Abstract
The work presented in this paper deals with developing a charge scheduling strategy for electric vehicles in a predefined geographical region. Charging stations in the geographical region are considered to provide multiple charging levels with separate piles with an individual queue for each charging level. Assigning a charging station to each electric vehicle is considered as an optimization problem to minimize travel time, queue time, recharging time, and cost of energy for battery recharging. The objective function is constrained to the reachability of the electric vehicle with the available state of charge of the battery to the allotted charging station without violating the maximum permissible depth of discharge limit and allowable charging rate. The optimization model empowers the users to prioritize the function variable based on travel requirements and battery specifications in different case studies using the Opposition-Based Marine Predator Algorithm. This proposed algorithm is an improved version of the recently reported Marine Predator Algorithm in which the opposition-based learning mechanism is included to improve the solution accuracy. The solution obtained and the analysis of results show that the proposed strategy significantly reduces travel time, queue time, recharging time, and energy cost while fulfilling the constraints imposed.
Similar content being viewed by others
Data Availability
Not applicable.
Abbreviations
- \({SoC}_{i}^{min}\) :
-
Minimum permissible state of charge of the ith vehicle battery
- \({SoC}_{i}^{max}\) :
-
Maximum permissible state of charge of the ith vehicle battery
- \({DoD}_{i}^{max}\) :
-
Maximum permissible depth of discharge of the ith vehicle battery
- \({SoC}_{i}^{t}\) :
-
State of charge of ith vehicle battery at time t
- \({B}_{i}\) :
-
Nominal energy rating of the ith vehicle battery (kWh)
- \({ECR}_{i}\) :
-
Energy consumption rate (km/kWh)
- \({d}_{ij}\) :
-
Distance between ith vehicle and jth charging station (km)
- \({v}_{ij}\) :
-
Average velocity of ith vehicle to reach jth charging station (km/s)
- \({t}_{ij}\) :
-
Driving time from ith vehicle's current location to the jth charging station (minutes)
- \({d}_{j{e}_{i}}\) :
-
Distance between jth charging station and destination of ith vehicle (km)
- \({v}_{j{e}_{i}}\) :
-
Average velocity of ith vehicle from jth charging station to reach the destination (km/s)
- \({t}_{j{e}_{i}}\) :
-
Driving time from jth charging station to the ith vehicle destination (minutes)
- \({SoC}_{i}^{req}\) :
-
State of charge level required by the ith vehicle battery
- \({R}_{k}\) :
-
Charging rate in kW
- \({t}_{{c}_{ik}}^{t}\) :
-
Time required to charge the battery of ith vehicle at kth charging pile (minutes)
- \({t}_{{q}_{ik}}\) :
-
Queuing time for the ith vehicle at kth charging pile (minutes)
- \({\eta }_{c}\) :
-
Charging efficiency
- \({r}_{k}\) :
-
The price per unit of electricity in rupees
- \({P}_{ik}\) :
-
Cost of electricity for charging ith vehicle at kth charging pile in rupees
- \({T}_{d}\left({s}_{i}\right)\) :
-
Total driving time of all the vehicles from present location to charging station and charging station to destination (minutes)
- \({T}_{w}\left({s}_{i}\right)\) :
-
Total waiting time of all the vehicles including queuing and charging time (minutes)
- \({d}_{i{s}_{i}}\) :
-
Distance between the current location and the allotted charging station of the vehicles (km)
- \({d}_{i}^{max}\) :
-
Maximum distance that the ith vehicles can travel with the current SoC (km)
- \({P}_{i{s}_{i}}\) :
-
Total charging cost of all the vehicles in rupees
- \({K}_{d},{K}_{q}, {K}_{p}\) :
-
Priority indices for optimizing driving time, charging cost and queuing time respectively
- \({K}_{c1},{K}_{c2}\) :
-
Conversion factors for driving and queuing time respectively
References
Salmasi, F.R.: Control strategies for hybrid electric vehicles: Evolution, classification, comparison, and future trends. IEEE Trans. Veh. Technol. 56(5 I), 2393–2404 (2007). https://doi.org/10.1109/TVT.2007.899933
IEA: Global EV Outlook 2016. OECD (2016). https://doi.org/10.1787/9789264279469-EN.
le Floch, C., Belletti, F., Moura, S.: Optimal charging of electric vehicles for load shaping: A dual-splitting framework with explicit convergence bounds. IEEE Trans. Transp. Electrific. 2(2), 190–199 (2016). https://doi.org/10.1109/TTE.2016.2531025
Habib, S., et al.: A framework for stochastic estimation of electric vehicle charging behavior for risk assessment of distribution networks. Front. Energy 14(2), 298–317 (2020). https://doi.org/10.1007/S11708-019-0648-5
Habib, S., Khan, M.M., Abbas, F., Sang, L., Shahid, M.U., Tang, H.: A comprehensive study of implemented international standards, technical challenges, impacts and prospects for electric vehicles. IEEE Access 6, 13866–13890 (2018). https://doi.org/10.1109/ACCESS.2018.2812303
Masoum, A.S., Deilami, S., Moses, P.S., Masoum, M.A.S., Abu-Siada, A.: Smart load management of plug-in electric vehicles in distribution and residential networks with charging stations for peak shaving and loss minimisation considering voltage regulation. IET Gener. Transm. Distrib. 5(8), 877–888 (2011). https://doi.org/10.1049/IET-GTD.2010.0574
Keane, E, Flynn, D.: Potential for electric vehicles to provide power system reserve. 2012 IEEE PES Innovative Smart Grid Technologies, ISGT 2012 (2012). https://doi.org/10.1109/ISGT.2012.6175701.
Hoogvliet, T.W., Litjens, G.B.M.A., van Sark, W.G.J.H.M.: Provision of regulating- and reserve power by electric vehicle owners in the Dutch market. Appl. Energy 190, 1008–1019 (2017). https://doi.org/10.1016/J.APENERGY.2017.01.006
Yang, Z., Sun, L., Ke, M., Shi, Z., Chen, J.: Optimal charging strategy for plug-in electric taxi with time-varying profits. IEEE Trans. Smart Grid 5(6), 2787–2797 (2014). https://doi.org/10.1109/TSG.2014.2354473
Niu, L., Zhang, D.: Charging guidance of electric taxis based on adaptive particle swarm optimization. Scientific World Journal 2015, 354952 (2015). https://doi.org/10.1155/2015/354952
Yang, Z., Sun, L., Chen, J., Yang, Q., Chen, X., Xing, K.: Profit maximization for plug-in electric taxi with uncertain future electricity prices, 1–1 (2015). https://doi.org/10.1109/PESGM.2015.7286255
Shafiee, S., Fotuhi-Firuzabad, M., Rastegar, M.: Investigating the impacts of plug-in hybrid electric vehicles on power distribution systems. IEEE Trans. Smart Grid 4(3), 1351–1360 (2013). https://doi.org/10.1109/TSG.2013.2251483
Galiveeti, H.R., Goswami, A.K., DevChoudhury, N.B.: Impact of plug-in electric vehicles and distributed generation on reliability of distribution systems. Eng. Sci. Technol. Int. J. 21(1), 50–59 (2018). https://doi.org/10.1016/J.JESTCH.2018.01.005
Tomić, J., Kempton, W.: Using fleets of electric-drive vehicles for grid support. J. Power Sources 168(2), 459–468 (2007). https://doi.org/10.1016/J.JPOWSOUR.2007.03.010
Sheikhi, A., Bahrami, S., Ranjbar, A.M., Oraee, H.: Strategic charging method for plugged in hybrid electric vehicles in smart grids; a game theoretic approach. Int. J. Electr. Power Energy Syst. 53(1), 499–506 (2013). https://doi.org/10.1016/J.IJEPES.2013.04.025
Tian, Z., et al.: Real-Time charging station recommendation system for electric-vehicle taxis. IEEE Trans. Intell. Transp. Syst. 17(11), 3098–3109 (2016). https://doi.org/10.1109/TITS.2016.2539201
Qin, H., Zhang, W.: Charging scheduling with minimal waiting in a network of electric vehicles and charging stations. Proceedings of the Annual International Conference on Mobile Computing and Networking, MOBICOM, 51–60 (2011). https://doi.org/10.1145/2030698.2030706
Gusrialdi, A., Qu, Z., Simaan, M.A.: Distributed scheduling and cooperative control for charging of electric vehicles at highway service stations. IEEE Trans. Intell. Transp. Syst. 18(10), 2713–2727 (2017). https://doi.org/10.1109/TITS.2017.2661958
del Razo, V., Jacobsen, H.A.: Smart charging schedules for highway travel with electric vehicles. IEEE Trans. Transp. Electrific. 2(2), 160–173 (2016). https://doi.org/10.1109/TTE.2016.2560524
Yang, S.N., Cheng, W.S., Hsu, Y.C., Gan, C.H., Lin, Y.B.: Charge scheduling of electric vehicles in highways through mobile computing. Proceedings of the International Conference on Parallel and Distributed Systems - ICPADS, 692–698 (2011). https://doi.org/10.1109/ICPADS.2011.42
Sweda, T.M., Klabjan, D.: Finding minimum-cost paths for electric vehicles. 2012 IEEE International Electric Vehicle Conference, IEVC 2012 (2012). https://doi.org/10.1109/IEVC.2012.6183286
Guo, T., You, P., Yang, Z.: Recommendation of geographic distributed charging stations for electric vehicles: A game theoretical approach. IEEE Power Energy Soc. Gen. Meet. 2018-January, 1–5 (2018). https://doi.org/10.1109/PESGM.2017.8274435
Moghaddam, Z., Ahmad, I., Habibi, D., Phung, Q.V.: Smart charging strategy for electric vehicle charging stations. IEEE Trans. Transp. Electrific. 4(1), 76–88 (2017). https://doi.org/10.1109/TTE.2017.2753403
Sowmya, R., Sankaranarayanan, V.: An Optimal Model for Electric Vehicle Battery Charging and Discharging Scheduling Strategy. 2019 National Power Electronics Conference, NPEC 2019 (2019). https://doi.org/10.1109/NPEC47332.2019.9034691
Kadam, V.S., Sowmya, R., Sankaranarayanan, V.: Optimal Coordinated Charging Strategy for Electric Vehicles at Geographically Distributed Charging Stations. 2019 National Power Electronics Conference, NPEC 2019 (2019). https://doi.org/10.1109/NPEC47332.2019.9034766
Dorigo, M., Maniezzo, V., Colorni, A.: Ant system: optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern. Part B (Cybernetics) 26(1), 29–41 (1996). https://doi.org/10.1109/3477.484436
Banaie-Dezfouli, M., Nadimi-Shahraki, M.H., Beheshti, Z.: R-GWO: Representative-based grey wolf optimizer for solving engineering problems. Appl. Soft Comput. 106, 107328 (2021). https://doi.org/10.1016/j.asoc.2021.107328
Premkumar, M., Sumithira, R.: Humpback whale assisted hybrid maximum power point tracking algorithm for partially shaded solar photovoltaic systems. J. Power Electron. 18(6), 1805–1818 (2018). https://doi.org/10.6113/JPE.2018.18.6.1805
Mirjalili, S., Gandomi, A.H., Mirjalili, S.Z., Saremi, S., Faris, H., Mirjalili, S.M.: Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems. Adv. Eng. Softw. 114, 163–191 (2017). https://doi.org/10.1016/j.advengsoft.2017.07.002
Mirjalili, S.: SCA: A Sine Cosine algorithm for solving optimization problems. Knowl.-Based Syst. 96, 120–133 (2016). https://doi.org/10.1016/j.knosys.2015.12.022
Zhao, X., Fang, Y., Liu, L., Li, J., Xu, M.: An improved moth-flame optimization algorithm with orthogonal opposition-based learning and modified position updating mechanism of moths for global optimization problems. Appl. Intell. 50(12), 4434–4458 (2020). https://doi.org/10.1007/s10489-020-01793-2
Faramarzi, A., Heidarinejad, M., Stephens, B., Mirjalili, S.: Equilibrium optimizer: A novel optimization algorithm. Knowl.-Based Syst. 191, 105190 (2020). https://doi.org/10.1016/j.knosys.2019.105190
Faramarzi, A., Heidarinejad, M., Mirjalili, S., Gandomi, A.H.: Marine predators algorithm: A nature-inspired metaheuristic. Expert Syst. Appl. 152, 113377 (2020). https://doi.org/10.1016/j.eswa.2020.113377
Kumar, C., Raj, T.D., Premkumar, M., Raj, T.D.: A new stochastic slime mould optimization algorithm for the estimation of solar photovoltaic cell parameters. Optik 223(August), 165277 (2020). https://doi.org/10.1016/j.ijleo.2020.165277
Ahmadianfar, I., Bozorg-haddad, O., Chu, X.: Gradient-based optimizer: A new metaheuristic optimization algorithm. Inf. Sci. 540, 131–159 (2020). https://doi.org/10.1016/j.ins.2020.06.037
Wolpert, D.H., Macready, W.G.: No Free Lunch Theorems for Optimization. IEEE Trans. Evol. Comput. 1(1), 67–82 (1997)
Tizhoosh, H.R.: Opposition-based learning: A new scheme for machine intelligence. Proceedings - International Conference on Computational Intelligence for Modelling, Control and Automation, CIMCA 2005 and International Conference on Intelligent Agents, Web Technologies and Internet. 1, 695–701 (2005). https://doi.org/10.1109/cimca.2005.1631345
Mahdavi, S., Rahnamayan, S., Deb, K.: Opposition based learning: A literature review. Swarm Evol. Comput. 39, 1–23 (2018). https://doi.org/10.1016/j.swevo.2017.09.010
Fan, Q., Huang, H., Yang, K., Zhang, S., Yao, L., Xiong, Q.: A modified equilibrium optimizer using opposition-based learning and novel update rules. Expert Syst. Appl. 170, 114575 (2021). https://doi.org/10.1016/j.eswa.2021.114575
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of Interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
R, S., Sankaranarayanan, V. Optimal Scheduling of Electric Vehicle Charging at Geographically Dispersed Charging Stations with Multiple Charging Piles. Int. J. ITS Res. 20, 672–695 (2022). https://doi.org/10.1007/s13177-022-00316-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13177-022-00316-2