# Analysis of Charging Infrastructure for Private, Battery Electric Passenger Cars: Optimizing Spatial Distribution Using a Genetic Algorithm

^{*}

## Abstract

**:**

## 1. Introduction

## 2. State-of-the-Art Works

## 3. Methodology

#### 3.1. Optimization Problem

#### 3.1.1. Optimization Method and Genetic Algorithm

#### 3.1.2. Criterion One: Capital Costs

#### 3.1.3. Criterion Two: Agent Detour

#### 3.2. Electric Vehicle Population

#### 3.3. Starting Population for Genetic Algorithm

#### 3.4. Charging Decision Model

#### 3.5. Simulation

## 4. Results

#### 4.1. Development across Generations

#### 4.2. Results of the Final Generation

#### 4.3. Analysis of Different Solutions of the Final Generation

#### 4.3.1. Bottom-Edge Solution

#### 4.3.2. Mid-Front Solution

#### 4.3.3. Top-Edge Solution

## 5. Discussion

#### 5.1. Results

#### 5.2. Methodology

## 6. Conclusions/Outlook

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Europäische Kommission. Electrification of the Transport System. 2017. Available online: https://ec.europa.eu/newsroom/horizon2020/document.cfm?doc_id=46372 (accessed on 21 December 2022).
- Umweltbundesamt. Europäische Abgas-Gesetzgebung. 2019. Available online: https://www.umweltbundesamt.de/themen/verkehr-laerm/emissionsstandards/pkw-leichte-nutzfahrzeuge#textpart-1 (accessed on 21 December 2022).
- Bundesministerium für Umwelt, Naturschutz, Bau und Reaktorsicherheit. Klimaschutzplan 2050: Klimaschutzpolitische Grundsätze und Ziele der Bundesregierung. Available online: https://www.bmwk.de/Redaktion/DE/Publikationen/Industrie/klimaschutzplan-2050.pdf?__blob=publicationFile&v=6 (accessed on 21 December 2022).
- Die Bundesregierung. Klimaschutzprogramm 2030 der Bundesregierung zur Umsetzung des Klimaschutzplans 2050. Available online: https://www.bundesregierung.de/resource/blob/974430/1679914/e01d6bd855f09bf05cf7498e06d0a3ff/2019-10-09-klima-massnahmen-data.pdf?download=1 (accessed on 21 December 2022).
- Ziemke, D.; Kaddoura, I.; Nagel, K. The MATSim Open Berlin Scenario: A multimodal agent-based transport simulation scenario based on synthetic demand modeling and open data. Procedia Comput. Sci.
**2019**, 151, 870–877. [Google Scholar] [CrossRef] - Pagany, R.; Ramirez Camargo, L.; Dorner, W. A review of spatial localization methodologies for the electric vehicle charging infrastructure. Int. J. Sustain. Transp.
**2019**, 13, 433–449. [Google Scholar] [CrossRef] [Green Version] - Asamer, J.; Reinthaler, M.; Ruthmair, M.; Straub, M.; Puchinger, J. Optimizing charging station locations for urban taxi providers. Transp. Res. Part A Policy Pract.
**2016**, 85, 233–246. [Google Scholar] [CrossRef] [Green Version] - Khadem, N.K.; Nickkar, A.; Shin, H.S. A Review of Different Charging Stations Optimal Localization Models and Analysis Functions for the Electric Vehicle Charging Infrastructure. In Proceedings of the International Conference on Transportation and Development 2020, Seattle, DC, USA, 26–29 May 2020; Zhang, G., Ed.; American Society of Civil Engineers: Reston, VA, USA, 2020; pp. 262–276. [Google Scholar] [CrossRef]
- Unterluggauer, T.; Rich, J.; Andersen, P.B.; Hashemi, S. Electric vehicle charging infrastructure planning for integrated transportation and power distribution networks: A review. eTransportation
**2022**, 12, 100163. [Google Scholar] [CrossRef] - Iqbal, S.; Habib, S.; Ali, M.; Shafiq, A.; ur Rehman, A.; Ahmed, E.M.; Khurshaid, T.; Kamel, S. The Impact of V2G Charging/Discharging Strategy on the Microgrid Environment Considering Stochastic Methods. Sustainability
**2022**, 14, 13211. [Google Scholar] [CrossRef] - Straub, F.; Maier, O.; Göhlich, D.; Zou, Y. Forecasting the spatial and temporal charging demand of fully electrified urban private car transportation based on large-scale traffic simulation. Green Energy Intell. Transp.
**2022**, 100039. [Google Scholar] [CrossRef] - Jahn, R.M.; Syré, A.; Grahle, A.; Schlenther, T.; Göhlich, D. Methodology for Determining Charging Strategies for Urban Private Vehicles based on Traffic Simulation Results. Procedia Comput. Sci.
**2020**, 170, 751–756. [Google Scholar] [CrossRef] - Jordán, J.; Palanca, J.; Del Val, E.; Julian, V.; Botti, V. Localization of charging stations for electric vehicles using genetic algorithms. Neurocomputing
**2021**, 452, 416–423. [Google Scholar] [CrossRef] - Efthymiou, D.; Chrysostomou, K.; Morfoulaki, M.; Aifantopoulou, G. Electric vehicles charging infrastructure location: A genetic algorithm approach. Eur. Transp. Res. Rev.
**2017**, 9, 27. [Google Scholar] [CrossRef] - Armas, R.; Aguirre, H.; Orellana, D. Evolutionary bi-objective optimization for the electric vehicle charging stand infrastructure problem. In Proceedings of the Genetic and Evolutionary Computation Conference, Boston, MA, USA, 9–13 July 2022; Fieldsend, J.E., Wagner, M., Eds.; ACM: New York, NY, USA, 2022; pp. 1139–1146. [Google Scholar] [CrossRef]
- Simon, D. Evolutionary Optimization Algorithms: Biologically-Inspired and Population-Based Approaches to Computer Intelligence; John Wiley & Sons Inc.: Hoboken, NJ, USA, 2013. [Google Scholar]
- Stroband, A. Verfahren zur Dimensionierung und Platzierung von Ladeinfrastruktur für Elektrofahrzeuge. Ph.D. Dissertation, RWTH Aachen University, Aachen, Germany, 2018. [Google Scholar]
- Nationale Plattform Elektromobilität. Ladeinfrastruktur für Elektrofahrzeuge in Deutschland: Statusbericht und Handlungsempfehlungen 2015. 2015. Available online: https://www.plattform-zukunft-mobilitaet.de/wp-content/uploads/2021/12/2015_Ladeinfrastruktur_fuer_Elektrofahrzeuge_in_Deutschland_Statusbericht_und_Handlungsempfehlungen.pdf (accessed on 21 December 2022).
- Nationale Plattform Zukunft der Mobilität. Elektromobilität. Brennstoffzelle. Alternative Kraftstoffe—Einsatzmöglichkeiten aus technologischer Sicht: 1. Kurzbericht der AG 2. Available online: https://www.plattform-zukunft-mobilitaet.de/wp-content/uploads/2019/11/NPM-AG-2-Elektromobilit%C3%A4t-Brennstoffzelle-Alternative-Kraftstoffe-Einsatzm%C3%B6glichkeiten-aus-technologischer-Sicht.pdf (accessed on 21 December 2022).
- Funke, S.A. Techno-ökonomische Gesamtbewertung heterogener Maßnahmen zur Verlängerung der Tagesreichweite von batterieelektrischen Fahrzeugen. Ph.D. Dissertation, Universität Kassel, Kassel, Germany, 2018. [Google Scholar]
- NetworkXDevelopers. Single_Source_Dijkstra_Path_Length. 2015. Available online: https://networkx.org/documentation/networkx-1.10/reference/generated/networkx.algorithms.shortest_paths.weighted.single_source_dijkstra_path_length.html#networkx.algorithms.shortest_paths.weighted.single_source_dijkstra_path_length (accessed on 21 December 2022).
- Gerike, R.; Hubrich, S.; Ließke, F.; Wittig, S.; Wittwer, R. Tabellen zum Forschungsprojekt Mobilität in Städten—SrV 2018. Available online: https://changing-cities.org/wp-content/uploads/2020/03/Berlin_Tabellen_Berlin_gesamt.pdf (accessed on 5 November 2021).
- infas Institut für angewandte Sozialwissenschaften. Mobilität in Deutschland: Tabellarische Grundauswertung. 2017. Available online: http://www.mobilitaet-in-deutschland.de/pdf/MiD2017_Tabellenband_Deutschland.pdf (accessed on 21 December 2022).
- ADAC Autotest. Renault Zoe R135 Z.E. 50 (52 kWh) Intens. 2020. Available online: https://assets.adac.de/image/upload/v1585140678/ADAC-eV/KOR/Text/PDF/Renault_Zoe_R135_ZE_50_cweozh.pdf (accessed on 21 December 2022).
- ADAC Autotest. Nissan Leaf (62 kWh) e+ Tekna. 2020. Available online: https://assets.adac.de/image/upload/v1584015200/ADAC-eV/KOR/Text/PDF/Nissan_Leaf_62_kWh_e__Tekna_opybhm.pdf (accessed on 21 December 2022).
- ADAC Autotest. Tesla Model 3 Long Range AWD. 2019. Available online: https://res.cloudinary.com/adacde/image/upload/v1571751244/ADAC-eV/KOR/Text/PDF/Tesla_Model_3_Long_Range_AWD_ybki8e.pdf (accessed on 21 December 2022).
- ADAC Autotest. Audi e-tron 55 quattro. 2019. Available online: https://www.adac.de/_ext/itr/tests/Autotest/AT5926_Audi_e_tron_55_quattro/Audi_e_tron_55_quattro.pdf (accessed on 21 December 2022).
- ADAC. ADAC Autotest Website. 2022. Available online: https://www.adac.de/rund-ums-fahrzeug/tests/autotest/ (accessed on 21 December 2022).
- ADAC e.V. Kosten für E-Autos: Ladeverluste Nicht Vergessen. 2020. Available online: https://presse.adac.de/meldungen/adac-ev/technik/ladeverlust.html (accessed on 21 December 2022).
- Dearborn, S. Charging Li-ion Batteries for Maximum Run Times. 2005. Available online: https://www.semanticscholar.org/paper/Charging-Li-ion-Batteries-for-Maximum-Run-Times-An-Dearborn/e46c5f4c635e1ae98dacc76bfca3e8aa71a2800d (accessed on 21 December 2022).
- Elektromobilität, N.P. Fortschrittsbericht 2018: Markthochlaufphase. 2018. Available online: https://www.plattform-zukunft-mobilitaet.de/wp-content/uploads/2021/12/2018_Fortschrittsbericht_2018_Markthochlaufphase.pdf (accessed on 21 December 2022).
- eon. Elektroautos zuhause laden: Gründe für eine Wallbox fürs Eigenheim. 2020. Available online: https://www.eon.de/de/pk/e-mobility/elektroauto-zuhause-laden-wallbox.html#:~:text=Wallboxen%20gibt%20es%20mit%20einer,sowieso%20nicht%20mehr%20Leistung%20aufnehmen (accessed on 21 December 2022).
- Europäisches Parlament. Europäische Richtlinie für den Ausbau von Infrastruktur für Alternative Kraftstoffe. Available online: https://eur-lex.europa.eu/legal-content/DE/TXT/PDF/?uri=CELEX:32014L0094&from=DE (accessed on 8 December 2020).
- Senatsverwaltung für Umwelt, Verkehr und Klimaschutz Berlin. Nahverkehrsplan Berlin 2019–2023. Available online: https://datenbox.stadt-berlin.de/ssf/s/readFile/share/4826/-8007172482696866025/publicLink/Brosch%C3%BCre_NVP_2019_201109_internet.pdf (accessed on 21 December 2022).
- Bundesverband CarSharing. CarSharing Stellplätze in den öffentlichen Straßenraum Bringen. Available online: https://www.carsharing.de/sites/default/files/uploads/bcs-leitfaden_cs-stellplaetze_im_oeffentlichen_raum_november_2019_online.pdf. (accessed on 21 December 2022).

**Table 2.**Distribution of vehicle classes in Berlin/Brandenburg ([p. 254] in [23]).

Vehicle Class Category | Share Berlin [%] | Share Brandenburg [%] |
---|---|---|

Small | 24 | 23 |

Compact | 34 | 36 |

Medium | 27 | 28 |

Large | 9 | 7 |

Nonassignable | 6 | 6 |

Vehicle Class | Model | Battery Capacity [kWh] | Energy Consumption (ic/ot/mw) * [kWh/100 km] |
---|---|---|---|

Small | Renault Zoe [24] | 41 | 15.4 (11.7/17.0/17.8) |

Compact | Nissan Leaf e+ [25] | 62 | 20.6 (15.6/21.8/24.5) |

Medium | Tesla Model 3 LR [26] | 75 | 17.5 (16.2/17.9/18.1) |

Large | Audi e-tron [27] | 83.6 | 22.9 (20.8/23.9/23.0) |

Parameter | Description | Value |
---|---|---|

Max. Vehicle SoC [%] | Maximum SoC the vehicles can be charged up to or agents start a charging process | 80 |

Min. Vehicle SoC [%] | SoC for which an agent classifies a charging process as necessary | 30 |

Min. Standing Time [s] | Minimum duration from arrival to departure necessary to start a charging process | 300 |

Tolerated Distance [m] | Maximum detour an agent will cover if the charging process is classified as not necessary | 500 |

Max. Distance [m] | Max. detour an agent will cover to execute a charging process | 1000 |

Number of Generations | Number of generations simulated | 100 |

Parameter | Mean Value Gen. 1 | Mean Value Gen. 100 |
---|---|---|

Charging points | 118,250 | 237,150 |

Capital costs [${10}^{6}$ €] | 2184 | 2876 |

Mean detour [m] | 581 | 405 |

Total detours [10${}^{6}$ m] | 398 | 411 |

Charging processes | 696,530 | 1,046,240 |

Temporal occupation rate [%] | 41.03 | 38.18 |

Mean SoC before first trip [%] | 85.93 | 85.93 |

Mean SoC after last trip [%] | 70.12 | 71.33 |

Share of AC charging points [%] | 79.2 | 89.9 |

Share of DC charging points [%] | 20.8 | 10.1 |

Agents with 0% SoC | 40,180 (3.0%) | 35,880 (2.68%) |

Parameter | Bottom Edge | Mid-Front | Top Edge |
---|---|---|---|

Charging points | 112,040 | 246,630 | 379,690 |

Capital costs [${10}^{6}$ €] | 624 | 2950 | 5692 |

Mean detour [m] | 591 | 378 | 254 |

Total detours [10${}^{6}$ m] | 400 | 416 | 317 |

Charging processes | 676,760 | 1,100,340 | 1,246,130 |

Temporal occupation rate [%] | 40.69 | 38.3 | 29.07 |

Mean SoC before first trip [%] | 85.93 | 85.93 | 85.93 |

Mean SoC after last trip [%] | 69.7 | 71.58 | 72.11 |

Share of AC charging points [%] | 97.1 | 89.2 | 85.8 |

Share of DC charging points [%] | 2.9 | 10.8 | 14.2 |

Agents with 0% SoC | 40,830 (3.05%) | 35,130 (2.63%) | 33,720 (2.52%) |

Charging Power | Number of Charging Points | Relative Share |
---|---|---|

3.7 kW | 59,390 | 53.00% |

11 kW | 25,000 | 22.32% |

22 kW | 24,360 | 21.74% |

50 kW | 1580 | 1.41% |

150 kW | 1710 | 1.53% |

Charging Power | Number of Charging Points | Relative Share |
---|---|---|

3.7 kW | 89,690 | 36.37% |

11 kW | 66,870 | 27.11% |

22 kW | 63,540 | 25.76% |

50 kW | 13,840 | 5.61% |

150 kW | 12,690 | 5.15% |

Charging Power | Number of Charging Points | Relative Share |
---|---|---|

3.7 kW | 113,480 | 29.89% |

11 kW | 106,430 | 28.03% |

22 kW | 105,860 | 27.88% |

50 kW | 27,100 | 7.14% |

150 kW | 26,820 | 7.06% |

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## Share and Cite

**MDPI and ACS Style**

Fadranski, D.; Syré, A.M.; Grahle, A.; Göhlich, D.
Analysis of Charging Infrastructure for Private, Battery Electric Passenger Cars: Optimizing Spatial Distribution Using a Genetic Algorithm. *World Electr. Veh. J.* **2023**, *14*, 26.
https://doi.org/10.3390/wevj14020026

**AMA Style**

Fadranski D, Syré AM, Grahle A, Göhlich D.
Analysis of Charging Infrastructure for Private, Battery Electric Passenger Cars: Optimizing Spatial Distribution Using a Genetic Algorithm. *World Electric Vehicle Journal*. 2023; 14(2):26.
https://doi.org/10.3390/wevj14020026

**Chicago/Turabian Style**

Fadranski, Diego, Anne Magdalene Syré, Alexander Grahle, and Dietmar Göhlich.
2023. "Analysis of Charging Infrastructure for Private, Battery Electric Passenger Cars: Optimizing Spatial Distribution Using a Genetic Algorithm" *World Electric Vehicle Journal* 14, no. 2: 26.
https://doi.org/10.3390/wevj14020026