# Wind Speed for Load Forecasting Models

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Background

#### 2.1. Multiple Linear Regression Models for Load Forecasting

_{t}is the expected load; Trend

_{t}is a chronological trend at time t; M

_{t}, W

_{t}and H

_{t}are class variables for month, day of a week, and hour of a day at time t; and T

_{t}is the coincidence temperature. Let $f({T}_{t})$ be defined as in Equation (2):

_{t}

_{−h}is the temperature of previous h

^{th}hours (h = 0, 1, 2, …); ${\tilde{T}}_{t,d}=\frac{1}{24}{\sum}_{h=24d-23}^{24d}{T}_{t-h}$ is the 24-h moving average temperature of the previous d

^{th}day (d = 0, 1, 2, …). These models are also known as recency effect models [15]. In this paper, we consider the benchmark model and three variations of the recency effect models to show the effectiveness of including the wind variables in load forecasting models with different levels of sophistication. Specifically, h ranges from 0 to 2; d is up to 1.

#### 2.2. Wind Chill Index

#### 2.3. Cross-Validation

#### 2.4. Out-of-Sample Test

## 3. Data

#### 3.1. Data Description

#### 3.2. Exploratory Data Analysis

## 4. Models

#### 4.1. Wind Speed-Related Variables

_{t}to denote the coincidence wind speed in summer.

#### 4.2. Two WCI-Based Models

## 5. Results and Discussion

#### 5.1. Out-of-Sample Test

_{1}), the base models plus the proposed wind speed terms (TM

_{2}), the base models with WCI replacing the temperature variables (TM

_{3}), and the base models plus the WCI terms (TM

_{4}).

_{2}models outperform the TM

_{1}models with the relative improvement on MAPE(s) ranging from 0.08% to 1.99%. That confirms the effectiveness of the proposed wind speed variables. On the other hand, TM

_{3}models are not as accurate as the TM

_{1}models. In other words, simply replacing temperature with the predefined WCI does not improve the forecast accuracy. Although the TM

_{4}models also outperform the TM

_{1}models, the TM

_{2}models have the lowest MAPE in most cases. The percentage values listed beside the base model label indicates the percentage of the number of zones where TM

_{2}returns better results than TM

_{4}. In sum, adding the proposed wind speed related variables brings more improvement to the base models on average than using the predefined WCI.

#### 5.2. Ex Ante Forecasting

#### 5.3. Future Research Directions

## 6. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Time series plot of the hourly load, temperature, wind chill index, and wind speed (2012–2015).

Zone | Weather Station | Load (MW) | Temperature (°F) | WCI (°F) | Wind Speed (MPH) | ||||
---|---|---|---|---|---|---|---|---|---|

Mean | STD. | Mean | STD. | Mean | STD. | Mean | STD. | ||

CT | KBDL | 3516.14 | 766.52 | 51.61 | 19.44 | 49.17 | 22.31 | 7.32 | 5.20 |

ME | KPWM | 1320.56 | 202.01 | 47.80 | 18.57 | 44.86 | 21.81 | 7.40 | 5.21 |

NEMASS | KBOS | 2914.24 | 571.68 | 52.08 | 17.95 | 48.79 | 21.86 | 10.47 | 2.33 |

NH | KCON | 1331.56 | 265.15 | 47.45 | 20.35 | 45.21 | 22.86 | 5.45 | 5.24 |

RI | KPVD | 934.15 | 202.94 | 52.17 | 18.20 | 49.62 | 21.30 | 8.41 | 5.23 |

VT | KBTV | 653.32 | 106.66 | 47.95 | 21.28 | 44.91 | 24.62 | 7.55 | 5.55 |

SEMASS | KPVD | 1711.79 | 387.60 | 52.17 | 18.20 | 49.62 | 21.30 | 8.41 | 5.23 |

WCMASS | KORH | 1980.58 | 379.29 | 48.69 | 18.99 | 44.81 | 23.30 | 9.92 | 5.06 |

ISONE | N/A | 14,362.35 | 2825.33 | 50.05 | 18.85 | 46.96 | 22.39 | 8.18 | 4.11 |

Base Model (h,d) | None | $\mathit{W}\mathit{S}{\mathit{S}}_{\mathit{t}}^{0.16}$ | $\mathit{W}\mathit{S}{\mathit{S}}_{\mathit{t}}^{0.16}$ ${\mathit{T}}_{\mathit{t}}\times \mathit{W}\mathit{S}{\mathit{S}}_{\mathit{t}}^{0.16}$ | $\mathit{W}\mathit{S}{\mathit{S}}_{\mathit{t}}^{0.16}$ ${\mathit{T}}_{\mathit{t}}\times \mathit{W}\mathit{S}{\mathit{S}}_{\mathit{t}}^{0.16}$ ${\mathit{H}}_{\mathit{t}}\times \mathit{W}\mathit{S}{\mathit{S}}_{\mathit{t}}^{0.16}$ |
---|---|---|---|---|

B_{1}(h = 0, d = 0) | 3.669 | 3.666 | 3.671 | 3.639 |

B_{2}(h = 0, d = 1) | 3.066 | 3.061 | 3.055 | 3.028 |

B_{3}(h = 1, d = 1) | 2.977 | 2.971 | 2.962 | 2.941 |

B_{4}(h = 2, d = 1) | 2.959 | 2.953 | 2.941 | 2.924 |

Tested Model Groups | Model Equation |
---|---|

$T{M}_{1}$ | $G\left({T}_{t}\right)$ |

$T{M}_{2}$ | $G\left({T}_{t}\right)+g\left(W{S}_{t}\right)$ |

$T{M}_{3}$ | $G\left(WC{I}_{t}\right)$ |

$T{M}_{4}$ | $G\left({T}_{t}\right)+g\left(WC{I}_{t}\right)$ |

© 2017 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/).

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**MDPI and ACS Style**

Xie, J.; Hong, T.
Wind Speed for Load Forecasting Models. *Sustainability* **2017**, *9*, 795.
https://doi.org/10.3390/su9050795

**AMA Style**

Xie J, Hong T.
Wind Speed for Load Forecasting Models. *Sustainability*. 2017; 9(5):795.
https://doi.org/10.3390/su9050795

**Chicago/Turabian Style**

Xie, Jingrui, and Tao Hong.
2017. "Wind Speed for Load Forecasting Models" *Sustainability* 9, no. 5: 795.
https://doi.org/10.3390/su9050795