# Optimal Control of Plug-In Electric Vehicles Charging for Composition of Frequency Regulation Services

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Reference Scenario and Problem Description

## 3. Nomenclature and Problem Formulation

- The current charging power level ${P}_{n,k}$;
- The maximum and the minimum possible charging power levels, respectively ${P}_{n}^{max}>0$ and ${P}_{n}^{min}$ (if ${P}_{n}^{min}<0$, the PEV is enabled to discharging);
- The current SOC level ${x}_{n,k}$;
- The time left until the end of the charging session, ${d}_{n,k}>0$;
- The error, ${e}_{n,k}$, between the desired SOC, ${x}_{n}^{ref}$, and the current one, ${x}_{n,k}$, i.e., ${e}_{n,k}:={x}_{n}^{ref}-{x}_{n,k}$;
- The power deviation, $\Delta {P}_{n,k}$, at time k, for the n-th PEV, due to the participation in the frequency regulation service. This value is computed from a droop curve.

**Assumption**

**1**

## 4. Proposed Local Droop Curves Design Algorithm

#### 4.1. Local Droop Curve Design Constraints

#### 4.2. Global Droop Curve Design Constraints

#### 4.3. Target Function

## 5. Numerical Tests

- 1
- Scenario 1: we run the algorithm in a balanced scenario, i.e., considering a set of charging sessions that are homogeneous in terms of power margin flexibility, SOC error, and charging time availability;
- 2
- Scenario 2: we run the algorithm in a scenario in which the charging sessions have different power margins, different SOC errors, and time flexibility.

#### 5.1. Scenario 1: Local Droop Curves Assignment in a Balanced Scenario

- The possible presence of different charging technologies in the load area, i.e., the fact that the charging sessions are characterized in general by different maximum power, depending on the charging technology;
- The presence of smart charging sessions, i.e., the fact that the charging sessions happen at different charging levels, which are in general different from the maximum possible charging level.

#### 5.2. Scenario 2: Local Droop Curves Assignment in an Unbalanced Scenario

#### 5.3. Notes on the Computational Complexity of the Algorithm

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CPO | Charging point operator |

DSO | Distribution system operator |

PEV | Plug-in electric vehicles |

SOC | State of charge |

## References

- Wang, Z.; Wu, W. Coordinated Control Method for DFIG-Based Wind Farm to Provide Primary Frequency Regulation Service. IEEE Trans. Power Syst.
**2018**, 33, 2644–2659. [Google Scholar] [CrossRef] - Buckspan, A.; Aho, J.; Fleming, P.; Jeong, Y.; Pao, L. Combining droop curve concepts with control systems for wind turbine active power control. In Proceedings of the 2012 IEEE Power Electronics and Machines in Wind Applications, Denver, CO, USA, 16–18 July 2012; pp. 1–8. [Google Scholar] [CrossRef]
- Jietan, Z.; Linan, Q.; Pestana, R.; Fengkui, L.; Libin, Y. Dynamic frequency support by photovoltaic generation with “synthetic” inertia and frequency droop control. In Proceedings of the 2017 IEEE Conference on Energy Internet and Energy System Integration (EI2), Beijing, China, 26–28 November 2017; pp. 1–6. [Google Scholar] [CrossRef]
- Lin, Y.; Barooah, P.; Meyn, S.; Middelkoop, T. Experimental Evaluation of Frequency Regulation From Commercial Building HVAC Systems. IEEE Trans. Smart Grid
**2015**, 6, 776–783. [Google Scholar] [CrossRef] - Hao, H.; Sanandaji, B.M.; Poolla, K.; Vincent, T.L. Frequency regulation from flexible loads: Potential, economics, and implementation. In Proceedings of the 2014 American Control Conference, Portland, OR, USA, 4–6 June 2014; pp. 65–72. [Google Scholar] [CrossRef]
- Ko, K.; Sung, D.K. The Effect of Cellular Network-Based Communication Delays in an EV Aggregator’s Domain on Frequency Regulation Service. IEEE Trans. Smart Grid
**2019**, 10, 65–73. [Google Scholar] [CrossRef] - Germanà, R.; De Santis, E.; Liberati, F.; Di Giorgio, A. On the Participation of Charging Point Operators to the Frequency Regulation Service using Plug-in Electric Vehicles and 5G Communications. In Proceedings of the 2021 IEEE International Conference on Environment and Electrical Engineering (EEEIC), Bari, Italy, 8–11 June 2021; pp. 1–6. [Google Scholar] [CrossRef]
- Taleb, T.; Samdanis, K.; Mada, B.; Flinck, H.; Dutta, S.; Sabella, D. On Multi-Access Edge Computing: A Survey of the Emerging 5G Network Edge Cloud Architecture and Orchestration. IEEE Commun. Surv. Tutor.
**2017**, 19, 1657–1681. [Google Scholar] [CrossRef] [Green Version] - H2020 Project 5G-Solutions. 5G Solutions for European Citizens. Available online: https://5gsolutionsproject.eu/ (accessed on 29 July 2021).
- Yao, E.; Wong, V.W.S.; Schober, R. A robust design of electric vehicle frequency regulation service. In Proceedings of the 2014 IEEE International Conference on Smart Grid Communications (SmartGridComm), Venice, Italy, 3–6 November 2014; pp. 698–703. [Google Scholar] [CrossRef]
- Yao, E.; Wong, V.W.S.; Schober, R. Optimization of Aggregate Capacity of PEVs for Frequency Regulation Service in Day-Ahead Market. IEEE Trans. Smart Grid
**2018**, 9, 3519–3529. [Google Scholar] [CrossRef] - Xia, S.; Bu, S.Q.; Luo, X.; Chan, K.W.; Lu, X. An Autonomous Real-Time Charging Strategy for Plug-In Electric Vehicles to Regulate Frequency of Distribution System With Fluctuating Wind Generation. IEEE Trans. Sustain. Energy
**2018**, 9, 511–524. [Google Scholar] [CrossRef] - Sanchez Gorostiza, F.; Gonzalez-Longatt, F. Optimised TSO–DSO interaction in unbalanced networks through frequency-responsive EV clusters in virtual power plants. IET Gener. Transm. Distrib.
**2020**, 14, 4908–4917. [Google Scholar] [CrossRef] - Kuang, Y.; Li, C.; Zhou, B.; Cao, Y.; Yang, H.; Zeng, L. Asynchronous Method for Frequency Regulation by Dispersed Plug-in Electric Vehicles. Int. J. Emerg. Electr. Power Syst.
**2018**, 19, 20170158. [Google Scholar] [CrossRef] - Liu, H.; Qi, J.; Wang, J.; Li, P.; Li, C.; Wei, H. EV Dispatch Control for Supplementary Frequency Regulation Considering the Expectation of EV Owners. IEEE Trans. Smart Grid
**2018**, 9, 3763–3772. [Google Scholar] [CrossRef] [Green Version] - Jia, H.; Li, X.; Mu, Y.; Xu, C.; Jiang, Y.; Yu, X.; Wu, J.; Dong, C. Coordinated control for EV aggregators and power plants in frequency regulation considering time-varying delays. Appl. Energy
**2018**, 210, 1363–1376. [Google Scholar] [CrossRef] - Hashemi, S.; Arias, N.B.; Andersen, P.B.; Christensen, B.; Træholt, C. Frequency regulation provision using cross-brand bidirectional V2G-enabled electric vehicles. In Proceedings of the 2018 IEEE International Conference on Smart Energy Grid Engineering (SEGE), Oshawa, ON, Canada, 12–15 August 2018; pp. 249–254. [Google Scholar]
- Cai, S.; Matsuhashi, R. Model Predictive Control for EV Aggregators Participating in System Frequency Regulation Market. IEEE Access
**2021**, 9, 80763–80771. [Google Scholar] [CrossRef] - Islam, M.M.; Zhong, X.; Sun, Z.; Xiong, H.; Hu, W. Real-time frequency regulation using aggregated electric vehicles in smart grid. Comput. Ind. Eng.
**2019**, 134, 11–26. [Google Scholar] [CrossRef] - Sbordone, D.A.; Carlini, E.M.; Di Pietra, B.; Devetsikiotis, M. The future interaction between virtual aggregator-TSO-DSO to increase DG penetration. In Proceedings of the 2015 International Conference on Smart Grid and Clean Energy Technologies (ICSGCE), Offenburg, Germany, 20–23 October 2015; pp. 201–205. [Google Scholar] [CrossRef]
- Germanà, R.; Liberati, F.; Di Giorgio, A. Decentralized Model Predictive Control of Plug-in Electric Vehicles Charging based on the Alternating Direction Method of Multipliers. In Proceedings of the 2020 28th Mediterranean Conference on Control and Automation (MED), Saint-Raphaël, France, 15–18 September 2020; pp. 739–745. [Google Scholar] [CrossRef]
- Di Giorgio, A.; Liberati, F.; Canale, S. Electric vehicles charging control in a smart grid: A model predictive control approach. Control Eng. Pract.
**2014**, 22, 147–162. [Google Scholar] [CrossRef] - TERNA, S.p.A. Pilot Project Fast Reserve. Available online: https://www.terna.it/en/electric-system/pilot-projects-pursuant-arera-resolution-300-2017-reel/fast-reserve-pilot-project (accessed on 29 July 2021).
- Bezanson, J.; Edelman, A.; Karpinski, S.; Shah, V.B. Julia: A fresh approach to numerical computing. SIAM Rev.
**2017**, 59, 65–98. [Google Scholar] [CrossRef] [Green Version] - Gurobi Optimization, LLC. Gurobi Optimizer Reference Manual. 2021. Available online: https://www.gurobi.com/documentation/9.1/matlab_html/matlab_html.html (accessed on 16 November 2021).

**Figure 5.**Scenario 1, balanced conditions: fraction of the maximum PEV power margin used for each PEV.

**Figure 6.**Scenario 1, different power margins: resulting local and global droop curves (request of 50% of the overall power margins).

**Figure 7.**Scenario 1, different power margins: fraction of the maximum PEV power margin used for each PEV (request of 50% of the overall power margins).

**Figure 8.**Scenario 1, different power margins: fraction of the maximum PEV power margin used for each PEV (request of 70% of the overall power margins).

**Figure 9.**Scenario 1, different power margins: resulting local and global droop curves (request of 70% of the overall power margins).

**Figure 10.**Scenario 2 balanced margins and unbalanced SOC errors: resulting local and global droop curves (request of 70% of the overall power margins).

**Figure 11.**Scenario 2 balanced margins and unbalanced SOC errors: fraction of the maximum PEV power margin used for each PEV (request of 70% of the overall power margins).

**Figure 12.**Scenario 2 balanced margins and unbalanced SOC errors and dwelling times: resulting local and global droop curves (request of 70% of the overall power margins).

**Figure 13.**Scenario 2 balanced margins and unbalanced SOC errors and dwelling times: fraction of the maximum PEV power margin used for each PEV (request of 70% of the overall power margins).

PEV ID | ${\mathit{P}}_{\mathit{n},\mathit{k}}$ [kW] | ${\mathit{P}}_{\mathit{n}}^{\mathit{max}}$ [kW] | ${\mathit{e}}_{\mathit{k}}$ [%] | ${\mathit{d}}_{\mathit{k}}$ [%] |
---|---|---|---|---|

1 | 75 | 150 | 10 | 10 |

2 | 50 | 100 | 10 | 10 |

3 | 25 | 50 | 10 | 10 |

PEV ID | ${\mathit{P}}_{\mathit{n},\mathit{k}}$ [kW] | ${\mathit{P}}_{\mathit{n}}^{\mathit{max}}$ [kW] | ${\mathit{e}}_{\mathit{k}}$ [%] | ${\mathit{d}}_{\mathit{k}}$ [%] |
---|---|---|---|---|

1 | 150 | 100 | 80 | 10 |

2 | 150 | 100 | 40 | 10 |

3 | 150 | 100 | 30 | 10 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Germanà, R.; Liberati, F.; De Santis, E.; Giuseppi, A.; Delli Priscoli, F.; Di Giorgio, A.
Optimal Control of Plug-In Electric Vehicles Charging for Composition of Frequency Regulation Services. *Energies* **2021**, *14*, 7879.
https://doi.org/10.3390/en14237879

**AMA Style**

Germanà R, Liberati F, De Santis E, Giuseppi A, Delli Priscoli F, Di Giorgio A.
Optimal Control of Plug-In Electric Vehicles Charging for Composition of Frequency Regulation Services. *Energies*. 2021; 14(23):7879.
https://doi.org/10.3390/en14237879

**Chicago/Turabian Style**

Germanà, Roberto, Francesco Liberati, Emanuele De Santis, Alessandro Giuseppi, Francesco Delli Priscoli, and Alessandro Di Giorgio.
2021. "Optimal Control of Plug-In Electric Vehicles Charging for Composition of Frequency Regulation Services" *Energies* 14, no. 23: 7879.
https://doi.org/10.3390/en14237879