# Pricing Strategy for a Virtual Power Plant Operator with Electric Vehicle Users Based on the Stackelberg Game

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- For the problem of orderly charging management of EV customers, based on Stackelberg theory, we propose a Stackelberg game model in which a VPP acts as the electricity sales operator and coordinates resources such as wind turbines, energy storage, and demand response loads to participate in the orderly charging management of EVs. Among them, the VPP guides EVs’ orderly charging by specifying a reasonable pricing strategy, which not only solves the problem of balanced benefit distribution between the VPP and EVs, but also realizes the advantages of multiple distributed resources to complement one another.
- (2)
- Based on the existing electric power communication network resources, this paper integrates multiple kinds of data such as demand response, energy storage management and other business systems, distributed energy, and EV charging station monitoring, and combines communication technologies such as broadband power line carriers, micropower wireless, Wi-Fi Halow, and 5G networks to build a communication structure for VPP–grid interaction. In addition, this paper also proposes a supporting operation model for the VPP to manage EVs’ participation in power market trading, in conjunction with the actual day-ahead market trading process.
- (3)
- Considering the impact of wind power output volatility on VPP operation revenue, this paper extends the deterministic Stackelberg game optimization model into a robust optimization model through a strong pairwise theory and robust optimization method, introduces the robust adjustment coefficient as a measure of risk–return for VPP operators, and compares the impacts of different robust adjustment coefficients on VPP operation revenue under nominal parameters in the calculation example. This can provide an important reference for VPPs to optimize their operation strategies according to their own risk preferences.
- (4)
- The impact of different maximum energy storage capacity on the VPP’s operating revenue is investigated for a given robust regulation factor, and the optimal maximum energy storage capacity for this VPP system is summarized by the analysis.

## 2. The Communication Structure of the VPP and Its Operation Mode

#### 2.1. Communication Structure of the VPP

#### 2.2. Operational Model of the VPP

- (1)
- Before the end of the energy market transaction on day (D), EV users shall submit to the operator the charging periods and power demand for day (D + 1). Based on the power demand of EV users, the VPP shall coordinate and optimize internal resources to determine the power demand for each period on day (D + 1) and draw up the corresponding power purchase and sale plan.
- (2)
- The VPP operator will promptly release the tariff information for each period on day (D + 1) to EV customers after signing a power purchase and sale contract with the grid in the day-ahead market. In addition, this paper stipulates that the VPP operator’s retail electricity price for selling electricity to EV users shall not be higher than the grid’s benchmark sale price, and that the average daily sale price shall be set to fully guarantee the basic interests of EV customers. For example, if the operator deliberately raises the price of electricity in a certain period, the price of electricity in other periods is required to be lower than the average price of electricity, and then the intelligent terminal will naturally choose the “valley price” period to charge EV users automatically.
- (3)
- After the EV is connected to the charging pile, the intelligent charging terminal on the pile will automatically control the EV’s charging and pay the charging fee for the user instantly. At the same time, the operator can assess the performance of EV users who do not charge at the agreed time.

## 3. The Stackelberg Game Model of the VPP and EVs

#### 3.1. The Objective Function of the Upper-Level Problem of the Stackelberg Game Model

- (1)
- The cost of the energy storage equipment [24]:

- (3)
- The transaction costs of the VPP in the day-ahead market:

#### 3.2. Constraints on the Upper-Level Problem of the Stackelberg Game Model

- (1)
- Constraints related to the price of electricity sold by VPP operators:

- (2)
- Constraints related to wind turbines:

- (3)
- Constraints related to energy storage devices:

- (4)
- Demand-response-related constraints:

- (5)
- Constraints related to the VPP’s purchase and sale of electricity:

- (6)
- Constraints related to power balance:

#### 3.3. The Objective Function and Constraints of the Lower-Level Problem of the Stackelberg Game Model

## 4. Solving Method

#### 4.1. Equivalent Nonlinear Programming Transformation of Stackelberg Game Models

#### 4.2. Robust Transformation of Deterministic Stackelberg Game Models

## 5. Case Study

#### 5.1. Basic Parameters of the Algorithm

#### 5.2. Optimal Solution with Standard Parameters

#### 5.3. Influence of EV Proportion on the Optimal Solution

#### 5.4. Impact of Robust Adjustment Factors on the VPP’s Operating Income

#### 5.5. Influence of Energy Storage Equipment Capacity on the Optimal Solution

## 6. Conclusions

- (1)
- In this paper, we propose a Stackelberg game model in which the VPP operator participates in the orderly charging management of EVs as the main objective of electricity market reform in China, with the opening up of the electricity sales side as the background. In the model, the VPP operator does not need to directly intervene in the charging behavior of EV customers but only issues charging tariffs, and EV customers are no longer just passive “price takers” but can freely choose charging periods according to their charging preferences. This optimal management idea takes into account both the response of EV users’ charging strategies to the VPP price and the influence of the pricing scheme on EV users’ charging behavior. The optimization result of the Stackelberg game achieves a win–win situation for both sides of the VPP and EV game.
- (2)
- In this paper, the nonlinear master–slave game model is transformed into a solvable robust mixed-integer linear programming problem by KKT conditions and strong dyadic theory, and the optimal pricing strategy for the VPP operator and the optimal charging scheme for the EV user are accurately derived. Under the nominal parameters, the optimal operating revenue of the VPP operator is CNY 5744.3, and the minimum charging cost to the EV user is CNY 7197.6.
- (3)
- The results of the algorithm can truly and reasonably reflect the change in the VPP operator’s revenue when the robust adjustment factor changes. Therefore, the operator can flexibly measure the relationship between risk and return according to the attitude towards the use of wind power output and the output characteristics of controllable resources in the VPP, while adjusting the robust adjustment factor to maximize its operating return in the energy market.
- (4)
- The results show that increasing the maximum capacity of the energy storage device within a certain range is an important way for the VPP operator to steadily increase their operating profit. By varying the maximum capacity of energy storage with different robust adjustment coefficients, the optimal maximum capacity of energy storage adapted to this VPP system is 3500 $(\mathrm{kW}\cdot \mathrm{h})$.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Mansouri, S.A.; Jordehi, A.R.; Marzband, M.; Tostado-Véliz, M.; Jurado, F.; Aguado, J.A. An IoT-enabled hierarchical decentralized framework for multi-energy microgrids market management in the presence of smart prosumers using a deep learning-based forecaster. Appl. Energy
**2023**, 333, 120560. [Google Scholar] [CrossRef] - Guo, C.X. Carbon neutrality by 2060 leads to fundamental changes in China’s economic system. J. Beijing Univ. Technol. (Soc. Sci. Ed.)
**2021**, 21, 64–77. [Google Scholar] - Mansouri, S.A.; Nematbakhsh, E.; Javadi, M.S.; Jordehi, A.R.; Shafie-khah, M.; Catalão, J.P. Resilience Enhancement via Automatic Switching considering Direct Load Control Program and Energy Storage Systems. In Proceedings of the 2021 IEEE International Conference on Environment and Electrical Engineering and 2021 IEEE Industrial and Commercial Power Systems Europe (EEEIC/I&CPS Europe), Bari, Italy, 7–10 September 2021; pp. 1–6. [Google Scholar] [CrossRef]
- Mansouri, S.A.; Ahmarinejad, A.; Sheidaei, F.; Javadi, M.S.; Jordehi, A.R.; Nezhad, A.E.; Catalao, J.P. A multi-stage joint planning and operation model for energy hubs considering integrated demand response programs. Int. J. Electr. Power Energy Syst.
**2022**, 140, 108103. [Google Scholar] [CrossRef] - Mansouri, S.A.; Ahmarinejad, A.; Nematbakhsh, E.; Javadi, M.S.; Jordehi, A.R.; Catalão, J.P. Energy Hub Design in the Presence of P2G System Considering the Variable Efficiencies of Gas-Fired Converters. In Proceedings of the 2021 International Conference on Smart Energy Systems and Technologies (SEST), Vaasa, Finland, 6–8 September 2021; pp. 1–6. [Google Scholar] [CrossRef]
- Zhang, L.; Zhu, L.Z.; Chen, N.; Zhao, D.; Qu, L. Review on generic model for renewable energy generation. Autom. Electr. Power Syst.
**2015**, 39, 129–138. [Google Scholar] - Song, J.Q.; Yang, Y.B.; Xu, Q.S.; Liu, Z.Q.; Zhang, X.Y. Robust Bidding Game Method for Multiple Virtual Power Plants to Participate in Day-ahead Power Market. Electr. Power Autom. Equip.
**2023**, 1–23. [Google Scholar] [CrossRef] - Mansouri, S.A.; Ahmarinejad, A.; Javadi, M.S.; Nezhad, A.E.; Shafie-Khah, M.; Catalão, J.P. Demand response role for enhancing the flexibility of local energy systems. Distrib. Energy Resour. Local Integr. Energy Syst.
**2021**, 9, 279–313. [Google Scholar] - Wei, W.; Chen, Y.; Liu, F.; Mei, S.W.; Tian, F.; Zhang, X. Stackelberg Game Based retailer pricing scheme and EV charging management in smart residential area. Power Syst. Technol.
**2015**, 39, 939–945. [Google Scholar] - Hou, H.; Wang, Y.; Zhao, B. Electric Vehicle Aggregator Dispatching Strategy Under Price and Incentive Demand Response. Power Syst. Technol.
**2022**, 46, 1259–1269. [Google Scholar] - Zang, H.Z.; Ye, Y.J.; Tang, Y. Constrained Electric Vehicle Charging and Discharging Strategy Based on Safe Reinforcement Learning. Power Syst. Technol.
**2023**, 1–12. [Google Scholar] [CrossRef] - Zhan, X.; Yang, J.; Han, S.; Zhou, T.; Wu, F.Z.; Liu, S. Two-stage Market Bidding Strategy of Charging Station Considering Schedulable Potential Capacity of Electric Vehicle. Autom. Electr. Power Syst.
**2021**, 45, 86–96. [Google Scholar] - Cai, G.W.; Jiang, Y.Q.; Huang, N.T.; Yang, D.Z.; Pan, X.; Shang, W.Y. Large-scale Electric Vehicles Charging and Discharging Optimization Scheduling Based on Multi-agent Two-level Game Under Electricity Demand Response Mechanism. Proc. CSEE
**2023**, 43, 85–98. [Google Scholar] - Bai, X.Y.; Fan, Y.F.; Wang, T.S.; Liu, Y.J.; Nie, X.L.; Yan, C.Y. Dynamic aggregation method of virtual power plants considering reliability of renewable energy. Electr. Power Autom. Equip.
**2022**, 42, 102–110. [Google Scholar] - Tian, L.; Cheng, L.; Guo, J.; Wang, X.; Yun, Q.; Gao, W. A Review on the Study of Management and Interaction Mechanism for Distributed Energy in Virtual Power Plants. Power Syst. Technol.
**2020**, 44, 2097–2108. [Google Scholar] - Kang, C.Q.; Chen, Q.X.; Su, J.; AI, Q.; Ji, Y.; Pan, W.W.; Gao, H.C.; Wu, M. Scientific Problems and Research Framework of Virtual Power Plant with Enormous Flexible Distributed Energy Resources in New Power System. Autom. Electr. Power Syst.
**2022**, 46, 3–14. [Google Scholar] - Zhou, B.; Lv, L.; Gao, H.; Liu, J.; Chen, Q.; Tan, X. Robust Day-Ahead Trading Strategy for Multiple Virtual Power Plants. Power Syst. Technol.
**2018**, 42, 2694–2703. [Google Scholar] - Yang, F.; Wang, W.Q.; He, S.; Zhao, H.L.; Cheng, J. Stochastic Planning of Wind-Storage-Vehicle Capacity Based on Multi-Scenario Operation Simulation. High Volt. Eng.
**2023**, 1–15. [Google Scholar] [CrossRef] - Li, Q.; Zhu, D.D.; Huang, D.; Wu, S.J.; Yang, Y.B.; Song, J.Q. Pricing strategy of Stackelberg game between virtual power plant operators and electric vehicles users. Electr. Power Eng. Technol.
**2022**, 41, 183–191. [Google Scholar] - Wang, H.; Wang, J.; Wang, C.; Zhang, G.; Fan, M. Risk-constrained Energy Management Modeling of Virtual Power Plant. Proc. CSEE
**2017**, 37, 5942–5950. [Google Scholar] - Qiu, H.; Gu, W.; Liu, P.; Sun, Q.; Wu, Z.; Lu, X. Application of two-stage robust optimization theory in power system scheduling under uncertainties: A review and perspective. Energy
**2022**, 251, 123942. [Google Scholar] [CrossRef] - Liu, Y.X.; Guo, L.; Wang, C.S. Economic Dispatch of Microgrid Based on Two Stage Robust Optimization. Proc. CSEE
**2018**, 38, 4013–4022. [Google Scholar] - Wang, W.Q.; Su, J.; Pan, J.; Zhang, H.; Gao, K.Q.; Liu, C. Prospect of Research on Communication Network Architecture and Key Technologies for Virtual Power Plant. Autom. Electr. Power Syst.
**2022**, 46, 15–25. [Google Scholar] - Sun, Z.X.; Liu, H.Q.; Zhao, Z.; Ding, J.; Chang, C. Research on economical efficiency of energy storage. Proc. CSEE
**2013**, 33, 54–58. [Google Scholar] - Zhou, Y.; Sun, G.; Huang, W.; Xu, Z.; Wei, Z.; Zhang, H.; Chu, Y. Strategic Bidding Model for Virtual Power Plant in Different Electricity Markets Considering Electric Vehicles and Demand Response. Power Syst. Technol.
**2017**, 41, 1759–1767. [Google Scholar] - Zhang, B.; Li, Q.; Wang, L.; Feng, W. Robust optimization for energy transactions in multi-microgrids under uncertainty. Appl. Energy
**2018**, 217, 346–360. [Google Scholar] [CrossRef] - Fortuny-Ama, J.; Mccarl, B. A representation and economic interpretation of a two-level programming problem. J. Oper. Res. Soc.
**1981**, 32, 783–792. [Google Scholar] [CrossRef] - Dominguez, R.; Baringo, L.; Conejo, A.J. Optimal offering strategy for a concentrating solar power plant. Appl. Energy
**2012**, 98, 316–325. [Google Scholar] [CrossRef] - Wang, X.Y.; Liu, D.N.; Liu, Q.; Liu, M.G.; Wang, J.N.; Gao, Y.; Wang, X.F.; Song, Y.H. Operation Mechanism and Key Technologies of Virtual Power Plant Under Ubiquitous Internet of Things. Power Syst. Technol.
**2019**, 43, 3175–3183. [Google Scholar] - China Electricity Council. NB/T 32011-2013 Technical Requirement of Power Forecasting System for PV Power Station; National Energy Administration of China: Beijing, China, 2013. (In Chinese)

**Figure 11.**Income of VPP operators under the maximum capacity of different energy storage equipment.

Period | EV1 | EV2 | EV3 | Period | EV1 | EV2 | EV3 |
---|---|---|---|---|---|---|---|

1 | 1 | 1 | 0 | 13 | 0 | 0 | 1 |

2 | 1 | 1 | 0 | 14 | 0 | 0 | 1 |

3 | 1 | 1 | 0 | 15 | 0 | 0 | 1 |

4 | 1 | 1 | 0 | 16 | 0 | 0 | 1 |

5 | 1 | 1 | 0 | 17 | 0 | 0 | 1 |

6 | 0 | 1 | 0 | 18 | 0 | 1 | 1 |

7 | 0 | 1 | 0 | 19 | 0 | 1 | 1 |

8 | 0 | 1 | 0 | 20 | 0 | 1 | 0 |

9 | 0 | 0 | 1 | 21 | 0 | 1 | 0 |

10 | 0 | 0 | 1 | 22 | 1 | 1 | 0 |

11 | 0 | 0 | 1 | 23 | 1 | 1 | 0 |

12 | 0 | 0 | 1 | 24 | 1 | 1 | 0 |

Parameters | EV1 | EV2 | EV3 |
---|---|---|---|

${E}_{\mathrm{EV},i}^{\mathrm{max}}/(\mathrm{kW}\cdot \mathrm{h})$ | 63 | 63 | 63 |

${E}_{\mathrm{EV},i,0}^{}/(\mathrm{kW}\cdot \mathrm{h})$ | 18.9 | 37.8 | 31.5 |

${\delta}_{i}$ | 0.95 | 0.85 | 0.90 |

${P}_{\mathrm{EV},i}^{\mathrm{max}}/(\mathrm{kW})$ | 7 | 7 | 7 |

Period | Valley Period 1:00–8:00 | Normal Period 13:00–17:00 22:00–24:00 | Peak Period 9:00–12:00 18:00–21:00 |
---|---|---|---|

Price/(CNY/(kW·h)) | 0.3167 | 0.5315 | 0.7463 |

Elements | Parameters | Values |
---|---|---|

Energy storage devices | ${P}_{\mathrm{ESS}}^{\mathrm{ch},\mathrm{max}}/\mathrm{kW}$ | 500 |

${P}_{\mathrm{ESS}}^{\mathrm{dis},\mathrm{max}}/\mathrm{kW}$ | 500 | |

${E}_{\mathrm{ESS}}^{\mathrm{max}}/(\mathrm{kW}\cdot \mathrm{h})$ | 3500 | |

${E}_{\mathrm{ESS},0}^{}/(\mathrm{kW}\cdot \mathrm{h})$ | 1000 | |

${\kappa}_{\mathrm{ESS}}$ | 0.25 | |

${\eta}_{\mathrm{ESS}}^{\mathrm{ch}}$ | 0.92 | |

${\eta}_{\mathrm{ESS}}^{\mathrm{dis}}$ | 0.90 | |

Demand response load | ${\kappa}_{\mathrm{ESS}}/(\mathrm{CNY}/(\mathrm{kW}\cdot \mathrm{h}))$ | 0.25 |

${E}_{\mathrm{DR}}^{\mathrm{total}}/(\mathrm{kW}\cdot \mathrm{h})$ | 5500 | |

${E}_{\mathrm{DR}}^{\mathrm{max}}/(\mathrm{kW}\cdot \mathrm{h})$ | 300 | |

${E}_{\mathrm{DR}}^{\mathrm{min}}/(\mathrm{kW}\cdot \mathrm{h})$ | 50 | |

Power interaction with the grid | ${P}_{\mathrm{DAM}}^{\mathrm{max}}/\mathrm{kW}$ | 1500 |

Periods | $\mathbf{Values}/\mathbf{kW}$ | Periods | $\mathbf{Values}/\mathbf{kW}$ | Periods | $\mathbf{Values}/\mathbf{kW}$ |
---|---|---|---|---|---|

1 | 1650 | 9 | 891 | 17 | 1023 |

2 | 1782 | 10 | 858 | 18 | 1237.5 |

3 | 1716 | 11 | 874.5 | 19 | 1171.5 |

4 | 1782 | 12 | 891 | 20 | 1237.5 |

5 | 1633.5 | 13 | 891 | 21 | 1353 |

6 | 1501.5 | 14 | 792 | 22 | 1303.5 |

7 | 1138.5 | 15 | 825 | 23 | 1237.5 |

8 | 676.5 | 16 | 1122 | 24 | 1518 |

$\mathbf{Robust}\mathbf{Adjustment}\mathbf{Coefficient}\left(\mathit{\beta}\right)$ | VPP’s Operating Income (CNY) | Charging Cost of EV (CNY) |
---|---|---|

0 | 5961.7 | 7197.6 |

0.1 | 5913.7 | |

0.2 | 5866.3 | |

0.3 | 5825.7 | |

0.4 | 5785.0 | |

0.5 | 5744.3 | |

0.6 | 5701.8 | |

0.7 | 5653.1 | |

0.8 | 5604.4 | |

0.9 | 5555.7 | |

1 | 5506.7 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 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**

Liu, Q.; Tian, J.; Zhang, K.; Yan, Q.
Pricing Strategy for a Virtual Power Plant Operator with Electric Vehicle Users Based on the Stackelberg Game. *World Electr. Veh. J.* **2023**, *14*, 72.
https://doi.org/10.3390/wevj14030072

**AMA Style**

Liu Q, Tian J, Zhang K, Yan Q.
Pricing Strategy for a Virtual Power Plant Operator with Electric Vehicle Users Based on the Stackelberg Game. *World Electric Vehicle Journal*. 2023; 14(3):72.
https://doi.org/10.3390/wevj14030072

**Chicago/Turabian Style**

Liu, Qiang, Jiale Tian, Ke Zhang, and Qingxin Yan.
2023. "Pricing Strategy for a Virtual Power Plant Operator with Electric Vehicle Users Based on the Stackelberg Game" *World Electric Vehicle Journal* 14, no. 3: 72.
https://doi.org/10.3390/wevj14030072