# Forecasting Electricity Demand Using a New Grey Prediction Model with Smoothness Operator

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## Abstract

**:**

## 1. Introduction

## 2. Basic Concepts

**Definition 1.**

- (1)
- If, for k = 2, 3, …, m${y}^{\left(0\right)}\left(k\right)-{y}^{\left(0\right)}\left(k-1\right)>0$, then${Y}^{\left(0\right)}$is a monotonic increasing sequence;
- (2)
- If, for$k=2,\text{}3,\text{}\cdots ,\text{}m$,${y}^{\left(0\right)}\left(k\right)-{y}^{\left(0\right)}\left(k-1\right)<0$, then${Y}^{\left(0\right)}$is a monotonic decreasing sequence;
- (3)
- If, for any$k$and$k=2,\text{}3,\text{}\cdots ,\text{}m$,$${y}^{\left(0\right)}\left(k\right)-{y}^{\left(0\right)}\left(k-1\right)>0\text{}\mathrm{and}\text{}{y}^{\left(0\right)}\left(k\right)-{y}^{\left(0\right)}\left(k-1\right)0,\text{}$$

**Definition 2.**

**Theorem 1.**

**Proof.**

## 3. Grey Prediction Model with Three Parameters

**Definition 3.**

**Definition 4.**

## 4. Improved GFM_TP Model (IGFM_TP) Based on a Smoothness Operator

## 5. Electricity Forecasting Using IGFM_TP

**Step 1**. Collecting modeling data.

**Step 2**. Computing smoothness sequence.

**Step 3**. Computing the parameters of the IGFM_TP model.

**Step 4**. Computing the simulated data and errors.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The ratio of China’s gross domestic product (GDP) and electric production compared to other countries.

Month | January | February | March | April | May | June | July |
---|---|---|---|---|---|---|---|

Electricity Consumption (Million Kilowatts) | 439 | 320 | 584 | 481 | 640 | 635 | 790 |

Month | ${\mathit{y}}^{\left(0\right)}\left(\mathit{k}\right)$ | IGFM_TP | Model in AUTHOR et al. | Classical GM(1,1) | Model in AUTHOR et al. | Model in AUTHOR et al. | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

${\widehat{\mathit{y}}}^{\left(0\right)}\left(\mathit{k}\right)$ | ${\mathbf{\Delta}}_{\mathit{k}}$ | ${\widehat{\mathit{y}}}^{\left(0\right)}\left(\mathit{k}\right)$ | ${\mathbf{\Delta}}_{\mathit{k}}$ | ${\widehat{\mathit{y}}}^{\left(0\right)}\left(\mathit{k}\right)$ | ${\mathbf{\Delta}}_{\mathit{k}}$ | ${\widehat{\mathit{y}}}^{\left(0\right)}\left(\mathit{k}\right)$ | ${\mathbf{\Delta}}_{\mathit{k}}$ | ${\widehat{\mathit{y}}}^{\left(0\right)}\left(\mathit{k}\right)$ | ${\mathbf{\Delta}}_{\mathit{k}}$ | ||

February | 320 | 320.0 | 0.0% | 409.4 | 27.9% | 405.2 | 26.6% | 371.0 | 16.0% | 334.7 | 4.6% |

March | 584 | 599.3 | 2.6% | 465.1 | 20.4% | 461.5 | 21.0% | 464.5 | 20.5% | 487.5 | 16.5% |

April | 481 | 428.1 | 11.0% | 528.5 | 9.9% | 525.6 | 9.3% | 548.4 | 14.1% | 583.2 | 21.2% |

May | 640 | 718.1 | 12.2% | 600.5 | 6.2% | 598.7 | 6.5% | 623.5 | 2.6% | 643.0 | 0.50% |

June | 635 | 558.7 | 12.0% | 682.4 | 7.5% | 681.9 | 7.4% | 691.0 | 8.8% | 680.5 | 7.2% |

July | 790 | 861.8 | 9.1% | 775.3 | 1.9% | 776.7 | 1.7% | 751.4 | 4.9% | 704.0 | 10.9% |

$\Delta $ | 7.8% | - | 12.3% | - | 12.1% | - | 11.1% | 10.1% |

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**MDPI and ACS Style**

Zhao, L.; Zhou, X.
Forecasting Electricity Demand Using a New Grey Prediction Model with Smoothness Operator. *Symmetry* **2018**, *10*, 693.
https://doi.org/10.3390/sym10120693

**AMA Style**

Zhao L, Zhou X.
Forecasting Electricity Demand Using a New Grey Prediction Model with Smoothness Operator. *Symmetry*. 2018; 10(12):693.
https://doi.org/10.3390/sym10120693

**Chicago/Turabian Style**

Zhao, Lianming, and Xueyu Zhou.
2018. "Forecasting Electricity Demand Using a New Grey Prediction Model with Smoothness Operator" *Symmetry* 10, no. 12: 693.
https://doi.org/10.3390/sym10120693