# Wind Power Short-Term Forecasting Hybrid Model Based on CEEMD-SE Method

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## Abstract

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## 1. Introduction

- (1)
- Ensure the quality of input data of the forecasting model. Most wind power forecasting models only adopt a single data preprocessing method. Thus, the accuracy is limited due to the fact that the complexity of original data is not properly dealt with. This paper first analyses the correlation of indicators, eliminates the indicators with low correlation degree to reduce data redundancy, and then uses CEEMD to decompose wind power to improve the quality of input data of the forecasting model, and use sample entropy (SE), which was proposed by Richman [42] to classify and reconstruct subsequences to reduce the computational complexity.
- (2)
- Realize multi-step forecasting of wind power. The hybrid wind power forecasting model constructed in this paper comprises three parts: data preprocessing, optimization and forecasting. Reasonable multi-level forecasting model can be more supportive for decision-making.
- (3)
- Balance model forecasting accuracy and stationarity. This paper uses a variety of methods to enhance the forecasting accuracy of wind power and improve the stability of the model. The KELM model with faster training speed is used, and the parameters of the KELM model are optimized by the HS algorithm to improve the search performance.
- (4)
- Verify the performance of the forecasting model comprehensively. According to the real measured data of wind farms in China, the ultra-short-term and short-term forecasting of wind power are carried out by adopting the model respectively, and the comprehensive performance of the forecasting model is investigated by calculating four forecasting accuracy evaluation indicators, which confirms the feasibility of multi-scenario application of the model.

## 2. Materials and Methods

#### 2.1. Pearson Correlation Coefficient

#### 2.2. Complementary Ensemble Empirical Mode decomposition (EMD)

#### 2.3. Sample Entropy Theory

#### 2.4. Harmony Search (HS) Algorithm

#### 2.5. Extreme Learning Machine with Kernel

## 3. Wind Power Forecasting Model

#### 3.1. Model Design

- (1)
- Screen the original data set through correlation analysis to obtain data indicators with high correlation, which can used as the input data of CEEMD-HS-KELM forecasting model;
- (2)
- Decompose the original wind power sequence $X$ through CEEMD method to obtain $n$ sub sequences components from high frequency to low frequency, which are $n-1$ intrinsic mode function $IM{F}_{i}\left(t\right)$ and one approximately monotonous residual $R\left(t\right)$;
- (3)
- Utilize SE theory to calculate the complexity of each subsequence and reconstruct the subsequence decomposed by CEEMD;
- (4)
- HS-KELM model is constructed for each subsequence and the forecast values of each subsequence are obtained;
- (5)
- Superimpose the wind power forecasting results of each subsequence to obtain the final forecasting results.

#### 3.2. Evaluation Criteria

^{2}. The calculation methods are as follows:

## 4. Short-Term Wind Power Forecasting

#### 4.1. Data Set Screening

#### 4.2. CEEMD Decomposition of Wind Power Sequence and Subsequence Reconstruction

#### 4.3. Wind Power Forecasting by CEEMD-SE-HS-KELM Model

#### 4.4. Comparative Analysis of Forecasting Models

^{2}and model error indexes such as Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) are calculated respectively, as shown in Table 3 and Figure 9.

- (1)
- Comparing EMD-SE-HS-KELM and CEEMD-SE-HS-KELM, the RMSE and MAE of the latter are improved by 53.63% and 24.36% respectively compared with EMD-SE-HS-KELM, which indicates that the hybrid model of data preprocessing based on CEEMD-HS has better processing effect.
- (2)
- Comparing HS-KELM and EMD-SE-HS-KELM, the RMSE and MAE of the latter are improved by 52.10% and 86.58%, respectively, compared with HS-KELM, which indicates that for non-stationary wind power series, pre-processing can effectively eliminate noise, ensure data quality and improve forecasting accuracy.
- (3)
- Comparing KELM and HS-KELM, the RMSE and MAE of the latter are improved by 37.67% and 45.23%, respectively, compared with KELM, which indicates that the parameters of KELM algorithm are optimized by HS algorithm, which effectively improves the search ability and the forecasting accuracy.
- (4)
- Compared with ELM, the RMSE and MAE of the KELM are improved by 25.02% and 24.06% respectively compared with ELM, which indicates that the forecasting accuracy of KELM algorithm is better than ELM model, and KELM has a stronger generalization ability.

## 5. Conclusions

- (1)
- KELM model has higher forecasting accuracy than ELM model, and has broad application prospects in wind power forecasting.
- (2)
- Compared with the single KELM model, HS can optimize the kernel parameters and penalty function of KELM to obtain higher forecasting accuracy, which indicates that HS-KELM model has stronger global search ability and more stable forecasting performance.
- (3)
- Compared with EMD-SE, the data preprocessing strategy based on CEMD-SE has better performance and effectively improves the forecasting accuracy. The hybrid model proposed in this paper can be well applied to short-term wind power forecasting.

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

NWP | Numerical weather prediction |

ANN | Artificial neural network |

SVM | Support vector machine |

LSSVM | Least squares support vector machine |

PCA | Principal component analysis |

WT | Wavelet transform |

EMD | Empirical mode decomposition |

EWT | Empirical wavelet transform |

CEEMD | Complementary ensemble empirical mode decomposition |

WAS | Wavelet neural network |

DWT | Discrete wavelet transform |

GARCH | Generalized autoregressive conditional heteroscedastic |

MkRVR | Multi-kernel relevance vector regression |

IMF | Intrinsic mode functions |

MLFFNN | Multilayer feed-forward neural network |

SVR | Support vector regression |

RBF | Radial basis function |

ANFIS | Adaptive neuro-fuzzy inference system |

PSO | Particle swarm optimization |

VMD | Variational mode decomposition |

BA | Bat algorithm |

ELM | Extreme learning machine |

CSO | Crisscross optimization algorithm |

KELM | Extreme learning machine with kernel |

HS | Harmony search |

SE | Sample entropy |

HM | Harmony memory |

HMS | Harmony memory size |

HMCR | Harmony memory considering rate |

PCR | Pitch adjusting rate |

BW | Bandwidth |

BPNN | Back propagation neural network |

RMSE | Root mean square error |

MAE | Mean absolute error |

R^{2} | Determining factor |

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**Figure 8.**Wind power forecasting results (5 min). (

**a**) configuration #1: ELM model; (

**b**) configuration #2: KELM model; (

**c**) configuration #3: HS-KELM model; (

**d**) configuration #4: EMD-SE-HS-KELM model; (

**e**) configuration #5: CEEMD-SE-HS-KELM model; (

**f**) comparison of forecasting values of different models.

**Figure 9.**Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) and R

^{2}of different forecasting models.

Indicators | Correlation | Indicators | Correlation | Indicators | Correlation | ||
---|---|---|---|---|---|---|---|

wind speed | 10 m | 0.788 | wind direction | 10 m | −0.391 | temperature | 0.227 |

30 m | 0.796 | 30 m | −0.308 | humidity | −0.51 | ||

50 m | 0.777 | 50 m | −0.025 | rainfall | 0.29 | ||

70 m | 0.764 | 70 m | 0.289 | pressure | −0.37 | ||

hub height | 0.764 | hub height | 0.289 | - |

New Subsequence Number | Initial Subsequence Number | New Subsequence Number | Initial Subsequence Number |
---|---|---|---|

1 | 1 | 5 | 7 |

2 | 2,3 | 6 | 8,9 |

3 | 4 | 7 | 10,11,12 |

4 | 5,6 | 8 | R |

Evaluation Index | ELM | KELM | HS-KELM | EMD-SE-HS-KELM | CEEMD-SE-HS-KELM |
---|---|---|---|---|---|

Configuration | #1 | #2 | #3 | #4 | #5 |

RMSE | 20.84 | 15.63 | 9.74 | 4.67 | 2.16 |

MAE | 9.29 | 7.05 | 3.86 | 0.52 | 0.39 |

R^{2} | 1.12 | 1.05 | 0.96 | 1.03 | 1.01 |

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## Share and Cite

**MDPI and ACS Style**

Wang, K.; Niu, D.; Sun, L.; Zhen, H.; Liu, J.; De, G.; Xu, X.
Wind Power Short-Term Forecasting Hybrid Model Based on CEEMD-SE Method. *Processes* **2019**, *7*, 843.
https://doi.org/10.3390/pr7110843

**AMA Style**

Wang K, Niu D, Sun L, Zhen H, Liu J, De G, Xu X.
Wind Power Short-Term Forecasting Hybrid Model Based on CEEMD-SE Method. *Processes*. 2019; 7(11):843.
https://doi.org/10.3390/pr7110843

**Chicago/Turabian Style**

Wang, Keke, Dongxiao Niu, Lijie Sun, Hao Zhen, Jian Liu, Gejirifu De, and Xiaomin Xu.
2019. "Wind Power Short-Term Forecasting Hybrid Model Based on CEEMD-SE Method" *Processes* 7, no. 11: 843.
https://doi.org/10.3390/pr7110843