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Increasing attention has been shown in recent years in the a.c. electrification of railway traction systems and a number of established systems now exist throughout the world. Where the traction system is supplied directly from a high-voltage national-grid network, a common component of such schemes is a step down transformer connection between the two systems. The electrical, mechanical and thermal design of these transformers is subject to a number of special considerations not normally encountered in the design of distribution-type transformers of similar rating and voltage class. The paper reviews the operating conditions peculiar to railway traction such as overvoltages, short circuits, cyclic and peak loadings and discusses how these conditions influence the design and construction of single-phase transformers supplying power for traction purposes. The paper describes the engineering practice and operating experience obtained with the British 25 kV a.c. railway-traction system in particular, but much of the system and transformer-design philosophy and operational experience referred to applies to a.c. traction systems elsewhere in the world.