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Article

Smart Charging of Electric Vehicles Considering SOC-Dependent Maximum Charging Powers

1
Institute of Logic and Computation, TU Wien, 1040 Vienna, Austria
2
Honda Research Institute Europe GmbH, 63073 Offenbach, Germany
*
Author to whom correspondence should be addressed.
Academic Editors: Fernando Lezama, Zita Vale, John Fredy Franco and João Soares
Energies 2021, 14(22), 7755; https://doi.org/10.3390/en14227755
Received: 27 October 2021 / Revised: 12 November 2021 / Accepted: 12 November 2021 / Published: 18 November 2021
The aim of this work is to schedule the charging of electric vehicles (EVs) at a single charging station such that the temporal availability of each EV as well as the maximum available power at the station are considered. The total costs for charging the vehicles should be minimized w.r.t. time-dependent electricity costs. A particular challenge investigated in this work is that the maximum power at which a vehicle can be charged is dependent on the current state of charge (SOC) of the vehicle. Such a consideration is particularly relevant in the case of fast charging. Considering this aspect for a discretized time horizon is not trivial, as the maximum charging power of an EV may also change in between time steps. To deal with this issue, we instead consider the energy by which an EV can be charged within a time step. For this purpose, we show how to derive the maximum charging energy in an exact as well as an approximate way. Moreover, we propose two methods for solving the scheduling problem. The first is a cutting plane method utilizing a convex hull of the, in general, nonconcave SOC–power curves. The second method is based on a piecewise linearization of the SOC–energy curve and is effectively solved by branch-and-cut. The proposed approaches are evaluated on benchmark instances, which are partly based on real-world data. To deal with EVs arriving at different times as well as charging costs changing over time, a model-based predictive control strategy is usually applied in such cases. Hence, we also experimentally evaluate the performance of our approaches for such a strategy. The results show that optimally solving problems with general piecewise linear maximum power functions requires high computation times. However, problems with concave, piecewise linear maximum charging power functions can efficiently be dealt with by means of linear programming. Approximating an EV’s maximum charging power with a concave function may result in practically infeasible solutions, due to vehicles potentially not reaching their specified target SOC. However, our results show that this error is negligible in practice. View Full-Text
Keywords: electric vehicles; charging scheduling; state-of-charge dependent maximum charging power; mixed integer linear programming electric vehicles; charging scheduling; state-of-charge dependent maximum charging power; mixed integer linear programming
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MDPI and ACS Style

Schaden, B.; Jatschka, T.; Limmer, S.; Raidl, G.R. Smart Charging of Electric Vehicles Considering SOC-Dependent Maximum Charging Powers. Energies 2021, 14, 7755. https://doi.org/10.3390/en14227755

AMA Style

Schaden B, Jatschka T, Limmer S, Raidl GR. Smart Charging of Electric Vehicles Considering SOC-Dependent Maximum Charging Powers. Energies. 2021; 14(22):7755. https://doi.org/10.3390/en14227755

Chicago/Turabian Style

Schaden, Benjamin, Thomas Jatschka, Steffen Limmer, and Günther Robert Raidl. 2021. "Smart Charging of Electric Vehicles Considering SOC-Dependent Maximum Charging Powers" Energies 14, no. 22: 7755. https://doi.org/10.3390/en14227755

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