# An Optimized Prediction Intervals Approach for Short Term PV Power Forecasting

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. ELM

#### 2.2. Improved DE

#### 2.3. PIs Construction and Assessment

#### 2.3.1. PI Formulation

#### 2.3.2. Metrics for PIs Quality

#### 2.4. Traditional Bootstrap Method for PIs Construction

#### 2.4.1. Variance of Model Uncertainty

#### 2.4.2. Variance of Data Noise

_{MLE}) by minimizing the cost function Equation (31).

## 3. Proposed Method

#### 3.1. PIs Based Cost Function

#### 3.2. Overall Procedures

## 4. Experimental Analysis

#### 4.1. Experimental Data Description

#### 4.2. Experimental Results and Analysis

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 4.**The 5-min ahead PV power forecasting results of four seasons in Singapore: (

**a**) northeast monsoon sunny conditions; (

**b**) Inter monsoon (NS); (

**c**) southwest monsoon; and, (

**d**) Inter monsoon (SN) (PIs constructed by proposed model, double bootstrap, MLE-bootstrap and PeEn respectively) with 90% confidence level.

**Figure 5.**The 5-min ahead photovoltaic (PV) power forecasting results of typical weather conditions: (

**a**) sunny conditions; (

**b**) cloudy conditions; and (

**c**) thunderstorm (PIs constructed by proposed model, double bootstrap, MLK bootstrap and PeEn, respectively) with 90% confidence level.

Seasons | PINC | Value | Persistence | BNN | Double Bootstrap | MLE Bootstrap | Proposed Bootstrap |
---|---|---|---|---|---|---|---|

Northeast monsoon | 90% | PICP | 76.74 | 94.65 | 93.75 | 94.10 | 94.79 |

MPIW | 19.01 | 13.19 | 17.83 | 16.90 | 12.53 | ||

95% | PICP | 79.86 | 96.21 | 95.28 | 95.93 | 96.38 | |

MPIW | 26.83 | 17.21 | 20.57 | 20.32 | 15.26 | ||

99% | PICP | 83.98 | 98.35 | 96.75 | 98.32 | 98.79 | |

MPIW | 37.12 | 18.92 | 20.82 | 22.90 | 18.53 | ||

Inter monsoon (NS) | 90% | PICP | 75.35 | 93.13 | 91.35 | 92.71 | 93.06 |

MPIW | 14.88 | 12.57 | 15.70 | 13.88 | 12.38 | ||

95% | PICP | 77.39 | 96.23 | 94.35 | 95.65 | 96.12 | |

MPIW | 24.71 | 14.92 | 18.12 | 16.15 | 14.84 | ||

99% | PICP | 78.81 | 98.50 | 96.78 | 97.69 | 98.52 | |

MPIW | 35.36 | 17.67 | 21.26 | 19.73 | 17.32 | ||

Southwest monsoon | 90% | PICP | 78.82 | 92.95 | 90.63 | 91.67 | 93.06 |

MPIW | 20.06 | 13.64 | 17.62 | 15.77 | 13.35 | ||

95% | PICP | 78.82 | 95.72 | 94.63 | 95.21 | 95.98 | |

MPIW | 26.06 | 16.59 | 20.15 | 18.59 | 16.23 | ||

99% | PICP | 78.82 | 97.36 | 90.63 | 91.67 | 97.25 | |

MPIW | 34.06 | 20.12 | 23.27 | 21.14 | 19.80 | ||

Inter monsoon (SN) | 90% | PICP | 75.27 | 92.68 | 89.93 | 90.28 | 92.71 |

MPIW | 26.54 | 13.25 | 17.66 | 14.09 | 12.57 | ||

95% | PICP | 76.93 | 95.57 | 94.93 | 95.28 | 95.62 | |

MPIW | 36.57 | 15.89 | 20.95 | 17.38 | 15.83 | ||

99% | PICP | 78.56 | 98.65 | 97.93 | 97.28 | 98.71 | |

MPIW | 46.51 | 19.53 | 22.16 | 20.17 | 19.13 |

**Table 2.**Performance comparison of various constructed prediction intervals (PIs) under different weather conditions.

Weather conditions | PINC | Value | Persistence | BNN | Double Bootstrap | MLE Bootstrap | Proposed Bootstrap |
---|---|---|---|---|---|---|---|

Sunny | 90% | PICP | 88.89 | 95.03 | 94.44 | 93.75 | 95.14 |

MPIW | 8.00 | 6.96 | 9.72 | 8.53 | 6.81 | ||

95% | PICP | 89.83 | 97.10 | 96.15 | 96.58 | 97.14 | |

MPIW | 16.12 | 12.15 | 15.81 | 13.87 | 11.76 | ||

99% | PICP | 91.65 | 98.93 | 97.64 | 98.15 | 98.87 | |

MPIW | 23.25 | 15.96 | 19.63 | 18.52 | 15.95 | ||

Cloudy | 90% | PICP | 81.94 | 93.15 | 92.36 | 93.06 | 93.18 |

MPIW | 17.55 | 9.79 | 14.94 | 11.76 | 9.83 | ||

95% | PICP | 83.94 | 96.68 | 95.03 | 95.37 | 96.79 | |

MPIW | 31.55 | 15.89 | 19.12 | 16.19 | 15.83 | ||

99% | PICP | 84.94 | 98.35 | 96.36 | 97.01 | 98.25 | |

MPIW | 39.65 | 16.57 | 23.06 | 19.76 | 16.23 | ||

Thunderstorm | 90% | PICP | 78.47 | 90.87 | 90.07 | 90.28 | 90.97 |

MPIW | 19.74 | 10.96 | 15.90 | 13.17 | 10.88 | ||

95% | PICP | 81.63 | 95.50 | 94.86 | 95.28 | 95.96 | |

MPIW | 39.74 | 16.70 | 20.14 | 18.20 | 16.65 | ||

99% | PICP | 84.57 | 98.15 | 96.39 | 96.28 | 98.03 | |

MPIW | 48.74 | 21.94 | 25.51 | 23.17 | 21.72 |

Method | Training Time (s) | Test Time (s) |
---|---|---|

BNN Bootstrap | 8579.32 | 5.730 |

MLE Bootstrap | 138.67 | 0.425 |

Double Bootstrap | 147.19 | 0.836 |

Proposed Bootstrap | 135.53 | 0.421 |

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## Share and Cite

**MDPI and ACS Style**

Ni, Q.; Zhuang, S.; Sheng, H.; Wang, S.; Xiao, J.
An Optimized Prediction Intervals Approach for Short Term PV Power Forecasting. *Energies* **2017**, *10*, 1669.
https://doi.org/10.3390/en10101669

**AMA Style**

Ni Q, Zhuang S, Sheng H, Wang S, Xiao J.
An Optimized Prediction Intervals Approach for Short Term PV Power Forecasting. *Energies*. 2017; 10(10):1669.
https://doi.org/10.3390/en10101669

**Chicago/Turabian Style**

Ni, Qiang, Shengxian Zhuang, Hanmin Sheng, Song Wang, and Jian Xiao.
2017. "An Optimized Prediction Intervals Approach for Short Term PV Power Forecasting" *Energies* 10, no. 10: 1669.
https://doi.org/10.3390/en10101669