# Hybrid Predictive Modeling for Charging Demand Prediction of Electric Vehicles

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## Abstract

**:**

## 1. Introduction

## 2. Models for Hybrid Strategy

#### 2.1. Statistical Model

#### 2.2. Machine Learning Techniques

## 3. Analysis

#### 3.1. Feature Extraction

#### 3.2. Preprocessing

#### 3.3. Results

- Mean of errors (ME): $\frac{1}{n}{\displaystyle \sum _{t=1}^{n}}{e}_{t}$;
- RMSE: $\sqrt{\frac{1}{n}{\displaystyle \sum _{t=1}^{n}}{e}_{t}^{2}}$;
- Mean of absolute errors (MAE): $\frac{1}{n}{\displaystyle \sum _{t=1}^{n}}\left|{e}_{t}\right|$;
- Mean of percentage errors (MPE): 100/n$\times {\displaystyle \sum _{t=1}^{n}}{e}_{t}/{y}_{t}^{{}^{\prime}}$;
- Mean of absolute percentage errors (MAPE): 100/n$\times {\displaystyle \sum _{t=1}^{n}}|{e}_{t}/{y}_{t}^{{}^{\prime}}|$.

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 7.**Comparison of accuracy measure between the original ML method and proposed hybrid strategy.

**Figure 8.**Comparison of the actual observation and prediction for each method. (

**a**) Line plot. (

**b**) Scatter plot.

Hyperparameter | Description | |
---|---|---|

RF | mtry | Number of features randomly selected as candidates at each split |

ntree | Number of trees to grow | |

nodesize | Minimum size of terminal nodes | |

XGBoost | nrounds | Number of boosting iterations |

eta | Learning rate | |

max_depth | Maximum depth of a tree | |

gamma | Minimum loss reduction required to make a split | |

min_chile_weight | Minimum sum of the instance weight needed in a child | |

subsample | Subsample ratio of training data | |

colsample_bytree | Ratio for subsampling of features |

Feature | Type | Description |
---|---|---|

Hour | Numeric | Hour of day when the EV charges |

Quarter | Categorical | 1 = January to March, 2 = April to June, 3 = July to September, 4 = October to December |

Weekday | Categorical | Thursday, Friday, Saturday (1 = Yes, 0 = No) |

Holiday | Categorical | Public holidays (1 = Yes, 0 = No) |

S1-24 | Numeric | Fourier daily term $\left(sin\left(2\pi t/24\right)\right)$ |

C1-24 | Numeric | Fourier daily term $\left(cos\left(2\pi t/24\right)\right)$ |

S2-24 | Numeric | Fourier daily term $\left(sin\left(4\pi t/24\right)\right)$ |

C2-24 | Numeric | Fourier daily term $\left(cos\left(4\pi t/24\right)\right)$ |

S1-168 | Numeric | Fourier weekly term $\left(sin\left(2\pi t/168\right)\right)$ |

C1-168 | Numeric | Fourier weekly term $\left(cos\left(2\pi t/168\right)\right)$ |

S2-168 | Numeric | Fourier weekly term $\left(sin\left(4\pi t/168\right)\right)$ |

C2-168 | Numeric | Fourier weekly term $\left(cos\left(4\pi t/168\right)\right)$ |

DHR | STLM | BSTS | ||
---|---|---|---|---|

${\beta}_{Hour}$ | 0.0261 | 0.0136 | 0.0751 | |

${\beta}_{Quarter}$ | 0.0362 | 0.0226 | 0.0000 | |

${\beta}_{Weekday}$ | 0.0676 | 0.0155 | 0.0701 | |

${\beta}_{Holiday}$ | 0.0330 | 0.0429 | 0.0000 | |

${\alpha}_{1}$ | 0.2367 | −0.0109 | − | |

${\alpha}_{2}$ | −0.0011 | 0.0023 | − | |

${\alpha}_{3}$ | 0.0184 | 0.0009 | − | |

${\alpha}_{4}$ | 0.0093 | 0.0001 | − | |

${\gamma}_{1}$ | −0.0397 | 0.0200 | − | |

${\gamma}_{2}$ | 0.0374 | −0.0068 | − | |

${\gamma}_{3}$ | 0.0145 | −0.0013 | − | |

${\gamma}_{4}$ | 0.0187 | −0.0005 | − | |

${\eta}_{t}$ | ${\varphi}_{1}$ | 1.2747 | 0.3468 | − |

${\varphi}_{2}$ | −0.1424 | − | − | |

${\varphi}_{3}$ | −0.1136 | − | − | |

${\varphi}_{4}$ | −0.0478 | − | − | |

${\varphi}_{5}$ | −0.1138 | − | − | |

${\theta}_{1}$ | −1.8849 | −0.9887 | − | |

${\theta}_{2}$ | 0.8903 | − | − |

RF | XGBoost | Stacking | |
---|---|---|---|

Stack.XGBoost | Stack.GLM | ||

mtry = 6 | nrounds = 957 | nrounds = 420 | ${\beta}_{0}$ = 0.002 |

ntree = 504 | eta = 0.080 | eta = 0.369 | ${\beta}_{RF}$ = 0.254 |

nodesize = 5 | max_depth = 6 | max_depth = 10 | ${\beta}_{XGBoost}$ = 0.732 |

gamma = 3.336 | gamma = 5.650 | ||

min_chile_weight = 4 | min_chile_weight = 6 | ||

subsample = 0.707 | subsample = 0.878 | ||

colsample_bytree = 0.699 | colsample_bytree = 0.431 |

Statistical Model | ML Model | ||||||
---|---|---|---|---|---|---|---|

DHR | STLM | BSTS | RF | XGBoost | Stack.XGBoost | Stack.GLM | |

ME | 0.024 | −0.064 | 0.200 | −0.072 | −0.015 | −0.046 | −0.035 |

RMSE | 0.729 | 0.311 | 0.392 | 0.299 | 0.301 | 0.303 | 0.300 |

MAE | 0.604 | 0.219 | 0.304 | 0.199 | 0.210 | 0.205 | 0.204 |

MPE | −2.168 | −1.153 | 3.160 | −1.805 | −0.934 | −1.483 | −1.300 |

MAPE | 11.691 | 4.239 | 5.570 | 4.107 | 4.285 | 4.233 | 4.203 |

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## Share and Cite

**MDPI and ACS Style**

Jeon, Y.-E.; Kang, S.-B.; Seo, J.-I.
Hybrid Predictive Modeling for Charging Demand Prediction of Electric Vehicles. *Sustainability* **2022**, *14*, 5426.
https://doi.org/10.3390/su14095426

**AMA Style**

Jeon Y-E, Kang S-B, Seo J-I.
Hybrid Predictive Modeling for Charging Demand Prediction of Electric Vehicles. *Sustainability*. 2022; 14(9):5426.
https://doi.org/10.3390/su14095426

**Chicago/Turabian Style**

Jeon, Young-Eun, Suk-Bok Kang, and Jung-In Seo.
2022. "Hybrid Predictive Modeling for Charging Demand Prediction of Electric Vehicles" *Sustainability* 14, no. 9: 5426.
https://doi.org/10.3390/su14095426