A generalised analysis method for N-phase induction machines is presented. The Nphase system is analysed using 2N degrees of freedom. A new conceptual view of a multi-phase system using an N-dimensional vector space has been developed. It is shown that such an N-dimensional vector space can be decoupled into 'h(N+PJ independent two dimensional vector planes, where if N is odd, p=l, otherwise P=O. Each vector plane is shown to be the combination oftwo positive and negative sequence components ofthe same phase order. Each vector space is shown to be independent and can be controlled separately by an N-phase inverter. Each inverter state is shown to have a location in every vector space. A vector control strategy has been realised for developing independent vectors in decoupled vector spaces, resulting in the desired voltage waveforms at the inverter outputs. A five-phase induction motor is designed, and constructed as an integral part of five-phase drive system. A five-phase decoupled vector space controller is implemented in a fixed-point digital signal processor and the practical five-phase inverter based drive system validates the proposed decoupled vector space theory. The analysis of multi-phase machines during imbalanced. electrical operation is considered using decoupled vector space theory. It is shown that each independent vector in the decoupled vector spaces produces unique flux distributions in an N-phase AC machine, but only one vector space develops fundamental rotor linked flux and thus fundamental torque. The interaction of decoupled vector spaces with winding harmonics is developed in order to analyse the effects of unbalanced currents in a i' practical induction motor. It is shown that torque is produced only by the primary vector space currents in a sinusoidally wound machine. The additional freedom available from auxiliary vector spaces can be used to compensate for imbalance caused by faulty machine phases. It is shown that there exists 2N-3 degrees of freedom for an N-phase system of fluxes of an N-phase machine with a floating neutral. These degrees of freedom can be used to compensate for the phase imbalance created by opencircuited inverter legs. The machine can still be fluxed to produce rotational power. At the pre-fault to post-fault transition, the current vectors of the operational phases are reoriented to produce a rotating fundamental flux. A five-phase induction motor drive system demonstrates the performance for the loss of one and two phases. Harmonic winding function generated flux interaction is analysed and interpreted in terms of a five-phase motor with single and two phase loss.