# Electricity Consumption Forecasting Scheme via Improved LSSVM with Maximum Correntropy Criterion

^{*}

^{†}

^{‡}

## Abstract

**:**

## 1. Introduction

## 2. Review of the LSSVM and MCC

#### 2.1. Least Square Support Vector Machine

#### 2.2. Maximum Correntropy Criterion

## 3. FoEC via LSSVM with MCC

- Step 1:
- Data preprocessing: Includes the processing of error data and data normalization.
- Step 2:
- Dataset constructing: The normalized data samples are divided into training and testing samples, which are used to train the LSSVM model and evaluate the performance of the trained model, respectively.
- Step 3:
- Parameter optimization: The parameters of the LSSVM model with the MCC are optimized by the grid search method.
- Step 4:
- Prediction: After training the LSSVM, the prediction accuracy and the generalization performance are demonstrated by the testing data.
- Step 5:
- Prediction result analysis: Applies certain evaluation criteria for performing evaluation tasks and analyzing the various elements that affect the result of such a forecast.

#### 3.1. Data Preprocessing

- (1)
- Error data and missing data processing.

- (2)
- Normalization processing.

#### 3.2. Selection of Influence Factors

- (1)
- The quantity of electricity data.

- (2)
- Regional temperature.

- (3)
- GDP.

- (4)
- Number of holidays and types of holidays.

#### 3.3. Parameter Optimization

#### 3.4. Performance Evaluation Function (PEF)

## 4. Prediction Results and Analysis

#### 4.1. Prediction Results of Large Industry in Shaanxi Province

#### 4.2. Prediction Result for Xi’an

#### 4.3. Prediction Results of Electricity Consumption in an Educational Institution in Xi’an

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Lu, B.; Zhao, S.; Tian, Y.; Yang, Y.; Li, B.; Chen, X.; Sun, L. Mid-long term electricity consumption forecasting based on improved NGM (1,1,k) gray model. power Syst. Prot. Control
**2015**, 43, 98–103. [Google Scholar] - Xue, B.; Cheng, C.; Ou, S.; Liu, A.; Wang, S. A linear regression model for forecasting monthly electricity sales considering comfortable temperature range and sudden variable. power Syst. Prot. Control
**2017**, 45, 15–20. [Google Scholar] - Cao, G.; Wu, L. Support vector regression with fruit fly optimization algorithm for seasonal electricity consumption forecasting. Energy
**2016**, 115, 734–745. [Google Scholar] [CrossRef] - Chae, Y.T.; Horesh, R.; Hwang, Y.; Lee, Y.M. Artificial neural network model for forecasting sub-hourly electricity usage in commercial buildings. Energy Build.
**2016**, 111, 184–194. [Google Scholar] [CrossRef] - Cabral, J.D.A.; Legey, L.F.L.; de Freitas Cabral, M. Electricity consumption forecasting in Brazil: A spatial econometrics approach. Energy
**2017**, 126, 124–131. [Google Scholar] [CrossRef] - Gunay, M.E. Forecasting annual gross electricity demand by artificial neural networks using predicted values of socio-economic indicators and climatic conditions: Case of Turkey. Energy Policy
**2016**, 90, 92–101. [Google Scholar] [CrossRef] - Amber, K.P.; Aslam, M.W.; Hussain, S.K. Electricity consumption forecasting models for administration buildings of the UK higher education sector. Energy Build.
**2015**, 90, 127–136. [Google Scholar] [CrossRef] - Santamouris, M.; Cartalis, C.; Synnefa, A.; Kolokotsa, D. On the impact of urban heat island and global warming on the power demand and electricity consumption of buildings—A review. Energy Build.
**2015**, 98, 119–124. [Google Scholar] [CrossRef] - Zhu, X.; Han, Z. Research on LS-SVM Wind Speed Prediction Method Based on PSO. Proc. CSEE
**2016**, 36, 6337–6342. [Google Scholar] - Bessa, R.J.; Miranda, V.; Gama, J. Entropy and correntropy against minimum square error in offline and online three-day ahead wind power forecasting. IEEE Trans. Power Syst.
**2009**, 24, 1657–1666. [Google Scholar] [CrossRef] - Chen, B.D.; Xing, L.; Zhao, H.; Zheng, N.; Principe, J.C. Generalized Correntropy for Robust Adaptive Filtering. IEEE Trans. Signal Proc.
**2016**, 64, 3376–3387. [Google Scholar] [CrossRef] - Liu, W.F.; Pokharel, P.P.; Principe, J.C. Correntropy: Properties and applications in non-Gaussian signal processing. IEEE Trans. Signal Proc.
**2007**, 55, 5286–5298. [Google Scholar] [CrossRef] - Chen, B.D.; Xing, L.; Liang, J.; Zheng, N.; Principe, J.C. Steady-State Mean-Square Error Analysis for Adaptive Filtering under the Maximum Correntropy Criterion. IEEE Signal Proc. Lett.
**2014**, 21, 880–884. [Google Scholar] - Chen, B.D.; Principe, J.C. Maximum correntropy estimation is a smoothed MAP estimation. IEEE Signal Proc. Lett.
**2012**, 19, 491–494. [Google Scholar] [CrossRef] - Chen, B.D.; Wang, J.; Zhao, H.; Zheng, N.; Príncipe, J.C. Convergence of a Fixed-Point Algorithm under Maximum Correntropy Criterion. IEEE Signal Proc. Lett.
**2015**, 22, 1723–1727. [Google Scholar] [CrossRef] - Vapnik, V.N.; Chervonenkis, A.Y. On the uniform convergence of relative frequencies of events to their probabilities. In Measures of Complexity; Springer: Cham, Switzerland, 2015; pp. 11–30. [Google Scholar]
- Chen, X.; Yang, J.; Liang, J.; Ye, Q. Recursive robust least squares support vector regression based on maximum correntropy criterion. Neurocomputing
**2012**, 97, 63–73. [Google Scholar] [CrossRef] - Nie, H.; Liu, G.; Liu, X.; Wang, Y. Hybrid of ARIMA and SVMs for Short-Term Load Forecasting. Energy Procedia
**2012**, 16, 1455–1460. [Google Scholar] [CrossRef] - Sidorov, D. Integral dynamical models. Singularities, signals and control. World Sci.
**2014**, 87, 9–12. [Google Scholar] - Chen, B.D.; Liang, J.; Zheng, N.; Principe, J.C. Kernel least mean square with adaptive kernel size. Neurocomputing
**2016**, 191, 95–106. [Google Scholar] [CrossRef] - He, R.; Zheng, W.-S.; Hu, B.-G. Maximum Correntropy Criterion for Robust Face Recognition. IEEE Trans. Pattern Anal. Mach. Intell.
**2011**, 33, 1561–1576. [Google Scholar] [PubMed] - Ma, W.T.; Qua, H.; Gui, G.; Chen, B. Maximum correntropy criterion based sparse adaptive filtering algorithms for robust channel estimation under non-Gaussian environments. J. Frankl. Inst.
**2015**, 352, 2708–2727. [Google Scholar] [CrossRef] - Chen, B.D.; Liu, X.; Zhao, H.; Principe, J.C. Maximum Correntropy Kalman Filter. Automatica
**2017**, 76, 70–77. [Google Scholar] [CrossRef] - Izanloo, R.; Fakoorian, S.A.; Yazdi, H.S.; Simon, D. Kalman filtering based on the maximum correntropy criterion in the presence of non-Gaussian noise. Inf. Sci. Syst.
**2016**, 64, 500–505. [Google Scholar] - Chen, B.D.; Xing, L.; Xu, B.; Zhao, H.; Zheng, N.; Príncipe, J.C. Kernel Risk-Sensitive Loss: Definition, Properties and Application to Robust Adaptive Filtering. IEEE Trans. Signal Proc.
**2017**, 65, 2888–2901. [Google Scholar] [CrossRef] - Azadeh, A.; Ghaderi, S.F.; Sohrabkhani, S. Annual electricity consumption forecasting by neural network in high energy consuming industrial sectors. Energy Convers. Manag.
**2008**, 49, 2272–2278. [Google Scholar] [CrossRef] - Zhang, Y.; Han, X.; Yang, Y.; Zhang, L.; Miao, X. A novel analysis and forecast method of electricity business expanding based on seasonal adjustment. In Proceedings of the 2016 IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC), Xi’an, China, 25–28 October 2016; pp. 707–711. [Google Scholar]

**Figure 10.**Three-dimensional map of prediction accuracy, varying with parameters $\gamma $ and ${\sigma}^{2}$.

Month | Real/kWh | MCC–LSSVM/kWh | MSE–LSSVM/kWh |
---|---|---|---|

1 | 3222141989 | 3289063235 | 3294523968 |

2 | 2807359588 | 2770660550 | 2753838956 |

3 | 2905625349 | 2835276855 | 2766953282 |

4 | 3258028408 | 3193065850 | 3193625474 |

5 | 3123940121 | 3140143741 | 3130143486 |

6 | 3146763568 | 3118571548 | 3113648647 |

7 | 3200783187 | 3204753934 | 3201236988 |

8 | 3330358001 | 3347137347 | 3297138647 |

9 | 3169671810 | 3146624356 | 3196624769 |

10 | 3094490648 | 3140563342 | 3134963398 |

11 | 3197240745 | 3233100710 | 3216824659 |

12 | 3253492846 | 3246565684 | 3227682398 |

Evaluation Index | MRE (%) | ${\mathit{\delta}}_{max}$/kWh | R |
---|---|---|---|

MCC–LSSVM | 0.9 | 73256684 | 0.9235 |

MSE–LSSVM | 3.12 | 140348494 | 0.8952 |

Month | Real/kWh | MCC–LSSVM/kWh | MSE–LSSVM/kWh |
---|---|---|---|

1 | 2664166276 | 2661798254 | 2641798254 |

2 | 2275553927 | 2276537980 | 2246537980 |

3 | 2021181824 | 2066396013 | 2066396013 |

4 | 2025719576 | 1904917602 | 1928943561 |

5 | 1850231091 | 1792863625 | 1792863625 |

6 | 2011974726 | 1904917602 | 1872354896 |

7 | 2215976398 | 2276963182 | 2192662853 |

8 | 2664937423 | 2717665734 | 2596348624 |

9 | 2326022304 | 2350413608 | 2348629858 |

10 | 1906840712 | 1818905227 | 1956189345 |

11 | 2038734324 | 1940165576 | 1889654236 |

12 | 2350000000 | 2303946621 | 2329946654 |

Evaluation Index | MRE (%) | ${\mathit{\delta}}_{max}$/kWh | R |
---|---|---|---|

MCC–LSSVM | 2.77 | 120801974 | 0.9534 |

MSE–LSSVM | 3.23 | 145653478 | 0.9316 |

Month | Real/kWh | MCC–LSSVM/kWh | MSE–LSSVM/kWh |
---|---|---|---|

1 | 5526468 | 5789523 | 6034028 |

2 | 6435286 | 6317452 | 6211205 |

3 | 6215832 | 6194268 | 6268253 |

4 | 6231532 | 6267145 | 6518210 |

5 | 6231102 | 6294423 | 6207253 |

6 | 6315468 | 6354652 | 5986242 |

7 | 6221536 | 6258553 | 5912131 |

8 | 6189358 | 6124125 | 6145128 |

9 | 6294825 | 6378632 | 6255368 |

10 | 6314653 | 6290058 | 6353895 |

11 | 6277436 | 6219389 | 6503896 |

12 | 6231862 | 6123568 | 6017658 |

Evaluation Index | MRE (%) | ${\mathit{\delta}}_{max}$/kWh | R |
---|---|---|---|

MCC–LSSVM | 3.98 | 2635648 | 0.9619 |

MSE–LSSVM | 6.41 | 3296821 | 0.9106 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Duan, J.; Qiu, X.; Ma, W.; Tian, X.; Shang, D.
Electricity Consumption Forecasting Scheme via Improved LSSVM with Maximum Correntropy Criterion. *Entropy* **2018**, *20*, 112.
https://doi.org/10.3390/e20020112

**AMA Style**

Duan J, Qiu X, Ma W, Tian X, Shang D.
Electricity Consumption Forecasting Scheme via Improved LSSVM with Maximum Correntropy Criterion. *Entropy*. 2018; 20(2):112.
https://doi.org/10.3390/e20020112

**Chicago/Turabian Style**

Duan, Jiandong, Xinyu Qiu, Wentao Ma, Xuan Tian, and Di Shang.
2018. "Electricity Consumption Forecasting Scheme via Improved LSSVM with Maximum Correntropy Criterion" *Entropy* 20, no. 2: 112.
https://doi.org/10.3390/e20020112