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Railway electrification is experiencing a very important transformation process today. The need of increasing its capacity has evidenced the drawbacks of conventional systems of dealing with the higher power required, whilst maintaining reasonable costs. Furthermore, the current trend undertaken by electrical systems towards smarter grids involves to rethink carefully the direction of evolution of these systems. However, the different technical progress at the time of railway electrification, and the particular historical and economic characteristics of the countries, have led to a great variety of configurations that require different solutions. The first main objective of this article is to classify and describe the principal electrical railway power supply systems existing and the most important proposals for their improvement found in the literature. The second main objective is to make a comparison of all presented systems based on economic and technical criteria capable of assessing their suitability and future projection. The right choice of the feeding system is decisive for the development of more competitive, efficient and reliable railway systems. (C) 2017 Elsevier Ltd. All rights reserved.