# Smart Control Strategies for Primary Frequency Regulation through Electric Vehicles: A Battery Degradation Perspective

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## Abstract

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## 1. Introduction

- We propose two novel frequency control strategies that aim at minimizing the EVs battery degradation. Differently from the existing contributions, which only address the need for frequency regulation service, our approach proposes a battery degradation model while ensuring the stabilization of grid frequency.
- We propose a profitability analysis to correlate the profit obtained by the EV’s user in participating in the frequency regulation service and the cost incurred by the battery degradation. Hence, we compare the proposed frequency control strategies with other related techniques in terms of energy that is exchanged with the main grid and degradation of the battery. The results obtained through numerical experiments based on a realistic power system model show the better performance of the proposed mechanisms under the actual operating conditions with respect to the reference strategies.

## 2. Preliminaries on Frequency Regulation

## 3. EV Battery Model

## 4. V2G for Load Frequency Regulation

#### 4.1. Elementary Control (ElCo)

#### 4.2. Balance Control (BaCo)

#### 4.3. Smart Charging Control (SmChCo)

#### 4.4. Bounded Control (BoCo)

#### 4.5. Low Degradation Control (LoDeCo)

## 5. Case Study

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

RES | Renewable energy source |

EV | Electric vehicle |

V2G | vehicle-to-grid |

FDC | Frequency droop control |

EVB | Electric-vehicle battery |

ESS | Energy storage system |

BESS | Battery energy storage system |

SoC | State of charge |

DoD | Depth of discharge |

SG | Synchronous generator |

PV | Photovoltaic |

PFR | Primary frequency regulation |

SFR | Secondary frequency regulation |

TFR | Tertiary frequency regulation |

ElCo | Elementary Control |

BoCo | Bounded Control |

BaCo | Balance Control |

SmChCo | Smart Charging |

LoDeCo | Low Degradation Control |

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**Figure 1.**Discrepancy between forecasts and real demand in Italy: (

**a**) hourly profile of 1 March 2019; (

**b**) hourly profile from January 1st 2019 to December 31st 2019. Data from Italian transmission system operator (Terna) [7].

**Figure 2.**The subsequent effects of primary, secondary, and tertiary frequency regulation after an unexpected loss of generation.

**Figure 3.**Degradation of lithium-ion batteries as a function of subsequent SoC: surface plot (

**a**) and contour plot (

**b**).

**Figure 4.**(

**a**) ElCo: V2G power flow control scheme. (

**b**) BaCo: V2G frequency droop as a function of the SoC for the charging and discharging cases (the SoC is kept around 0.5 by using ${\mathrm{SoC}}_{i}^{\mathrm{max}}=0.9$, ${\mathrm{SoC}}_{i}^{\mathrm{min}}=0.1$, ${\mathrm{SoC}}_{i}^{\mathrm{high}}=0.8$ and ${\mathrm{SoC}}_{i}^{\mathrm{low}}=0.2$ [32]). (

**c**) SmChCo: V2G power flow control scheme [32].

**Figure 5.**V2G frequency droop as a function of the SoC for the charging and discharging cases for the BoCo approach (

**a**). V2G frequency droop as a function of the SoC for the charging and discharging cases for the LoDeCo approach (

**b**). V2G frequency droop as a function of the SoC for the LoDeCo for different $\tau $ values (

**c**).

**Figure 7.**Number of cycles of the battery with respect to the SoC profile for the five considered strategies: (

**a**) ElCo; (

**b**) BaCo; (

**c**) SmChCo; (

**d**) BoCo; and, (

**e**) LoDeCo.

**Figure 8.**Battery SoC profile for the five considered strategies: (

**a**) ElCo; (

**b**) BaCo; (

**c**) SmChCo; (

**d**) BoCo; (

**e**) LoDeCo.

**Figure 9.**Power grid frequency for the different considered control strategies: focus on the first 200 time slots.

ElCo | BoCo | BaCo | SmChCo | LoDeCo | |
---|---|---|---|---|---|

Degradation [%] | 5.0122 | 3.2667 | 2.3556 | 10.4521 | 0.5163 |

Exchanged energy [MWh] | 0.2924 | 0.2923 | 0.2643 | 1.1779 | 0.1955 |

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## Share and Cite

**MDPI and ACS Style**

Scarabaggio, P.; Carli, R.; Cavone, G.; Dotoli, M. Smart Control Strategies for Primary Frequency Regulation through Electric Vehicles: A Battery Degradation Perspective. *Energies* **2020**, *13*, 4586.
https://doi.org/10.3390/en13174586

**AMA Style**

Scarabaggio P, Carli R, Cavone G, Dotoli M. Smart Control Strategies for Primary Frequency Regulation through Electric Vehicles: A Battery Degradation Perspective. *Energies*. 2020; 13(17):4586.
https://doi.org/10.3390/en13174586

**Chicago/Turabian Style**

Scarabaggio, Paolo, Raffaele Carli, Graziana Cavone, and Mariagrazia Dotoli. 2020. "Smart Control Strategies for Primary Frequency Regulation through Electric Vehicles: A Battery Degradation Perspective" *Energies* 13, no. 17: 4586.
https://doi.org/10.3390/en13174586