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This paper deals with the generalization of the Clarke components to polyphase current and voltage systems. Two definitions are proposed and their relative merits are discussed. It is shown that the second definition is to be preferred, since it is not only valid for completely symmetrical networks, but also for networks containing elements with only partial symmetry, such as the stator of an electric machine or an untransposed polyphase transmission line. The considerations of this paper may be used in the classroom to provide the student with a complete understanding of the principles of the decomposition techniques of polyphase quantities.