# Deterministic and Probabilistic Wind Power Forecasting Based on Bi-Level Convolutional Neural Network and Particle Swarm Optimization

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## Abstract

**:**

## 1. Introduction

- (1)
- The wind power data is preprocessed using VMD and PSR to obtain data that are better suited for CNNs.
- (2)
- A forecasting model based on a bi-level CNN and PSO is developed; the model makes full use of the characteristics of CNNs to extract deep features and obtain the probabilistic forecasting interval via PSO.
- (3)
- The superiority of the proposed method is verified using the wind power data of a Chinese wind farm and the modeled wind power data of the United States Renewable Energy Laboratory.

## 2. Data Preprocessing

#### 2.1. Variational Mode Decomposition

#### 2.2. Phase Space Reconstruction

_{i}constitutes the phase point of the multi-dimensional phase space L phase points that jointly constitute the phase space trajectory reconstructed by the modes.

## 3. Convolutional Neural Network

#### 3.1. Convolutional Layer

#### 3.2. Pooling Layer

#### 3.3. Back-Propagation Training of the CNN

## 4. Proposed Approach for Forecasting the Wind Power Intervals

#### 4.1. Wind Power Forecasting Model Based on CNN

#### 4.1.1. Wind Power Data Preprocessing by VMD and PSR

#### 4.1.2. The Second-Layer CNN

#### 4.2. Wind Power Probability Interval Prediction

#### 4.2.1. Optimizing the Objective Function

#### 4.2.2. PSO of the Prediction Interval in Different Power Segments

## 5. Case Analysis

#### 5.1. Investigations of a Wind Farm in Gansu Province

#### 5.1.1. Experimental Settings

#### 5.1.2. Experimental Results

#### 5.2. Investigations on the Danforth Wind Farm

#### 5.2.1. Experimental Settings

#### 5.2.2. Experimental Results

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Schematic diagram of the proposed point-based forecasting model. VMD: variational mode decomposition; PSR: phase space reconstruction.

**Figure 4.**The overall architecture of the proposed approach for probabilistic wind power forecasting.

**Figure 5.**Forecasting results of the first-layer CNN based on the VPBC + PSO. VPBC: VMD + PSR + bi-level CNN.

**Figure 14.**Number of iterations needed to obtain the optimal solution for the PSO and GA optimization.

**Table 1.**Forecasting error indices of the different methods. NMAE: normalized mean absolute error; NRSME: normalized root mean square error; MAPE: mean absolute percentage error; VPCB: VMD + PSR + CNN-BPNN.

Method | NMAE | NRSME | MAPE |
---|---|---|---|

VPBC | 3.69% | 0.3339 | 6.46% |

CNN | 6.52% | 0.3811 | 11.41% |

VPCB | 4.64% | 0.3663 | 8.11% |

Persistence | 5.01% | 0.3375 | 8.56% |

**Table 2.**Performance indicators for the interval forecasting of the different methods. PINC: prediction interval nominal confidence; PICP: prediction interval coverage probability; PINAW: prediction interval normalized average width.

Method | PINC 80% | PINC 85% | PINC 90% | |||
---|---|---|---|---|---|---|

PICP | PINAW | PICP | PINAW | PICP | PINAW | |

VPBC + PSO | 85.14% | 0.1371 | 87.86% | 0.1587 | 91.86% | 0.1876 |

VPCB + PSO | 81.29% | 0.1521 | 85.43% | 0.1725 | 89.57% | 0.2041 |

CNN + PSO | 83.71% | 0.2182 | 86.00% | 0.2477 | 90.14% | 0.2885 |

**Table 3.**Comparison of the performance indicators for wind power interval forecasting using PSO and GA optimization. GA: genetic algorithm.

Method | PINC 80% | PINC 85% | PINC 90% | |||
---|---|---|---|---|---|---|

PICP | PINAW | PICP | PINAW | PICP | PINAW | |

VPBC + PSO | 85.14% | 0.1371 | 87.86% | 0.1587 | 91.86% | 0.1876 |

VPBC + GA | 83.86% | 0.1381 | 86.29% | 0.1624 | 91.14% | 0.1880 |

Method | NMAE | NRSME | MAPE |
---|---|---|---|

VPBC | 1.39% | 0.2548 | 2.65% |

CNN | 3.14% | 0.3295 | 5.97% |

VPCB | 2.10% | 0.2686 | 3.99% |

Persistence | 1.42% | 0.2313 | 2.69% |

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**MDPI and ACS Style**

Yang, X.; Zhang, Y.; Yang, Y.; Lv, W.
Deterministic and Probabilistic Wind Power Forecasting Based on Bi-Level Convolutional Neural Network and Particle Swarm Optimization. *Appl. Sci.* **2019**, *9*, 1794.
https://doi.org/10.3390/app9091794

**AMA Style**

Yang X, Zhang Y, Yang Y, Lv W.
Deterministic and Probabilistic Wind Power Forecasting Based on Bi-Level Convolutional Neural Network and Particle Swarm Optimization. *Applied Sciences*. 2019; 9(9):1794.
https://doi.org/10.3390/app9091794

**Chicago/Turabian Style**

Yang, Xiyun, Yanfeng Zhang, Yuwei Yang, and Wei Lv.
2019. "Deterministic and Probabilistic Wind Power Forecasting Based on Bi-Level Convolutional Neural Network and Particle Swarm Optimization" *Applied Sciences* 9, no. 9: 1794.
https://doi.org/10.3390/app9091794