# Maximising Distribution Grid Utilisation by Optimising E-Car Charging Using Smart Meter Gateway Data

^{*}

## Abstract

**:**

## 1. Introduction

_{2}, has announced its intention to achieve climate neutrality by 2060. Neighboring countries such as South Korea and Japan aim to achieve this goal even earlier—by 2050. The EU also plans to follow suit by reducing greenhouse gas emissions by 55% by 2030 compared to 1990 levels, becoming completely climate-neutral by 2050.

_{2}emissions is the electrification of freight and passenger transport [1]. Registrations of electric vehicles (EVs) and vans in Europe significantly increased in 2020, reaching nearly 1,325,000 units, up from 550,000 units in 2019. This represents a 3.5% increase, accounting for 11% of total new registrations in just one year. Furthermore, the share of electric vans increased from 1.4% of total new registrations in 2019 to 2.2% in 2020. Battery electric vehicles, rather than plug-in hybrids, accounted for the majority of electric van and passenger car registrations in 2020 [2]. While Norway has the largest share of EV registrations among European countries, Germany leads the European market for plug-in electric car sales. In Norway, which has a population of around 5.4 million people, every second newly registered car is a battery electric vehicle [3].

## 2. State of the Art

_{2}emissions and fuel cost compared to other methods. Other algorithms such as particle swarm optimisation [10] and artificial bee colony [11] algorithms have also been applied to achieve power flow optimisation.

_{2}minimisation or cost reduction for energy generation. Instead, the study reported in [17] addressed the control of residential EV chargers connected to a low-voltage power grid with a tree-like operational structure. The available capacity of the power grid, measured by distribution-level phasor measurement units, was divided in a proportionally fair manner among connected EVs, considering their demands and self-declared deadlines. This approach is closest to that investigated in our study. However, the proposed optimisation method requires measuring units to be installed at every node in the considered grid, as pointed out by Zishan et al. [17].

## 3. Materials and Methods

#### 3.1. The Principle of the Algorithm

- Household load profiles: Predicted household profiles are needed so that the optimiser can shift the EV chargings in order to react to fluctuating household loads;
- Grid topology: Knowledge of the grid topology, such as line impedances and lengths, transformer nominal power, and the positions of the charging stations, is required for correct calculations of node voltages and currents on the lines;
- Customer requests: Desired target SOCs and times, as well as start SOCs and times, are required for optimisation to prioritise which EVs to charge;
- Settings for time: The optimiser requires time settings to know which horizon (e.g., 24 h) to predict and at what resolution (e.g., 15 min).

- Only a single grid line is considered;
- House connection lines (and their impedances) are not considered;
- Node voltages are considered over time for the SOC calculation;
- Only the real part of line impedances is considered [22].

#### 3.2. Linear Programming Design

#### 3.2.1. Sets

- The set of time steps ($\mathcal{T}=\{1,\cdots ,n\}$) in the considered horizon;
- The set of nodes ($\mathcal{N}=\{1,\cdots ,n\}$) of the considered grid line;
- The set of nodes with a charging station attached (${\mathcal{N}}_{\mathrm{EV}}=\{1,\cdots ,n\}$) in the considered grid line, where ${\mathcal{N}}_{\mathrm{EV}}\subseteq \mathcal{N}$;
- The set of lines ($\mathcal{L}=\{1,\cdots ,n\}$) of the considered grid line.

#### 3.2.2. Variables

#### 3.2.3. Parameters

- The impedances of the respective lines: ${Z}_{l}\phantom{\rule{1.em}{0ex}}\forall l\in \mathcal{L}$;
- The voltages at the respective nodes: ${U}_{n}\phantom{\rule{1.em}{0ex}}\forall n\in \mathcal{N}$;
- The currents of the respective household loads: ${I}_{t,n}^{\mathrm{HH}}\phantom{\rule{1.em}{0ex}}\forall t,n\in \mathcal{T}\times \mathcal{N}$;
- The battery capacity of the respective EVs: $En\phantom{\rule{1.em}{0ex}}\forall n\in {\mathcal{N}}_{\mathrm{EV}}$;
- The maximum permittable charging current of the respective EVs: ${I}_{n}^{\mathrm{max}}\phantom{\rule{1.em}{0ex}}\forall n\in {\mathcal{N}}_{\mathrm{EV}}$;
- The maximum permittable current of the respective lines: ${I}_{l}^{\mathrm{max}}\phantom{\rule{1.em}{0ex}}\forall l\in \mathcal{L}$;
- The start SOCs of the respective EVs: $SO{C}_{n}^{\mathrm{start}}\phantom{\rule{1.em}{0ex}}\forall n\in {\mathcal{N}}_{\mathrm{EV}}$;
- The start time steps of the respective EVs: ${t}_{n}^{\mathrm{start}}\phantom{\rule{1.em}{0ex}}\forall n\in {\mathcal{N}}_{\mathrm{EV}}$;
- The requested target SOCs of the respective EVs: $SO{C}_{n}^{\mathrm{target}}\phantom{\rule{1.em}{0ex}}\forall n\in {\mathcal{N}}_{\mathrm{EV}}$;
- The requested target time steps of the respective EVs: ${t}_{n}^{\mathrm{target}}\phantom{\rule{1.em}{0ex}}\forall n\in {\mathcal{N}}_{\mathrm{EV}}$;
- The conceded target fulfillment of the respective EVs: ${S}_{n}\phantom{\rule{1.em}{0ex}}\forall n\in {\mathcal{N}}_{\mathrm{EV}}$.

- The voltage on the transformer low-voltage side: ${U}_{0}$;
- The transformer nominal power: ${P}_{\mathrm{Trafo}}$;
- The minimum permittable node voltage: ${U}_{\mathrm{min}}$;
- The maximum permittable difference among EV charging currents: $\Delta {I}_{\mathrm{max}}$;
- The duration of a time step: $\Delta t$.

#### 3.2.4. Objective Function

#### 3.2.5. Constraints

#### 3.2.6. Additional Constraints for Fair Charging

#### 3.2.7. Bounds of the Variables

#### 3.3. Hardware Used for Optimisation

## 4. Results

- The length of the individual lines is 20 m each;
- The specific impedance of the individual lines is $2\times {10}^{-4}\Omega $${\mathrm{m}}^{-1}$ each;
- All the individual lines are expected to be able to conduct the same current;
- The battery capacity of the individual EVs is 50 kWh each;
- The nominal power of the individual charging stations is 11 kW (three-phase total) each;
- The household load profiles are taken from [23];
- The time resolution is 6 min;
- The considered time horizon is 24 h.

#### 4.1. Scenario 1: Demonstrate Load Shifting

#### 4.2. Scenario 2: Demonstrate Scalability

#### 4.3. Scenario 3: Comparison over One Week

#### 4.4. Scenario 4: Fair Charging under Extreme Conditions

#### 4.5. Scenario 5: Detailed Comparison of Fair Charging

#### 4.6. Time Required to Solve the Optimisation Model

## 5. Discussion/Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

EV | Electric vehicle |

GLO | Grid line optimiser |

SMG | Smart meter gateway |

GTE | Grid topology estimation |

GSE | Grid state estimation |

EMO | Simulation environment |

## Appendix A. Source Code of the Optimisation

`test_optimization.py`is the executable script. The scripts

`optimization.py`,

`household.py`, and

`battery_electric_vehicle.py`hold the necessary definitions. The script

`EMO.py`holds the code for the simulation environment (code is adapted from the author of [21]). The comments given in the source code are sufficient as a description. In case of further questions, the corresponding author may be contacted.

## Appendix B. Detailed Customer Requests of the Scenarios

Node Nr. | Start SOC (%) | Target SOC (%) | Start Time (h) | Target Time (h) |
---|---|---|---|---|

1 | 20 | 80 | 2 | 10 |

2 | 20 | 70 | 2 | 16 |

3 | 30 | 80 | 2 | 18 |

4 | 20 | 90 | 2 | 18 |

5 | 25 | 80 | 2 | 17 |

6 | 40 | 70 | 2 | 20 |

Wish | Lower Bound | Mean | Upper Bound |
---|---|---|---|

Start SOC (%) | 10 | 10 | 10 |

Target SOC (%) | 100 | 100 | 100 |

Start time (h) | 12 | 12 | 12 |

Target time (h) | 18 | 18 | 18 |

Wish | Lower Bound | Mean | Upper Bound |
---|---|---|---|

Start SOC (%) | 20 | 30 | 40 |

Target SOC (%) | 60 | 80 | 100 |

Start time (h) | 8 | 10 | 12 |

Target time (h) | 15 | 19 | 23 |

Wish | Lower Bound | Mean | Upper Bound |
---|---|---|---|

Start SOC (%) | 20 | 30 | 40 |

Target SOC (%) | 60 | 80 | 100 |

Start time (h) | 8 | 10 | 12 |

Target time (h) | 15 | 19 | 23 |

Node Nr. | Start SOC (%) | Target SOC (%) | Start Time (h) | Target Time (h) |
---|---|---|---|---|

1 | 10 | 100 | 12 | 21 |

2 | — | — | — | — |

3 | — | — | — | — |

4 | — | — | — | — |

5 | — | — | — | — |

6 | 30 | 100 | 16 | 21 |

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**Figure 1.**System structure (SMG: smart meter gateway; GTE: grid topology estimation; GSE: grid state estimation; GLO: grid line optimiser; EMO: simulation environment).

**Figure 10.**Results of optimisation for Scenario 3—difference between sorted timelines for transformer load in the case of optimisation and control.

Observed Criterion | Unit | Allowed Limit |
---|---|---|

Transformer load | % | ≤100 |

Line load | % | ≤100 |

Node voltage | $\%{U}_{\mathrm{nominal}}$ | ≤$\pm 6$ [18] |

Device | Processor | RAM |
---|---|---|

Dell Inspiron 15 | Intel Core i5 8250U; 1.80 GHz | 8 GB |

Raspberry Pi 3 | ARMv8; 1.20 GHz | 1 GB |

Scenario | Transformer Nominal Power [kVA] | Nodes | EVs | Control | “Fairness” |
---|---|---|---|---|---|

1 | 150 | 6 | 6 | no | no |

2 | 200 | 40 | 40 | yes | no |

3 | 250 | 40 | 40 | yes | no |

4 | 220 | 40 | 40 | no | yes |

5 | 15 | 6 | 2 | no | yes |

Device | Number of EVs | |||||||
---|---|---|---|---|---|---|---|---|

10 | 20 | 30 | 40 | 50 | 60 | |||

Laptop | Create problem | [s] | $0.29$ | $0.61$ | $0.84$ | $1.1$ | $1.51$ | $1.91$ |

Solve problem | [s] | $0.36$ | $0.61$ | $0.74$ | $1.04$ | $1.56$ | $2.13$ | |

Raspberry Pi | Create problem | [s] | $0.74$ | $1.79$ | $3.04$ | $4.65$ | $6.44$ | $8.37$ |

Solve problem | [s] | $0.91$ | $1.91$ | $3.25$ | $5.2$ | $8.41$ | $16.02$ |

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## Share and Cite

**MDPI and ACS Style**

Ulrich, A.; Baum, S.; Stadler, I.; Hotz, C.; Waffenschmidt, E.
Maximising Distribution Grid Utilisation by Optimising E-Car Charging Using Smart Meter Gateway Data. *Energies* **2023**, *16*, 3790.
https://doi.org/10.3390/en16093790

**AMA Style**

Ulrich A, Baum S, Stadler I, Hotz C, Waffenschmidt E.
Maximising Distribution Grid Utilisation by Optimising E-Car Charging Using Smart Meter Gateway Data. *Energies*. 2023; 16(9):3790.
https://doi.org/10.3390/en16093790

**Chicago/Turabian Style**

Ulrich, André, Sergej Baum, Ingo Stadler, Christian Hotz, and Eberhard Waffenschmidt.
2023. "Maximising Distribution Grid Utilisation by Optimising E-Car Charging Using Smart Meter Gateway Data" *Energies* 16, no. 9: 3790.
https://doi.org/10.3390/en16093790