# Sparse Measurement-Based Coordination of Electric Vehicle Charging Stations to Manage Congestions in Low Voltage Grids

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Sparse Measurement-Based Detection of Feeder Congestions

#### 2.1.1. Mathematical Formulation

- The aggregate active (${P}_{f}^{in}$) and reactive power injection (${Q}_{f}^{in}$), defined in Equations (2a) and (2b), flows through the same line segment of the feeder.
- This line segment is subject to the lowest feeder voltage (${U}_{f}^{min}$).
- This line segment has the lowest thermal limit current (${I}_{f}^{th,min}$) of all line segments.$${P}_{f}^{in}={P}_{f}^{src,in}+{{\displaystyle \sum}}_{i=1}^{{N}_{f}}{P}_{f,i}^{CP,in},$$$${Q}_{f}^{in}={Q}_{f}^{src,in}+{Q}_{f}^{c}+{{\displaystyle \sum}}_{i=1}^{{N}_{f}}{Q}_{f,i}^{CP,in},$$$${P}_{f}^{src,in}=0,\mathrm{for}{P}_{f}^{src}0;\mathrm{and}{P}_{f}^{src,in}={P}_{f}^{src},\mathrm{for}{P}_{f}^{src}\ge 0,$$$${P}_{f,i}^{CP,in}=0,\mathrm{for}{P}_{f,i}^{CP}0;\mathrm{and}{P}_{f,i}^{CP,in}={P}_{f,i}^{CP},\mathrm{for}{P}_{f,i}^{CP}\ge 0,$$$${Q}_{f}^{src,in}=0,\mathrm{for}{Q}_{f}^{src}0;\mathrm{and}{Q}_{f}^{src,in}={Q}_{f}^{src},\mathrm{for}{Q}_{f}^{src}\ge 0,$$$${Q}_{f,i}^{CP,in}=0,\mathrm{for}{Q}_{f,i}^{CP}0;\mathrm{and}{Q}_{f,i}^{CP,in}={Q}_{f,i}^{CP},\mathrm{for}{Q}_{f,i}^{CP}\ge 0.$$

#### 2.1.2. Application to Real LV Grid

${I}_{f}^{th,min}$ | Derived from grid data |

${P}_{f}^{src,in},$${Q}_{f}^{src,in}$$\mathrm{and}{U}_{f}^{min}$ | Derived from measurements |

${P}_{f,i}^{CP,in},{Q}_{f,i}^{CP,in}\mathrm{and}{Q}_{f}^{c}$ | Estimated |

- Grid Data

- Measurements

- Estimations

#### 2.2. Detection of DTR Congestions

#### 2.3. Coordination Algorithms

- Reduce until next permission

- Reduce for 30 min

- Reduce until end of charging

#### 2.4. Test Setup

#### 2.4.1. Simulation Software

^{®}SINCAL 16.0, while the algorithms are implemented in MATLAB R2019b. Both tools are connected through the COM-interface.

#### 2.4.2. Power System Model

- Low voltage grid

- Customer plants

- Scenario definition

## 3. Results

#### 3.1. Sparse Measurement-Based Detection of Feeder Congestions

#### 3.1.1. Simultaneous Charging in the Evening

#### 3.1.2. Simultaneous Charging in the Morning

#### 3.1.3. Charging throughout the Day

#### 3.2. Coordination Algorithms

#### 3.2.1. Simultaneous Charging in the Evening

#### 3.2.2. Simultaneous Charging in the Morning

#### 3.2.3. Charging throughout the Day

## 4. Discussion

#### 4.1. Sparse Measurement-Based Detection of Feeder Congestions

#### 4.2. CoordinationAalgorithms

#### 4.3. Applicability of the Concept

## 5. Conclusions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

CP | Customer Plant | EVCS | Electric Vehicle Charging Station |

DER | Distributed energy resource | LF | Load flow |

Dev | Device | LV | Low voltage |

DSO | Distribution system operator | OLTC | On-load tap changer |

DSSE | Distribution system state estimation | Pr | Producer |

DTR | Distribution transformer | PV | Photovoltaic |

EV | Electric vehicle | St | Storage |

${P}_{f}^{src}$$,{Q}_{f}^{src}$ | Active and reactive power flows at the beginning of feeder f. |

${P}_{f,i}^{CP}$$,{Q}_{f,i}^{CP}$ | Active and reactive power contributions of CP i connected to feeder f. |

$\Delta {P}_{f}$$,\Delta {Q}_{f}$ | Active and reactive power losses in the series impedances of all line segments of feeder f. |

${Q}_{f}^{c}$ | Reactive power production of the shunt capacitances of all line segments of feeder f. |

${P}_{f}^{in}$$,{Q}_{f}^{in}$ | Aggregate active and reactive power injections into feeder f. |

${U}_{f}^{min}$ | Minimal voltage of feeder f. |

${I}_{f}^{th,min}$ | Minimal thermal limit current of all line segments of feeder f. |

${U}_{prim}^{DTR}$ | Voltage at the primary bus bar of the DTR. |

${U}_{sec}^{DTR}$ | Voltage at the secondary bus bar of the DTR. |

${P}_{f}^{src,in}$$,{Q}_{f}^{src,in}$ | Active and reactive power injections at the beginning of feeder f. |

${P}_{f,i}^{CP,in}$$,{Q}_{f,i}^{CP,in}$ | Active and reactive power injections of CP i connected to feeder f. |

${N}_{f}$ | Number of customer plants connected to feeder f. |

$F$ | Number of feeders. |

$Loadin{g}_{f}^{max}$ | Estimated value of the maximum line segment loading of feeder f. |

$C{F}_{f}$ | Congestion flag related to feeder f. |

${S}_{f}^{src,in}$ | Apparent power injection at the beginning of feeder f. |

$Loadin{g}_{f}^{limit}$ | Limit of the line segment loading of feeder f. |

${I}_{f,{l}_{m}}^{th,main}$ | Thermal limit current of line segment ${l}_{m}$, which is part of the main strands of feeder $f$. |

${U}_{f,j}$ | Voltage measurement $j$ at feeder $f$. |

${P}_{f,i}^{Dev}$$,{Q}_{f,i}^{Dev}$ | Aggregate active and reactive power contributions of all consuming devices included in CP i connected to feeder f. |

${P}_{f,i}^{Pr}$$,{Q}_{f,i}^{Pr}$ | Aggregate active and reactive power contributions of all producers included in CP i connected to feeder f. |

${P}_{f,i}^{St}$$,{Q}_{f,i}^{St}$ | Aggregate active and reactive power contributions of all storages included in CP i connected to feeder f. |

${P}_{f,i}^{Pr,max}$$,{Q}_{f,i}^{Pr,max}$ | Maximal active and reactive power injections of the producer included in CP i connected to feeder f. |

${S}_{rated}^{DTR}$ | Rated apparent power of the distribution transformer. |

$Loadin{g}^{DTR}$ | Loading of the distribution transformer. |

$C{F}_{DTR}$ | Congestion flag related to the distribution transformer. |

$Loadin{g}_{DTR}^{limit}$ | Limit of the distribution transformer loading. |

${P}_{nom,f,i}^{Dev}$$,{Q}_{nom,f,i}^{Dev}$ | Active and reactive power contributions of the device model included in CP i connected to feeder f for nominal supply voltage. |

${U}_{f,i}^{CP,pu}$ | Normalized supply voltage of CP i connected to feeder f. |

${U}_{f,i}^{CP}$ | Supply voltage of CP i connected to feeder f. |

$So{C}_{f,i}^{St}$ | State-of-charge of the electric vehicle battery included in CP i connected to feeder f. |

${P}_{nom,f,i}^{St}$ | Active power contribution of the storage model included in CP i connected to feeder f for nominal supply voltage. |

$\Delta t$ | Resolution of the load profiles. |

${E}_{f,i}^{St,max}$ | Storage capacity of the electric vehicle battery included in CP i connected to feeder f. |

$t$ | Instant of time. |

${t}_{f,i}^{St,start}$ | Instant of time in which the charging process of the electric vehicle battery included in CP i connected to feeder f is started. |

$\Delta E$ | Energy loss of the complete low voltage grid. |

${T}_{avg}$ | Average charging time per electric vehicle battery. |

$\Delta {P}^{DTR}$ | Active power loss of the distribution transformer. |

$\Delta {P}_{l}^{line}$ | Active power loss of the line segment l. |

${T}_{e}^{EVCS}$ | Charging time of electric vehicle charging station e. |

${N}^{EVCS}$ | Number of electric vehicle charging stations. |

${N}_{correct,f}^{t}$ | Number of instants of time in which the congestion flag related to feeder f is correctly set. |

${N}_{total}^{t}$ | Number of simulated instants of time. |

$accurac{y}_{f}$ | Detection accuracy related to feeder f. |

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**Figure 4.**Overview of the coordination algorithms executed by different devices: (

**a**) central controller; (

**b**) different options for the distributed electric vehicle charging stations (EVCSs).

**Figure 5.**Power system model: (

**a**) simplified one-line diagram of the LV grid; (

**b**) customer plants (CP) structure.

**Figure 6.**Load profiles of different CP components: (

**a**) device (Dev)-model; (

**b**) producer (Pr)-model.

**Figure 7.**Simulation results for the scenario ‘Simultaneous charging in the evening’ without any coordination: (

**a**) SoCs of all EV batteries; (

**b**) equipment loading; (

**c**) grid state at 18:46.

**Figure 8.**Line segment loadings and congestion flag of different feeders for the scenario ‘Simultaneous charging in the evening’ without any coordination.

**Figure 9.**Simulation results for the scenario ‘Simultaneous charging in the morning’ without any coordination: (

**a**) SoCs of all EV batteries; (

**b**) equipment loading; (

**c**) grid state at 10:33.

**Figure 10.**Line segment loadings and congestion flag of different feeders for the scenario ‘Simultaneous charging in the morning’ without any coordination.

**Figure 11.**Simulation results for the scenario ‘Charging throughout the day’ without any coordination: (

**a**) SoCs of all EV batteries; (

**b**) equipment loading; (

**c**) grid state at 16:47.

**Figure 12.**Line segment loadings and congestion flag of different feeders for the scenario ‘Charging throughout the day’ without any coordination.

**Figure 13.**LV equipment loading and SoCs of all EV batteries for the scenario ‘Simultaneous charging in the evening’ with coordination and different algorithms in EVCS level: (

**a**) reduce until next permission; (

**b**) reduce for 30 min; (

**c**) reduce until end of charging.

**Figure 14.**LV equipment loading and SoCs of all EV batteries for the scenario ‘Simultaneous charging in the morning’ with coordination and different algorithms in EVCS level: (

**a**) reduce until next permission; (

**b**) reduce for 30 min; (

**c**) reduce until end of charging.

**Figure 15.**LV equipment loading and SoCs of all EV batteries for the scenario ‘Charging throughout the day’ with coordination and different algorithms in EVCS level: (

**a**) reduce until next permission; (

**b**) reduce for 30 min; (

**c**) reduce until end of charging.

Feeder | Cable Share in % | Maximal Feeder Length in km | Total Line Length in km | Number of Connected CPs | |
---|---|---|---|---|---|

In Total | With EVCS and PV System | ||||

1 | 51.92 | 0.49 | 1.040 | 26 | 10 |

2 | 100 | 0.15 | 0.205 | 4 | 3 |

3 | 100 | 0.43 | 0.810 | 18 | 9 |

4 | 93.55 | 0.61 | 1.550 | 23 | 15 |

5 | 100 | 0.27 | 0.490 | 7 | 3 |

6 | 61.36 | 0.61 | 0.880 | 13 | 6 |

Scenario | Coordination Algorithm | |
---|---|---|

Central Controller | Distributed EVCSs | |

Simultaneous charging in the evening | None | None |

Specify permissions | Reduce until next permission | |

Reduce for 30 min | ||

Reduce until end of charging | ||

Simultaneous charging in the morning | None | None |

Specify permissions | Reduce until next permission | |

Reduce for 30 min | ||

Reduce until end of charging | ||

Charging throughout the day | None | None |

Specify permissions | Reduce until next permission | |

Reduce for 30 min | ||

Reduce until end of charging |

PV Production | Scenario | Detection Accuracy by the Feeder in % | |||||
---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | ||

Estimated | Simultaneous charging in the evening | 92.92 | 100 | 89.11 | 81.26 | 100 | 100 |

Simultaneous charging in the morning | 91.46 | 100 | 81.54 | 77.17 | 100 | 100 | |

Charging throughout the day | 100 | 100 | 89.45 | 73.07 | 100 | 100 | |

Exact | Simultaneous charging in the evening | 92.92 | 100 | 89.11 | 82.03 | 100 | 100 |

Simultaneous charging in the morning | 97.57 | 100 | 88.27 | 79.67 | 100 | 100 | |

Charging throughout the day | 100 | 100 | 100 | 87.30 | 100 | 100 |

Scenario | Coordination Algorithm | Energy Loss in kWh | Average Charging Time in min | |
---|---|---|---|---|

Central Controller | Distributed EVCSs | |||

Simultaneous charging in the evening | None | None | 56.65 | 161.00 |

Specify permissions | Reduce until next permission | 44.54 | 233.43 | |

Reduce for 30 min | 39.38 | 273.89 | ||

Reduce until end of charging | 37.80 | 285.50 | ||

Simultaneous charging in the morning | None | None | 22.28 | 161.00 |

Specify permissions | Reduce until next permission | 16.15 | 248.11 | |

Reduce for 30 min | 15.19 | 279.74 | ||

Reduce until end of charging | 14.76 | 287.04 | ||

Charging throughout the day | None | None | 21.31 | 161.00 |

Specify permissions | Reduce until next permission | 21.00 | 183.41 | |

Reduce for 30 min | 20.31 | 213.24 | ||

Reduce until end of charging | 19.63 | 233.59 |

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## Share and Cite

**MDPI and ACS Style**

Schultis, D.-L.
Sparse Measurement-Based Coordination of Electric Vehicle Charging Stations to Manage Congestions in Low Voltage Grids. *Smart Cities* **2021**, *4*, 17-40.
https://doi.org/10.3390/smartcities4010002

**AMA Style**

Schultis D-L.
Sparse Measurement-Based Coordination of Electric Vehicle Charging Stations to Manage Congestions in Low Voltage Grids. *Smart Cities*. 2021; 4(1):17-40.
https://doi.org/10.3390/smartcities4010002

**Chicago/Turabian Style**

Schultis, Daniel-Leon.
2021. "Sparse Measurement-Based Coordination of Electric Vehicle Charging Stations to Manage Congestions in Low Voltage Grids" *Smart Cities* 4, no. 1: 17-40.
https://doi.org/10.3390/smartcities4010002