# A Time-Varying Potential Evaluation Method for Electric Vehicle Group Demand Response Driven by Small Sample Data

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## Abstract

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## 1. Introduction

#### 1.1. Motivation and Background

#### 1.2. Literature Overview

- The short-term DR potential of EVs is directly related to the vehicle scheduling strategy. Different DR control types and methods have a direct impact on the potential. It is necessary to consider travel needs and willingness to participate, so as to achieve non-inductive DR control and maximize potential.
- It is difficult to obtain refined travel data and charging load data of large-scale EVs. How to evaluate the potential of large-scale EVs based on the small sample data in the DR pilot project is an urgent problem to be solved.
- Due to the randomness of the time and space of EV travel, and the state changes of vehicles in DR, the DR potential is diverse at different times of day, and the potential during DR also changes with time. Considering the time-varying nature can further improve the accuracy of potential evaluation.

#### 1.3. Contributions

- The travel activity model of large-scale EVs is established. Based on the actual travel data of a sample of residents, the probability distributions of the key parameters in the travel model are obtained by kernel density estimation (KDE) and probability statistical fitting. The fitting results reflect the irregular distribution of variables, with high accuracy and robustness.
- Considering the temporal and spatial distribution of the SOC and the travel demand of the EVs, the non-inductive control strategies of three DR modes (peak-cutting, V2G discharge, and valley-filling) are analyzed. The three DR strategies are independent of each other, which maximizes the DR potential while meeting the travel needs of the EVs.
- Based on the three DR strategies, the time-varying characteristics of DR are analyzed separately, including the change in potential with the duration of DR and the change at different periods of in a day. Furthermore, the power change index is defined to quantify the DR potential.

## 2. DR Potential Evaluation Method of EV

#### 2.1. EV Load Model

#### 2.2. DR Control Strategy Analysis of EVs

#### 2.2.1. Peak-Shaving DR Strategy

#### 2.2.2. Valley-Filling DR Strategy

#### 2.2.3. V2G Discharge Strategy

#### 2.3. DR Potential Evaluation of EVs

## 3. Model of EV Behavior

#### 3.1. Time–Space Activity Model of EVs

#### 3.1.1. Travel Chain Model

#### 3.1.2. Probability Distribution of Characteristic Values

#### 3.2. Charging and Discharging Behavior Model of EVs

- After the EV arrives at the parking location, if the remaining power is not enough to support the next drive, it must be charged. There are two charging powers to choose from: slow charge or fast charge. Slow charge is preferred; however, if in the slow charge mode the supplementary power is still not enough to support the next drive, then the fast charge mode is adopted.
- If the remaining power is sufficient for the next drive, slow charging or no charging can be selected. Considering factors such as battery safety and remaining power anxiety, every residential consumer has his own minimum acceptable SOC. ${\mathrm{SOC}}_{n,low}^{H}$ is the minimum acceptable SOC at home, and ${\mathrm{SOC}}_{n,low}^{W/O}$ is the minimum acceptable SOC at the work place or other location. If the remaining SOC of the battery is lower than the minimum SOC, the slow charge is still selected for charging.

#### 3.3. Travel Chain and Load Simulation of EVs

- Enter the probability distribution of the characteristic values of the travel chain ${t}_{l,0}^{n}$, ${d}_{(i-1,i)}^{n}$, ${t}_{p,i}^{n}$, $P[typ{e}_{i}^{n}|{t}_{l,i}^{n},typ{e}_{i-1}^{n}]$,${P}_{L}^{n}$.
- Sampling to obtain the total length ${L}^{n}$ of the travel chain.
- Sampling to obtain the time ${t}_{l,0}^{n}$ of the first trip of the day.
- Sampling to obtain the travel destination. According to the current location type and travel time, select the corresponding spatial transition probability and conduct sampling.
- Sampling to obtain the driving distance. Considering the starting point and end point of the drive, select the corresponding probability distribution for sampling.
- Calculate travel time. Considering different driving periods, calculate the corresponding driving time based on Equation (11). Calculate the arrival time at the destination based on Equation (4).
- Sampling to obtain the parking time. Calculate the next travel time based on Equation (5).
- Return to step (4) and re-enter the loop until the travel chain length meets the requirements.

## 4. Case Study

#### 4.1. Calculation of Characteristic Values in the Travel Chain

#### 4.2. Verification of Simulation Results of the Travel Chain

#### 4.3. Simulation Results of Charge Load

#### 4.4. DR Potential Calculation Results

#### 4.4.1. Peak-Shaving DR Potential

#### 4.4.2. Valley-Filling DR Potential

#### 4.4.3. V2G Discharge DR Potential

#### 4.4.4. Comparative Analysis of Three Types of Potential

#### 4.4.5. Interaction Analysis of Potential in Different Periods

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

DR | Demand response | i | Index of trips and locations |

EV | Electric vehicle | ${\eta}_{c/d}$ | Charging and discharging efficiency of EV |

H | Region type–Home | N | Number of EVs |

KDE | Kernel density estimation | n | Index of EVs |

MC | Monte Carlo | $P[typ{e}_{i}^{n}|{t}_{l,i}^{n},typ{e}_{i-1}^{n}]$ | Spatial transition probability |

NHTS | National household travel survey | ${P}_{L}$ | Travel chain length probability |

O | Region type–Other location | ${P}_{c/d}$ | Charge and discharge power |

RMSE | Root Mean Squared Error | $S$ | State of EV connected to the power grid |

SOC | State of charge | ${\mathrm{SOC}}_{n,low}^{H}$ | Minimum SOC for charging at home |

V2G | Vehicle-to-grid | ${\mathrm{SOC}}_{n,low}^{W/O}$ | Minimum SOC for charging at work or other location |

W | Region type–Work place | t | Index of times |

Variables | ${t}_{a,i}^{n}$ | Time when EV n arrives at location i | |

$C$ | Battery capacity of EV | ${t}_{l,i}^{n}$ | Time when EV n leaves location i |

$D$ | Cruising distance of EV | ${t}_{d(i-1,i)}^{n}$ | The time for EV n to arrive at location i from location i−1 |

$\widehat{DR}\left(t\right)$ | Time-varying potential of the EV at time t | ${t}_{p,i}^{n}$ | Parking time of EV n at location i |

${d}_{(i-1,i)}^{n}$ | Distance from location i−1 to location i | $typ{e}_{i}^{n}$ | Type of location i |

$G$ | DR potential generalized function of EV | ${v}_{(i-1,i)}^{n}$ | The average speed of the vehicle from location i−1 to location i |

${\epsilon}_{(i-1,i)}^{n}$ | Distance error from location i−1 to location i |

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**Figure 9.**The comparison of simulated value and actual value. (

**a**) Total driving distance, (

**b**) Home time.

Years | Peak-Shaving Type/Times | Valley- Filling Type/Times | Peak-Shaving Response/10,000 kW | Valley-Filling Response/10,000 kW | Number of Participating Users/Number | Number of Participating Provinces /Number |
---|---|---|---|---|---|---|

2016 | 9 | 0 | 419.1 | 0 | 3340 | 2 |

2017 | 2 | 0 | 7.7 | 0 | 36 | 2 |

2018 | 8 | 5 | 244.8 | 374.3 | 2394 | 6 |

2019 | 51 | 16 | 703.3 | 543.6 | 111,218 | 8 |

2020 | 16 | 18 | 477.8 | 1007.2 | 18,862 | 8 |

Time | 1 | 2 | 3 | 4 | 5 | Average | |
---|---|---|---|---|---|---|---|

Index | |||||||

Total driving distance | RMSE | 0.0013 | 0.0014 | 0.0017 | 0.0014 | 0.0012 | 0.0014 |

r | 0.9600 | 0.9527 | 0.9322 | 0.9512 | 0.9608 | 0.9522 | |

Home time | RMSE | 0.0139 | 0.0112 | 0.0081 | 0.0110 | 0.0118 | 0.0112 |

r | 0.9555 | 0.9719 | 0.9859 | 0.9725 | 0.9669 | 0.9705 |

DR Event Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

DR start time | 0:00 | 2:00 | 4:00 | 6:00 | 8:00 | 10:00 | 12:00 | 14:00 | 16:00 | 18:00 | 20:00 | 22:00 |

DR end time | 2:00 | 4:00 | 6:00 | 8:00 | 10:00 | 12:00 | 14:00 | 16:00 | 18:00 | 20:00 | 22:00 | 24:00 |

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**MDPI and ACS Style**

Ding, S.; Xu, C.; Rao, Y.; Song, Z.; Yang, W.; Chen, Z.; Zhang, Z.
A Time-Varying Potential Evaluation Method for Electric Vehicle Group Demand Response Driven by Small Sample Data. *Sustainability* **2022**, *14*, 5281.
https://doi.org/10.3390/su14095281

**AMA Style**

Ding S, Xu C, Rao Y, Song Z, Yang W, Chen Z, Zhang Z.
A Time-Varying Potential Evaluation Method for Electric Vehicle Group Demand Response Driven by Small Sample Data. *Sustainability*. 2022; 14(9):5281.
https://doi.org/10.3390/su14095281

**Chicago/Turabian Style**

Ding, Sheng, Chengmei Xu, Yao Rao, Zhaofang Song, Wangwang Yang, Zexu Chen, and Zitong Zhang.
2022. "A Time-Varying Potential Evaluation Method for Electric Vehicle Group Demand Response Driven by Small Sample Data" *Sustainability* 14, no. 9: 5281.
https://doi.org/10.3390/su14095281