# Incentive Compensation Mechanism for the Infrastructure Construction of Electric Vehicle Battery Swapping Station under Asymmetric Information

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Electric Vehicle Battery Swapping Station

#### 2.2. The Application of Principal–Agent Theory in Optimal Compensation Mechanisms

## 3. The Model

## 4. Equilibrium Solutions

#### 4.1. First-Best Solution: Symmetric Information

**Proposition**

**1.**

**Proof.**

#### 4.2. Optimal Mechanism: Asymmetric Information

- (i)
- $s\in \mathrm{arg}\mathrm{max}{U}_{S}\left(s,\widehat{s}\right)$ (IC),
- (ii)
- $\forall s,{U}_{S}\left(s,s\right)\ge {U}_{S}\left(0\right)$ (IR),
- (iii)
- $\forall s,b\left(s\right)\ge 0,k\left(s\right)\ge 0$.

**Definition**

**1.**

**Proposition**

**2.**

**Proposition**

**3.**

#### 4.3. Comparison between the Optimal Mechanism and the First-Best Solution

**Proposition**

**4.**

## 5. Numerical Results

## 6. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Proof**

**of**

**Proposition**

**1.**

**Proof**

**of**

**Proposition**

**2.**

**Proof**

**of**

**Proposition**

**3.**

**Proof**

**of**

**Proposition**

**4.**

## References

- Kühne, O.; Koegst, L.; Zimmer, M.L.; Schäffauer, G. “… Inconceivable, Unrealistic and Inhumane”. Internet Communication on the Flood Disaster in West Germany of July 2021 between Conspiracy Theories and Moralization—A Neopragmatic Explorative Study. Sustainability
**2021**, 13, 11427. [Google Scholar] [CrossRef] - Adnan, M.; Xiao, B.; Xiao, P.; Zhao, P.; Bibi, S. Heavy Metal, Waste, COVID-19, and Rapid Industrialization in This Modern Era—Fit for Sustainable Future. Sustainability
**2022**, 14, 4746. [Google Scholar] [CrossRef] - Kim, D.; Kim, K.T.; Park, Y.K. A comparative study on the reduction effect in greenhouse gas emissions between the combined heat and power plant and boiler. Sustainability
**2020**, 12, 5144. [Google Scholar] [CrossRef] - Byrne, M.P.; Tobin, J.T.; Forrestal, P.J.; Danaher, M.; Nkwonta, C.G.; Richards, K.; Cummins, E.; Hogan, S.A.; O’Callaghan, T.F. Urease and nitrification inhibitors—As mitigation tools for greenhouse gas emissions in sustainable dairy systems: A review. Sustainability
**2020**, 12, 6018. [Google Scholar] [CrossRef] - Clémençon, R. The two sides of the Paris climate agreement: Dismal failure or historic breakthrough? J. Environ. Dev.
**2016**, 25, 3–24. [Google Scholar] [CrossRef] [Green Version] - Perissi, I.; Jones, A. Investigating European Union Decarbonization Strategies: Evaluating the Pathway to Carbon Neutrality by 2050. Sustainability
**2022**, 14, 4728. [Google Scholar] - Yaacob, N.F.F.; Mat Yazid, M.R.; Abdul Maulud, K.N.; Ahmad Basri, N.E. A review of the measurement method, analysis and implementation policy of carbon dioxide emission from transportation. Sustainability
**2020**, 12, 5873. [Google Scholar] [CrossRef] - Hannan, M.A.; Lipu, M.H.; Ker, P.J.; Begum, R.A.; Agelidis, V.G.; Blaabjerg, F. Power electronics contribution to renewable energy conversion addressing emission reduction: Applications, issues, and recommendations. Appl. Energy
**2019**, 251, 113404. [Google Scholar] [CrossRef] - Zhou, S.; Tong, Q.; Pan, X.; Cao, M.; Wang, H.; Gao, J.; Ou, X. Research on low-carbon energy transformation of China necessary to achieve the Paris agreement goals: A global perspective. Energy Econ.
**2021**, 95, 105137. [Google Scholar] [CrossRef] - Bartholdsen, H.K.; Eidens, A.; Löffler, K.; Seehaus, F.; Wejda, F.; Burandt, T.; Oei, P.-Y.; Kemfert, C.; von Hirschhausen, C. Pathways for Germany’s low-carbon energy transformation towards 2050. Energies
**2019**, 12, 2988. [Google Scholar] [CrossRef] [Green Version] - Hu, J.; Wood, R.; Tukker, A.; Boonman, H.; de Boer, B. Global transport emissions in the Swedish carbon footprint. J. Clean. Prod.
**2019**, 226, 210–220. [Google Scholar] [CrossRef] - Jacobs, A.J. Hyundai Motor Part I: From Construction to Cars, Beginnings to 1987. In The Korean Automotive Industry; Palgrave Macmillan: Cham, Switzerland, 2022; Volume 1, pp. 239–267. [Google Scholar]
- Karali, N.; Shah, N. Bolstering supplies of critical raw materials for low-carbon technologies through circular economy strategies. Energy Res. Soc. Sci.
**2022**, 88, 102534. [Google Scholar] [CrossRef] - Qiu, D.; Wang, Y.; Zhang, T.; Sun, M.; Strbac, G. Hybrid Multi-Agent Reinforcement Learning for Electric Vehicle Resilience Control Towards a Low-Carbon Transition. In IEEE Transactions on Industrial Informatics; IEEE: Piscataway, NJ, USA, 2022. [Google Scholar]
- Titus, F.; Thanikanti, S.B.; Deb, S.; Kumar, N.M. Charge Scheduling Optimization of Plug-In Electric Vehicle in a PV Powered Grid-Connected Charging Station Based on Day-Ahead Solar Energy Forecasting in Australia. Sustainability
**2022**, 14, 3498. [Google Scholar] - XU, S.X.; XIE, B.; QIN, W.; CHENG, H.B. Pricing and Investment Strategies for Electric Vehicle Battery Charging and Swapping. J. Transp. Syst. Eng. Inf. Technol.
**2021**, 21, 183. [Google Scholar] - Xie, P.; Zhu, J.; Xuan, P. Analysis of controllable capacity for electric vehicle battery swapping stations. J. Eng.
**2017**, 13, 2125–2129. [Google Scholar] [CrossRef] - Chang, C.S.; Cheng, P.T.; Lee, D.S.; Yang, K.H. A mathematical theory for multistage battery switching networks. IEEE Trans. Netw. Sci. Eng.
**2017**, 5, 171–183. [Google Scholar] [CrossRef] - Wang, S.; Yu, L.; Wu, L.; Dong, Y.; Wang, H. An improved differential evolution algorithm for optimal location of battery swapping stations considering multi-type electric vehicle scale evolution. IEEE Access
**2019**, 7, 73020–73035. [Google Scholar] [CrossRef] - Lin, M.D.; Liu, P.Y.; Yang, M.D.; Lin, Y.H. Optimized allocation of scooter battery swapping station under demand uncertainty. Sustain. Cities Soc.
**2021**, 71, 102963. [Google Scholar] [CrossRef] - Ayad, A.; El-Taweel, N.A.; Farag, H.E. Optimal Design of Battery Swapping-Based Electrified Public Bus Transit Systems. IEEE Trans. Transp. Electrif.
**2021**, 7, 2390–2401. [Google Scholar] [CrossRef] - You, P.; Yang, Z.; Zhang, Y.; Low, S.H.; Sun, Y. Optimal charging schedule for a battery switching station serving electric buses. IEEE Trans. Power Syst.
**2015**, 31, 3473–3483. [Google Scholar] [CrossRef] - Revankar, S.R.; Kalkhambkar, V.N. Grid integration of battery swapping station: A review. J. Energy Storage
**2021**, 41, 102937. [Google Scholar] [CrossRef] - Alok, S.; Gopalan, R. Managerial compensation in multidivision firms. Manag. Sci.
**2018**, 64, 2856–2874. [Google Scholar] [CrossRef] [Green Version] - Sun, Y.; Gong, H.; Guo, Q.; Schonfeld, P.; Li, Z. Regulating a public transit monopoly under asymmetric cost information. Transp. Res. Part B Methodol.
**2020**, 139, 496–522. [Google Scholar] [CrossRef] - Nunes, A.; Woodley, L.; Rossetti, P. Re-thinking procurement incentives for electric vehicles to achieve net-zero emissions. Nat. Sustain.
**2022**, 1–6. [Google Scholar] [CrossRef] - Shokouhandeh, H.; Kamarposhti, M.A.; Asghari, F.; Colak, I.; Eguchi, K. Distributed Generation Management in Smart Grid with the Participation of Electric Vehicles with Respect to the Vehicle Owners’ Opinion by Using the Imperialist Competitive Algorithm. Sustainability
**2022**, 14, 4770. [Google Scholar] [CrossRef] - Sarker, M.R.; Pandžić, H.; Ortega-Vazquez, M.A. Optimal operation and services scheduling for an electric vehicle battery swapping station. IEEE Trans. Power Syst.
**2014**, 30, 901–910. [Google Scholar] [CrossRef] - Yang, S.; Yao, J.; Kang, T.; Zhu, X. Dynamic operation model of the battery swapping station for EV (electric vehicle) in electricity market. Energy
**2014**, 65, 544–549. [Google Scholar] [CrossRef] - Wu, H.; Pang, G.K.H.; Choy, K.L.; Lam, H.Y. An optimization model for electric vehicle battery charging at a battery swapping station. IEEE Trans. Veh. Technol.
**2017**, 67, 881–895. [Google Scholar] [CrossRef] - Mahoor, M.; Hosseini, Z.S.; Khodaei, A. Least-cost operation of a battery swapping station with random customer requests. Energy
**2019**, 172, 913–921. [Google Scholar] [CrossRef] - Asadi, A.; Pinkley, S.N. A stochastic scheduling, allocation, and inventory replenishment problem for battery swap stations. Transp. Res. Part E Logist. Transp. Rev.
**2021**, 146, 102212. [Google Scholar] [CrossRef] - Esmaeili, S.; Anvari-Moghaddam, A.; Jadid, S. Optimal operation scheduling of a microgrid incorporating battery swapping stations. IEEE Trans. Power Syst.
**2019**, 34, 5063–5072. [Google Scholar] [CrossRef] - Raeesi, R.; Zografos, K.G. The electric vehicle routing problem with time windows and synchronised mobile battery swapping. Transp. Res. Part B Methodol.
**2020**, 140, 101–129. [Google Scholar] [CrossRef] - Verma, A. Electric vehicle routing problem with time windows, recharging stations and battery swapping stations. EURO J. Transp. Logist.
**2018**, 7, 415–451. [Google Scholar] [CrossRef] - Zhang, X.; Peng, L.; Cao, Y.; Liu, S.; Zhou, H.; Huang, K. Towards holistic charging management for urban electric taxi via a hybrid deployment of battery charging and swap stations. Renew. Energy
**2020**, 155, 703–716. [Google Scholar] [CrossRef] - Mak, H.Y.; Rong, Y.; Shen, Z.J.M. Infrastructure planning for electric vehicles with battery swapping. Manag. Sci.
**2013**, 59, 1557–1575. [Google Scholar] [CrossRef] [Green Version] - Holmstrom, B. Moral hazard in teams. Bell J. Econ.
**1982**, 13, 324–340. [Google Scholar] [CrossRef] - Baron, D.P.; Myerson, R.B. Regulating a monopolist with unknown costs. Econom. J. Econom. Soc.
**1982**, 50, 911–930. [Google Scholar] [CrossRef] [Green Version] - Aghion, P.; Bolton, P. Incomplete social contracts. J. Eur. Econ. Assoc.
**2003**, 1, 38–67. [Google Scholar] [CrossRef] [Green Version] - DeMarzo, P.M.; Sannikov, Y. Optimal security design and dynamic capital structure in a continuous-time agency model. J. Financ.
**2006**, 61, 2681–2724. [Google Scholar] [CrossRef] - Biais, B.; Mariotti, T.; Rochet, J.C.; Villeneuve, S. Large risks, limited liability, and dynamic moral hazard. Econometrica
**2010**, 78, 73–118. [Google Scholar] - He, Z. A model of dynamic compensation and capital structure. J. Financ. Econ.
**2011**, 100, 351–366. [Google Scholar] [CrossRef] - Gryglewicz, S.; Hartman-Glaser, B. Investment timing and incentive costs. Rev. Financ. Stud.
**2020**, 33, 309–357. [Google Scholar] [CrossRef] - Di Tella, S. Optimal regulation of financial intermediaries. Am. Econ. Rev.
**2019**, 109, 271–313. [Google Scholar] [CrossRef] [Green Version] - Silaghi, F.; Sarkar, S. Agency problems in public-private partnerships investment projects. Eur. J. Oper. Res.
**2021**, 290, 1174–1191. [Google Scholar] [CrossRef] - Xu, S.X. Overexploitation Risk in “Green Mountains and Clear Water”. Ecol. Econ.
**2021**, 179, 106804. [Google Scholar] - Yang, R.; Mai, Y.; Lee, C.Y.; Teo, C.P. Tractable Compensation Plan under Asymmetric Information. Prod. Oper. Manag.
**2020**, 29, 1212–1218. [Google Scholar] [CrossRef] - Wang, S.; Gurnani, H.; Subramanian, U. The informational role of buyback contracts. Manag. Sci.
**2021**, 67, 279–296. [Google Scholar] [CrossRef] - Laffont, J.J.; Martimort, D. The Theory of Incentives; Princeton University Press: Princeton, NJ, USA, 2009. [Google Scholar]
- Bernardo, A.E.; Cai, H.; Luo, J. Capital budgeting and compensation with asymmetric information and moral hazard. J. Financ. Econ.
**2001**, 61, 311–344. [Google Scholar] [CrossRef] [Green Version]

Parameters | $\mathit{n}$ | $\mathit{\gamma}$ | $\mathit{a}$ | $\mathit{\lambda}$ | $\mathit{\sigma}$ | ${\mathit{U}}_{\mathit{s}}\left(0\right)$ |
---|---|---|---|---|---|---|

Value | 0.1 | 0.3 | 0.1 | 0.1 | 0.4 | 300,000 |

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**MDPI and ACS Style**

Cheng, H.; Zheng, S.
Incentive Compensation Mechanism for the Infrastructure Construction of Electric Vehicle Battery Swapping Station under Asymmetric Information. *Sustainability* **2022**, *14*, 7041.
https://doi.org/10.3390/su14127041

**AMA Style**

Cheng H, Zheng S.
Incentive Compensation Mechanism for the Infrastructure Construction of Electric Vehicle Battery Swapping Station under Asymmetric Information. *Sustainability*. 2022; 14(12):7041.
https://doi.org/10.3390/su14127041

**Chicago/Turabian Style**

Cheng, Huibing, and Shanshui Zheng.
2022. "Incentive Compensation Mechanism for the Infrastructure Construction of Electric Vehicle Battery Swapping Station under Asymmetric Information" *Sustainability* 14, no. 12: 7041.
https://doi.org/10.3390/su14127041