

**Figure 6.**Graphics of the change of yearly average values of Performance Ratio (PR) for a 10-year period.

**Figure 7.**The ratio between the average monthly values of PV system energy efficiency (η

_{syst}) and the wind speed (v) for 10-year measurements.

**Figure 8.**Scatter plot of two numerical variables, PV electricity and POA radiation on PV array with fitted line—red line.

Location | Power (kW) | PV Technology | Final Yield (h/d) | System Efficiency (%) | PR (%) | CF (%) | Climate | Year/Duration (Years) |
---|---|---|---|---|---|---|---|---|

Serbia—current study | 2 | c-Si | 3.23 | 10.49 | 87 | 13.45 | Temperate/continental | 2022/10 |

Ireland | 1.72 | c-Si | 2.4 | 12.6 | 81.5 | 10.1 | Temperate/oceanic | / |

Norway | 2.1 | p-Si | 2.55 | 13–14 | 83.06 | 10.58 | Temperate/subarctic | / |

Brazil | 2.2 | p-Si | 4.6 | 13.3 | 82.9 | 19.2 | Tropical/subtropical | / |

China | 3 | p-Si | 2.86 | 10.73 | 80.6 | / | Humid subtropical | 2009/3 |

Morocco | 2.4 | c-Si, p-Si | 4.34 | 11.67 | 76.7 | 18.16 | Hot semi-arid subtropical | 2018/4 |

Morocco | 2.04 | c-Si | 4.34 | 11.7 | 76.7 | / | Hot semi-arid subtropical | 2015/2 |

India | 2 | p-Si | / | / | 70 | / | tropical | 2019/1 |

Spain | 2 | / | 7.11 | 64.5 | Subtropical/Mediterranean | 1997/1 | ||

Turkey | 2.35 | c-Si, p-Si | / | 13.26 | 91 | / | Humid subtropical | 2014/1 |

Oman | 1.4 | p-Si | / | / | 84.6 | 21 | Hot desert | / |

Korea | 3 | c-Si | / | 7.9 | 63.3 | 11.5 | Humid subtropical | 2003/1 |

Source | DF | Sum of Squares | Mean Square | F Ratio |
---|---|---|---|---|

Model | 1 | 421,038.40 | 421,038 | 472.2001 |

Error | 110 | 98,081.77 | 892 | Prob> F |

C. Total | 111 | 519,120.17 | <0.0001 |

Term | Estimate | Std Error | t Ratio | Prob > |t| |
---|---|---|---|---|

Intercept | 58.326117 | 7.002889 | 8.33 | <0.0001 |

POA radiation on PV array (kWh) | 0.0685116 | 0.003153 | 21.73 | <0.0001 |

Source | DF | Sum of Squares | Mean Square | F Ratio | Prob > F |
---|---|---|---|---|---|

Month | 11 | 81,047,311 | 7,367,937 | 85.1508 | <0.0001 |

Error | 100 | 8,652,807 | 86,528 | ||

C. Total | 111 | 89,700,118 |

Level | Mean | |||||
---|---|---|---|---|---|---|

July | A | 3204.6841 | ||||

August | A | 3194.4330 | ||||

June | B | 2715.8129 | ||||

May | B | 2629.4805 | ||||

September | B | 2470.4103 | ||||

April | B | 2409.3351 | ||||

Marth | C | 1918.8154 | ||||

October | C | 1810.7883 | ||||

February | D | 1158.8864 | ||||

November | D | E | 1054.8455 | |||

January | D | E | 776.5689 | |||

December | E | 667.1575 |

Source | DF | Sum of Squares | Mean Square | F Ratio | Prob > F |
---|---|---|---|---|---|

Year | 9 | 3305.57 | 367.29 | 0.0696 | 0.9999 |

Error | 107 | 564,654.35 | 5277.14 | ||

C. Total | 116 | 567,959.92 |

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**MDPI and ACS Style**

Todorović, D.D.; Stojanović Krasić, M.; Jovanović, S.; Drljača, B.; Kevkić, T.
A Statistical Analysis of Long-Term Grid-Connected PV System Operation in Niš (Serbia) under Temperate Continental Climatic Conditions. *Appl. Sci.* **2023**, *13*, 6229.
https://doi.org/10.3390/app13106229

**AMA Style**

Todorović DD, Stojanović Krasić M, Jovanović S, Drljača B, Kevkić T.
A Statistical Analysis of Long-Term Grid-Connected PV System Operation in Niš (Serbia) under Temperate Continental Climatic Conditions. *Applied Sciences*. 2023; 13(10):6229.
https://doi.org/10.3390/app13106229

**Chicago/Turabian Style**

Todorović, Dragana D., Marija Stojanović Krasić, Slavica Jovanović, Branko Drljača, and Tijana Kevkić.
2023. "A Statistical Analysis of Long-Term Grid-Connected PV System Operation in Niš (Serbia) under Temperate Continental Climatic Conditions" *Applied Sciences* 13, no. 10: 6229.
https://doi.org/10.3390/app13106229