# Optimized Integration of Electric Vehicles in Low Voltage Distribution Grids

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## Abstract

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## 1. Introduction

_{2}emissions in Germany. Besides its contribution to global warming, road transportation is responsible for 30% of NO

_{X}and 12% of particulate matter emissions, which have shown to have a significant impact on human life expectancy [2]. Electric vehicles (EVs) are an emerging clean technology, with battery EVs generating zero direct CO

_{2}emissions in the atmosphere. So far, EVs have been in the center of most strategies to mitigate GHG emissions and reach the set climate targets. Since EVs create no tailpipe emissions, these hazardous pollutants can be reduced, especially in urban areas. Supported by incentive programs, the number of EVs has risen to three million units in 2017, an increase of 50% in comparison to 2016 [3]. According to the Global EV Outlook [3], the number of EVs worldwide could exceed 130 million by 2030 under the assumption that government policies continue supporting the expansion of electromobility.

## 2. Related Work

#### 2.1. Modeling of Low Voltage Grids

#### 2.2. Charging Strategies

- Model a realistic and representative semi-urban low voltage grid in a simulation environment.
- Evaluate the impact of uncoordinated charging on low voltage networks realistically and as representatively as possible using criteria such as voltage drop, voltage unbalance, and thermal rating of cables used in the grid.
- Use the representative grid model to test and asses different optimized strategies, based on different objectives, such as cost reduction or grid-friendliness.

## 3. Methodology

#### 3.1. Modeling Framework

#### 3.2. Electrical Grid Model

#### 3.3. Charging Strategies

- End consumers, who want to charge as much self-produced electricity as possible. Additionally, they possibly want to minimize the GHG emissions of the energy mix which is used for charging EVs.
- Distribution system operators, who have to ensure safe operating conditions and want to minimize network losses.
- Aggregators, who want to maximize their profits by obtaining energy as cheaply as possible.

$\tilde{N}$ | : | Number of vehicles |

$\tilde{T}$ | : | Number of discrete time steps |

$\tilde{O}$ | : | Number of PV installations |

N | : | Set of vehicles $N=\left(\right)open="\{"\; close="\}">1,2,\dots ,\tilde{N}$ |

T | : | Set of time steps $T=\left(\right)open="\{"\; close="\}">1,2,\dots ,\tilde{T}$ |

$\mathsf{\Omega}$ | : | Set of PV installations $\mathsf{\Omega}=\left(\right)open="\{"\; close="\}">1,2,\dots ,\tilde{O}$ |

$\Delta t$ | : | Time step length (e.g., $0.25$ h) |

n | : | Vehicle index $n\in N$ |

t | : | Time step index $t\in T$ |

o | : | PV installation index $o\in \mathsf{\Omega}$ |

${R}_{n}$ | : | Number of departures/arrivals of vehicle $n\in N$ |

${T}_{n}^{\mathrm{arr}}$ | : | Set of arrival times of vehicle $n\in N$: ${T}_{n}^{\mathrm{arr}}=\left(\right)open="\{"\; close="\}">0,{t}_{n,1}^{\mathrm{arr}},\dots ,{t}_{n,{R}_{n}}^{\mathrm{arr}}$ |

${T}_{n}^{\mathrm{dep}}$ | : | Set of departure times of vehicle $n\in N$: ${T}_{n}^{\mathrm{dep}}=\left(\right)open="\{"\; close="\}">{t}_{n,0}^{\mathrm{dep}},\dots ,{t}_{n,{R}_{n}}^{\mathrm{dep}}$ |

${x}_{n,t}$ | : | Charging power of n-th vehicle at time step $t\in T$ |

${\mathrm{ce}}_{t}$ | : | Electricity price at time step $t\in T$ |

${b}_{t}$ | : | Baseload function of aggregated household baseloads at time step $t\in T$ |

$p{v}_{o,t}$ | : | PV feed-in of PV-installation $o\in \mathsf{\Omega}$ at time step $t\in T$ |

$B{C}_{n}$ | : | Battery capacity of vehicle $n\in N$ |

${\mathrm{co}}_{t}$ | : | GHG emissions at time step $t\in T$ |

$lc{p}_{n}$ | : | Charging power rate of vehicle $n\in N$ |

$LT$ | : | Transformer apparent power limit/cap |

${t}_{n,j}^{\mathrm{arr}}$ | : | j-th arrival time of vehicle $n\in N:$ ${t}_{n,j}^{\mathrm{arr}}\in {T}_{n}^{\mathrm{arr}}$ |

${t}_{n,j}^{\mathrm{dep}}$ | : | j-th departure time of vehicle $n\in N:$ ${t}_{n,j}^{\mathrm{dep}}\in {T}_{n}^{\mathrm{dep}}$ |

$SO{C}_{{t}_{n,j}^{\mathrm{arr}}}$ | : | State-of-Charge at arrival time ${t}_{n,j}^{\mathrm{arr}}\in {T}_{n}^{\mathrm{arr}};\phantom{\rule{3.33333pt}{0ex}}SO{C}_{{t}_{n,j}^{\mathrm{arr}}}\in [0,1]$ |

$\mu $ | : | Mean of the sum of the baseload ${b}_{t}$ and all charging powers ${x}_{n,t}$ over all time steps $t\in T$ |

#### 3.3.1. Cost Optimized Strategy

#### 3.3.2. Valley Filling (VF) Optimized Strategy

#### 3.3.3. GHG Emission Optimized Strategy

_{2}eq/kWh produced by energy source $z\in Z$. The values are taken from [39]. ${E}_{z,t}$ is the current share of energy source z in total energy generation at time step t. For the total energy generation we take electricity production data for one week in the winter and one week in the summer into account. Z is the set of different energy sources (e.g., solar energy, wind energy, lignite, gas).

#### 3.4. Scenario Definition

#### 3.5. Analysis Criteria

#### 3.5.1. Voltage Drop

#### 3.5.2. Thermal Rating of Cables

#### 3.5.3. Voltage Unbalance

#### 3.5.4. PV Self-Consumption

#### 3.5.5. Electrical Grid Losses

## 4. Results

#### 4.1. Uncoordinated Charging

#### 4.2. Coordinated Charging

#### 4.2.1. Cost Optimized Strategy

_{2}eq. Network transmission losses are decreasing from 1.332 kVA to 0.895 kVA, due to the lower current peaks and the quadratic relation between current and losses. A summary of the changes in economic key figures and a comparison between the results for the different CC strategies can be also found in Table 3.

#### 4.2.2. VF Optimized Strategy

_{2}eq and $89.05$€, respectively. SC is comparably low with 1.13% for the heavy load winter scenario, as the EVs are scheduled to charge predominantly at night.

#### 4.2.3. GHG Emission Optimized Strategy

_{2}eq in the case of uncoordinated charging (2050) to 517.50 kg CO

_{2}eq when GHG-optimized charging is employed. The summed up electricity cost for the charging demand of the EVs lies at $76.39$€, which is comparably low due to the deployment of renewable energy sources. As the charging process is shifted into the night hours, a decrease in SC from 4.04% to 0.18% can be observed. Additionally, due to the shift into the night, the ADL drops to 1.105 kVA, which is caused by lower current flows in the network.

#### 4.3. Discussion of the Results

## 5. Outlook and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Single line diagram of the Distribution System Operator Observatory (DSOO) semi-urban low voltage grid #13 [12].

**Figure 2.**Conceptual approach, with input and output data and models employed. SOC = state of charge; EV = electric vehicles; PV = photovoltaics.

**Figure 3.**Comparison of voltage and current violations duration for different EV penetration rates between the heavy and light load scenarios.

**Figure 4.**Comparison of voltage and current violations duration for different EV penetration rates between the summer and winter week for the heavy load case.

**Figure 5.**Comparison of the apparent power at the transformer for the baseline and 2050 scenario (70% EVs, 33% PV penetration) for a week in the winter and the heavy load case.

**Figure 6.**Comparison of voltage unbalance factors at buses 50, 66, and 114 for evenly distributed EV phase connections and for 70% of connections massed on a single phase.

**Figure 7.**Phase voltages at bus 114 and phase currents at bus 1 for UC with massed connection at R and EVs distributed at the end of the grid.

**Figure 9.**Phase voltages at bus 114 and phase currents at bus 1 for cost optimized vehicle charging.

**Figure 13.**Phase voltages at bus 114 and phase currents at bus 1 for GHG emission optimized vehicle charging.

Baseline | 2030 | 2050 | |
---|---|---|---|

EV penetration | 0% | 30% | 70% |

PV penetration | 13% | 20% | 33% |

**Table 2.**Comparsion of indicators for the uncoordinated charging (UC) scenario, values over one week. GHG = greenhouse gas; SC = self-consumption rate.

Energy Cost in EUR | GHG Production in kg CO_{2}eq | ADL in kVA | SC in % | |
---|---|---|---|---|

Winter’s week | 125.99 | 924.54 | 1.332 | 2.64 |

Summer’s week | 145.90 | 851.25 | 1.108 | 41.59 |

**Table 3.**Total energy cost, GHG emissions, average electrical distribution losses, and PV self-consumption, for different optimization approaches. Data was calculated for a winter’s week, Scenario 2050.

Energy Cost in € | GHG Production in kg CO_{2}eq | ADL in VA | SC in % | |
---|---|---|---|---|

2050 UC | 125.99 | 924.54 | 1332 | 2.64 |

Cost optimized | 60.05 | 548.89 | 895 | 0.75 |

VF | 89.05 | 890.85 | 636 | 1.13 |

GHG-optimized | 76.39 | 517.50 | 1105 | 0.06 |

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## Share and Cite

**MDPI and ACS Style**

Spitzer, M.; Schlund, J.; Apostolaki-Iosifidou, E.; Pruckner, M.
Optimized Integration of Electric Vehicles in Low Voltage Distribution Grids. *Energies* **2019**, *12*, 4059.
https://doi.org/10.3390/en12214059

**AMA Style**

Spitzer M, Schlund J, Apostolaki-Iosifidou E, Pruckner M.
Optimized Integration of Electric Vehicles in Low Voltage Distribution Grids. *Energies*. 2019; 12(21):4059.
https://doi.org/10.3390/en12214059

**Chicago/Turabian Style**

Spitzer, Martin, Jonas Schlund, Elpiniki Apostolaki-Iosifidou, and Marco Pruckner.
2019. "Optimized Integration of Electric Vehicles in Low Voltage Distribution Grids" *Energies* 12, no. 21: 4059.
https://doi.org/10.3390/en12214059