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Since variable speed electric drive systems are supplied from power electronic converters, it is possible to utilize ac machines with a phase number higher than three. It is shown in the paper, using general theory of electrical machines, that an increase of the stator phase number to at least five (or more) enables completely independent vector control of two (or more) multiphase machines that are supplied from a single current-controlled voltage source inverter. In order to achieve such an independent control it is necessary to connect multiphase stator windings of the machines in series and perform an appropriate phase sequence transposition. The concept is equally applicable to any multiphase ac machine type and its major advantage, compared to an equivalent multimotor three-phase drive system, is the saving of a certain number of inverter legs. The actual saving depends on the number of phases. The concept is introduced using an n-phase induction machine as the starting point and further analysis is restricted to an odd number of phases, for the reason explained in the paper. Classification of all the possible cases that may arise is given, followed by presentation of connection diagrams for selected phase numbers. Detailed verification of the proposed concept is provided by simulating the operation of a seven-phase three-motor drive system, controlled using indirect rotor flux oriented control principles. Some preliminary experimental results, which confirm the feasibility of a two-motor series-connected drive system, are included as well. The main advantages and drawbacks of the concept, when compared with an equivalent three-phase multimotor drive system, are finally addressed.