#
Simulating Electric Vehicle Diffusion and Charging Activities in France and Germany^{ †}

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

How is it possible to combine the modeling of PEV adoption, charging behavior, and load-shifting potentials in energy-system analysis for France and Germany?

## 2. Related Work

_{2}emissions. In addition, despite the high PEV-specific granularity, the approach presented in this study intends to keep simulations feasible in terms of calculation costs, while maintaining a good approximation of reality at the same time.

## 3. Method: A Hybrid Modelling Approach

#### 3.1. Plug-In Electric Vehicle (PEV) Diffusion and Adoption

#### 3.1.1. Bass Diffusion Model

#### 3.1.2. Binary Logistic PEV Adoption Model

#### 3.1.3. Hybrid PEV Diffusion Modeling Approach

**Pseudocode**

**of**

**Method**

**1**

**for all**$\tilde{t}$

**do**

**end while**

**end for**

**Pseudocode**

**of**

**Method**

**2**

**for all**$\tilde{t}$

**end while**

**while**${a}_{\widehat{i}}\in {\widehat{A}}_{\tilde{t}}^{Adopterset}$

**end while**

**end for**

#### 3.2. PEV Charging

## 4. Results

#### 4.1. PEV Diffusion and Adoption

^{−4}and q = 0.4; Germany: p = 2.5 × 10

^{−5}and q = 0.5). The innovation coefficients for Germany and France in our results are somewhat higher (France: p = 1.44 × 10

^{−4}; Germany p = 4.31 × 10

^{−5}), but relatively low in comparison to other common innovation coefficients averaging p = 0.03 [52,53]. The estimated imitation coefficients are slightly below the average of q = 0.38 [52,53] (France: q = 0.31; Germany: q = 0.32), but are comparable with other innovations [53]. Differences could be due to the fact that only sales figures of zero-emission PEV were included in [52], but all types of plug-in PEV are considered in our study.

#### 4.2. PEV Charging

#### 4.3. Effects of Re-Sampling Approach

## 5. Discussion

#### 5.1. Hybrid Diffusion and Adoption Model for PEV

#### 5.2. Sensitivity Analysis for PEV Charging

#### 5.3. Limitations

## 6. Conclusions and Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Cumulated daily PEV load of direct and controlled PEV charging in (

**a**) France and (

**b**) Germany in 2030.

**Figure 4.**Average hourly cumulated PEV load of original and reduced sample directly charging in 2030.

**Figure 5.**Sensitivity analysis concerning total energy charged and total energy flexibly charged, depending on (

**a**) varying battery capacity, minimum range, and (

**b**) charging power. Base case: charging with (

**a**) 60 kWh battery capacity, 100 km minimum range, and (

**b**) 3.7 kW.

PEV Stock | France | Germany | ||
---|---|---|---|---|

End 2009 | - | [47] | 3032 | [48] |

End 2010 | 3368 | 4404 | ||

End 2011 | 6167 | 8670 | ||

End 2012 | 12,805 | 13,582 | ||

End 2013 | 22,217 | 23,208 | ||

End 2014 | 33,595 | 36,175 | ||

End 2015 | 54,282 | 48,688 | ||

End 2016 | 79,856 | 54,997 | ||

Mid 2017 [1] | 101,799 | 92,731 | ||

Expectation 2030 | 6,000,000 [49] | 6,000,000 [50] | ||

Total vehicle stock (M) * | 32,675,972 [47] | 45,803,560 [48] |

Parameter | France | Germany | ||
---|---|---|---|---|

Mean | Std. Dev. | Mean | Std. Dev. | |

$p$ | $4.31\times {10}^{-5}$ | $2.67\times {10}^{-5}$ | $1.44\times {10}^{-4}$ | $1.82\times {10}^{-5}$ |

$q$ | 0.32 | 0.004 | 0.31 | 0.0015 |

${t}_{0}$ | 2008.22 | 5.82 | 2010.01 | 1.05 |

R^{2} | ~1 | ~1 |

France | Germany | ||||
---|---|---|---|---|---|

Original Sample | Reduced Sample | Original Sample | Reduced Sample | ||

PEV adopters charging in sample | 4942 | 967 | 4487 | 930 | |

Represented number of PEV adopters charging | 5.9 mn | 6.0 mn | 5.5 mn | 5.1 mn | |

Charging events of sampled PEV adopters | 8873 | 1700 | 8590 | 1756 | |

Represented charging events | 11.8 mn | 12.2 mn | 10.4 mn | 9.5 mn | |

Plug-in time $\Delta {t}_{x}^{plug}$ | Mean | 10.36 h | 9.94 h | 9.93 h | 10.59 h |

Std. Dev. | 7.23 h | 7.76 h | 7.75 h | 7.24 h | |

Median | 9.67 h | 11.64 h | 11.42 h | 9.58 h | |

Active charging time $\Delta {t}_{x}^{active}$ | Mean | 1.56 h | 1.35 h | 1.39 h | 1.70 h |

Std. Dev. | 2.18 h | 2.32 h | 2.39 h | 2.19 h | |

Median | 0.82 h | 0.77 h | 0.79 h | 0.82 h | |

Load-shifting potential $\Delta {t}_{x}^{LSP}$ | Mean | 8.80 h | 8.59 h | 8.53 h | 8.88 h |

Std. Dev. | 7.12 h | 7.59 h | 7.58 h | 7.16 h | |

Median | 7.81 h | 9.09 h | 8.66 h | 7.89 h | |

Energy charged per charging event | Mean | 5.77 kWh | 4.99 kWh | 5.15 kWh | 6.31 kWh |

Std. Dev. | 8.07 kWh | 8.60 kWh | 8.86 kWh | 8.12 kWh | |

Median | 3.04 kWh | 2.84 kWh | 2.92 kWh | 3.04 kWh | |

Total energy charged per day ${E}^{total}$ | 60.82 GWh | 60.82 GWh | 59.96 GWh | 59.96 GWh | |

Total energy directly charged per day ${E}^{direct}$ | 1.65 GWh | 2.26 GWh | 2.06 GWh | 2.92 GWh | |

Total energy flexibly charged per day ${E}^{flex}$ | 59.16 GWh | 58.56 GWh | 57.90 GWh | 57.04 GWh |

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**MDPI and ACS Style**

Ensslen, A.; Will, C.; Jochem, P.
Simulating Electric Vehicle Diffusion and Charging Activities in France and Germany. *World Electr. Veh. J.* **2019**, *10*, 73.
https://doi.org/10.3390/wevj10040073

**AMA Style**

Ensslen A, Will C, Jochem P.
Simulating Electric Vehicle Diffusion and Charging Activities in France and Germany. *World Electric Vehicle Journal*. 2019; 10(4):73.
https://doi.org/10.3390/wevj10040073

**Chicago/Turabian Style**

Ensslen, Axel, Christian Will, and Patrick Jochem.
2019. "Simulating Electric Vehicle Diffusion and Charging Activities in France and Germany" *World Electric Vehicle Journal* 10, no. 4: 73.
https://doi.org/10.3390/wevj10040073