# Photovoltaic Power Forecasting Based on EEMD and a Variable-Weight Combination Forecasting Model

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. PV Power Prediction Modelling Theory

#### 2.1. EEMD

#### 2.2. Method of the Optimal Weight Determination

_{i}is the error of model i at each time point.

_{it}is the error of model i at time point t, k

_{it}is the weights of model i at time point t.

#### 2.3. Variable Weight Prediction Modelling

_{1}, y

_{1}), an auxiliary set (x

_{2}, y

_{2}), and a test set (x

_{3}, y

_{3}). Models a, b, and c are obtained using the decision tree, SVM, and ensemble methods to conduct fitting of the training set. By using these models for the prediction of the auxiliary set x

_{2}, the prediction results, y

_{2a}, y

_{2b}, and y

_{2c}, of the auxiliary set are obtained. These are then subtracted from y

_{2}to give the errors e

_{a}, e

_{b}, and e

_{c}, respectively. By using the HM or QP methods the optimal weights for the three prediction methods, w

_{2a}, w

_{2b}, and w

_{2c}, can be obtained. The ensemble method is then used to fit x

_{2}with w

_{2a}, w

_{2b}, and w

_{2c}and predict the test set x

_{3}to obtain the weights w

_{3a}, w

_{3b}, and w

_{3c}of each time point for each method. In addition, models a, b, and c are used to predict the test set x

_{3}and obtain the prediction results y

_{3a}, y

_{3b}, and y

_{3c}. Finally, the variable weights of the three models are combined using the formula y = y

_{3a}× w

_{3a}+ y

_{3b}× w

_{3b}+ y

_{3c}× w

_{3c}, and the final prediction result is obtained. The design logic is shown in Figure 1.

## 3. PV Power Prediction Modelling Based on EEMD and the Variable-Weight Combination Forecasting Model

#### 3.1. Input Variable Selection

#### 3.2. Modelling Procedure

#### 3.3. Forecasting Results Evaluation

## 4. Empirical Analysis

#### 4.1. Data Source and Parameter Initialization

#### 4.2. EEMD and Variable Weight Combination Model

#### 4.3. Comparison of the Models and Forecast Results

#### 4.4. Discussion on the Effects of Input Variables

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Flowchart of EEMD-VWCF model. PV: photovoltaic; RC: residual component; HF: high-frequency sequence; MF: intermediate-frequency component; LF: low-frequency component; VWCF: variable-weight combination forecasting; EEMD: ensemble empirical mode decomposition.

**Figure 4.**Comparison of forecasting results of the models. QP: quadratic programming method; HM: harmonic mean method.

**Table 1.**Comparison of the evaluation indicators of the models. MAE: mean absolute error; MSE: mean square error.

Model | MAE | MSE |
---|---|---|

TREE | 0.0761 | 0.0199 |

EEMD + TREE | 0.0682 | 0.0114 |

EEMD + VWCF (QP) | 0.0697 | 0.0123 |

EEMD + VWCF (HM) | 0.0622 | 0.0107 |

Model | MAE | MSE |
---|---|---|

Random Forest | 0.0833 | 0.0140 |

Back Propagation (BP) Neural Network | 0.0816 | 0.0157 |

EMD + TREE | 0.0713 | 0.0130 |

EMD + VWCF (HM) | 0.0684 | 0.0127 |

EEMD + VWCF (HM) | 0.0622 | 0.0107 |

MAE of Different States | QP | HM |
---|---|---|

Optimal forecasting of LF | 0.0192 | 0.0267 |

Last forecasting of LF | 0.0308 | 0.0313 |

Optimal forecasting of MF | 0.0278 | 0.0381 |

Last forecasting of MF | 0.0544 | 0.0556 |

Optimal forecasting of HF | 0.0287 | 0.0460 |

Last forecasting of HF | 0.0723 | 0.0717 |

Last forecasting | 0.0697 | 0.0622 |

MAE | 6 Variables | 13 Variables |
---|---|---|

TREE | 0.0761 | 0.0900 |

EEMD + TREE | 0.0682 | 0.0826 |

EEMD + VWCF (HM) | 0.0622 | 0.0773 |

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**MDPI and ACS Style**

Wang, H.; Sun, J.; Wang, W. Photovoltaic Power Forecasting Based on EEMD and a Variable-Weight Combination Forecasting Model. *Sustainability* **2018**, *10*, 2627.
https://doi.org/10.3390/su10082627

**AMA Style**

Wang H, Sun J, Wang W. Photovoltaic Power Forecasting Based on EEMD and a Variable-Weight Combination Forecasting Model. *Sustainability*. 2018; 10(8):2627.
https://doi.org/10.3390/su10082627

**Chicago/Turabian Style**

Wang, Hui, Jianbo Sun, and Weijun Wang. 2018. "Photovoltaic Power Forecasting Based on EEMD and a Variable-Weight Combination Forecasting Model" *Sustainability* 10, no. 8: 2627.
https://doi.org/10.3390/su10082627