# Optimal Electric Vehicle Fleet Charging Management with a Frequency Regulation Service

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## Abstract

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## 1. Introduction

- Maximize the regulatory reserve by using an EV charging algorithm based on preventive actions, replacing the planning problem with one on the fly;
- Avoid the use of hard constraints, as well as reducing the number of decision variables and the number of constraints to reduce computation time and memory usage;
- Take into account the efficiency of the charger and its dependence on power and therefore maximizing charging efficiency;
- Take into account the SoC and temperature dependence of regulation capacity and keeping the total regulation capacity in the optimal zone;
- Control the bi-directional charging of EVs (V2G), taking into account both the power demand of the grid operator and the satisfaction of the SoC target of the EVs’ users.

## 2. Optimization Problem Modeling

- Case 1 (namely P1): the standard power dispatch problem with a frequency disturbance. In this context, the main goal is to charge EVs, but the idea is to also keep a regulation capability of up and down, i.e., to keep EVs in an optimal region to be able to better face the second case;
- Case 2 (namely P2): the frequency regulation problem with a power request from or to the power grid. The main goal, then, becomes to answer this power demand emerging from the power grid, while trying to consider EVs charging expectations.

- To charge its battery in order to obtain a high SoC to meet the EV owner needs (>0.7);
- To keep the SoC within an optimal range to improve the capability of the fleet to answer a frequency control request (>0.4 and <0.6).

## 3. Simulations and Results

#### 3.1. Impacts of the Charger Efficiency

#### 3.2. Impacts of the Number of EVs

#### 3.3. Impact of Long Frequency Drops and the Maximum Charging Rate

#### 3.4. Discussions about EV Usage in the Frequency Regulation Market

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

${w}_{1},{w}_{2},{w}_{3},{w}_{4}$ | Weighting factors |

${E}_{i}$ | Total available energy stored in the EVs |

${N}_{EV}$ | Number of EVs |

${P}_{i}^{j}$ | Charging power of the j-th EV at time i |

$\Delta t$ | Sampling time |

${E}_{i}^{ref}$ | Energy reference at time i |

$So{C}_{i}^{j}$ | State of charge of the j-th EV in time step i |

${E}_{batt}^{j}$ | Battery capacity of the j-th EV |

$So{H}^{j}$ | State of health of the j-th EV’ battery |

$So{C}_{i}^{ref}$ | SoC reference at time i |

${P}_{i}^{ref}$ | Power reference at time i |

${E}^{saturation}$ | Energy threshold of the charging station |

$So{C}^{limit}$ | Maximum SoC limit |

${E}_{i}^{remain}$ | Remaining energy before reaching |

${E}^{saturation}$ | time i |

${t}_{op}$ | Station opening hours |

${P}_{i}^{request}$ | Power request at time i |

$\eta $ | Charger efficiency |

${C}_{i}^{j}$, ${D}_{i}^{j}$ | Power upper/lower bound of the j-th EV during time step i |

${s}_{i}^{j}$] | State of the j-th EV at time i |

${\alpha}_{i}^{j,ub}$, ${\alpha}_{i}^{j,lb}$ | Binary variables depending on the SoC of the j-th EV at time i |

${P}_{i}^{j,max+}$, ${P}_{i}^{j,max-}$ | Maximal authorized charging/discharging rate for j-th EV at time step i |

${P}_{chpt+}^{j}$, ${P}_{chpt-}^{j}$ | Maximum charging/discharging power of the charging point of the j-th EV |

${P}_{charger+}^{j}$, ${P}_{charger-}^{j}$ | Maximum power of the j-th charger in charging or discharging mode |

${P}_{Bat+,i}^{j}$, ${P}_{Bat-,i}^{j}$ | Maximum accepted/delivered battery’s power of the j-th EV at time i |

depending on the SoC and the battery’s temperature | |

${P}_{total}$ | Maximum transformer power of the charging station |

${m}^{j}$ | Mass of the j-th EV battery |

${C}_{p}^{j}$ | Specific heat coefficient of the j-th EV battery |

${T}_{i}^{j}$ | Temperature of the j-th EV battery at time i |

${P}_{joule,i}^{j}$ | Power dissipated by the joule effect of the j-th EV battery at time i |

${P}_{convective,i}^{j}$ | Power heat transfer between the battery and the outside of the j-th EV battery |

at time i | |

${k}^{j}$ | Thermal factor depending on the thermal inertia of the j-th EV battery |

${T}_{i}^{out}$ | Outside temperature at time i |

${R}_{th\_out}^{j}$ | Heat convection coefficient between the j-th EV battery and outside |

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**Figure 1.**Optimal capability region for charging or discharging lithium−ion batteries, depending on their SoC.

Parameters | Value |
---|---|

Sampling time | 5 min |

Maximum number of EVs | 20 |

Battery capacity | 60 kWh |

Starting SoC | $[0.1,0.6]$ |

Desired SoC | $[0.3,0.9]$ |

Maximum/minimum SoC | 0.9/0.2 |

**Table 2.**Simulation parameters of EVs in Section 3.1.

Parameters | Time (h) |
---|---|

Arrival times | 8 h |

Departure times | 18 h |

**Table 3.**Simulation parameters of the EVs in Section 3.2.

Parameters | Time (h) |
---|---|

Arrival times | $\mathcal{N}(9,0.5)$ |

Departure times | $\mathcal{N}(17,0.5)$ |

**Table 4.**General condition of the primary and secondary reserves [24].

Primary Reserve | Secondary Reserve | |
---|---|---|

Dynamic of activation | $50\%$ within 15 s and $100\%$ of the reserve enabled within 30 s | $100\%$ of the reserve activated within 5 min |

Duration of activation | Maximum of 15 min | unlimited during the duration of the contract |

Minimum power | 1 MW | 5 MW |

Power direction | Negative AND Positive | Negative OR Positive |

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**MDPI and ACS Style**

Dahmane, Y.; Chenouard, R.; Ghanes, M.; Alvarado Ruiz, M.
Optimal Electric Vehicle Fleet Charging Management with a Frequency Regulation Service. *World Electr. Veh. J.* **2023**, *14*, 152.
https://doi.org/10.3390/wevj14060152

**AMA Style**

Dahmane Y, Chenouard R, Ghanes M, Alvarado Ruiz M.
Optimal Electric Vehicle Fleet Charging Management with a Frequency Regulation Service. *World Electric Vehicle Journal*. 2023; 14(6):152.
https://doi.org/10.3390/wevj14060152

**Chicago/Turabian Style**

Dahmane, Yassir, Raphaël Chenouard, Malek Ghanes, and Mario Alvarado Ruiz.
2023. "Optimal Electric Vehicle Fleet Charging Management with a Frequency Regulation Service" *World Electric Vehicle Journal* 14, no. 6: 152.
https://doi.org/10.3390/wevj14060152