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Recent developments in power electronic AC/AC converters, capable of bidirectional energy transfer with good approximations to sinusoidal waveforms, have caused renewed interest in the doubly-fed connection of the self-cascaded or concatenated induction machine. These are referred to as brushless doubly-fed machines (BDFM). Work on this configuration is directed towards a potential means of economical variable-speed generators, adjustable-speed drives, and ' pumped-storage systems. The unusual connections of stator coil groups, which enable the co-existence of two different pole numbers within the same windings, and rotor cage configurations peculiar to the BDFM, make it necessary to develop a unique model if detailed design is to be undertaken and dynamic performance is to be understood without neglecting potentially troublesome transients and internal harmonic effects. The model development starts from a consideration of the basic stator coils and the basic nested loops that constitute the rotor cage. The simple time domain interactions that occur between the basic machine components are developed into the performance equations of the BDFM by application of the appropriate connection matrices.These matrices represent the internal connection of stator coil groups and the final connections to two independent three-phase supplies of different frequency and voltage. The resulting model of electrical performance and the associated torque equations are suitable for solution as a set of state variable equations. This will enable the simulation of the system interactions that occur between the machine, its power converter, and the utility supply in any combination of motoring or generating, synchronous or asynchronous, modes that are possible with the BDFM. I "The use of a cascade connection of induction motors of different numbers of poles to enable speed changing was a useful technique employed for many years before the development of static frequency changers. It was first shown by Hunt [ l ] that an ingenious connection of stator windings, and a special rotor configuration, enabled the effects of cascading to be incorporated within one machine frame. Later work by Broadway and Burbridge [2] advanced the design of the rotor to a more mechanically manageable form whilst retaining the compatibility needed for fields of two different pole numbers and different frequencies.Analyses of the self-cascaded machine in available literature have always begun by reverting to an equivalent connection of two magnetically separate machines with some electrical interconnection and a common shaft. These analyses invariably assume ideal sinusoidal winding disposition which is markedly untrue in selfcascaded windings-particularly for the higher pole number connection. The models based on these assumptions result in equivalent circuit analyses [2,3,4] for steady-state performance, or idealized two-axis (d-q) models [5] for stability studies and are adequate as applied. However, for investigations of detailed design alternatives and for...

This paper presents a Hopf bifurcation analysis for a Single-Machine Infinite-Bus (SMIB) power system experiencing SSR by applying a Hopf bifurcation theorem combined with numerically solving for the Monodromy matrices. A Hopf bifurcation in the system is predicted, together with stable periodic orbits.

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