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Fast charging is an essential stakeholder concern for achieving a deeper penetration of Electric Vehicles (EVs), as optimizing the charging times of conventional vehicles is as yet a bottleneck to be solved. An important drawback of EV's fast charging lies in the degradation suffered by the Li-ion Batteries (LIBs) at high charging currents. A deep understanding of the how these fast-charging activities affect the LIBs' degradation is necessary in order to design appropriate fast charging stations and EV powertrains for different scenarios and contexts. In this regard, the present paper analyzes the effect of fast charging on Libs' degradation under operation profiles from real driving cycles. Specifically, Battery Electric Buses (BEBs) driving profiles from three demos in European Cities (Gothenburg, Osnabrück and Barcelona) have been used in this analysis. In order to deduce the best practices for the design of the charging stations, different sizes for the chargers have been simulated, focusing on the analysis of the LIB degradation under each situation. Besides, for the design of the EV powertrain, different LIB sizes and LIB chemistries (Lithium Nickel Manganese Cobalt-NMC, Lithium Iron Phosphate-LFP, and Lithium Titanate Oxide-LTO) have also been proposed and compared in terms of LIB degradation. The results demonstrated that LTO batteries exhibited the lowest degradation, with capacity fade values under 1.5%/year in the nominal scenario (nominal charger and LIB sizes). As long as a full charging is ensured, reducing the fast charger size has been found to be a cost-effective measure, as the LTO degradation can be reduced at least to 1.21%/year. In addition, increasing the battery (BT) size has also been found to be a cost-effective approach for LTO batteries. In this case, it was found that for a 66% increase in capacity, the degradation can be reduced at least to 0.74%/year (more than 50% reduction). The obtained conclusions are seen as useful for the design of charging stations and EV's BT systems that undergo fast charging. [ABSTRACT FROM AUTHOR]