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Optimal Scheduling of Electric Vehicle Charging at Geographically Dispersed Charging Stations with Multiple Charging Piles

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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.

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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

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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

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