Determination of converter control algorithms for brushless doubly-fed induction motor drives using Floquet and Lyapunov techniques

This paper presents a method of analyzing the stability of brushless doubly-fed machines (BDFM) in the synchronous mode of operation. Unlike the stability analysis of conventional induction and synchronous machines for which the linearized state equations are time-invariant, the linearized state equations of the BDFM are time-varying and, consequently, their eigenvalue analysis cannot be performed directly. However, since the system matrix of the linearized equations is a periodic function of time, the generalized theory of Floquet can be applied to transform the time-varying system of equations into an equivalent set of equations with a constant system matrix. Eigenvalue analysis can then be employed to analyze the stability characteristics of given equilibrium points. Investigation into the stability of a proof-of-concept BDFM in the synchronous mode of operation using the transformed linearized model shows good correlation between theoretical and experimental results. In addition, the possibility of designing a BDFM drive with inherent open-loop stability over the entire speed range is demonstrated. Finally, under stable steady state synchronous operation, power converter control methods are discussed and it is shown that scalar control methodologies similar to those for induction motor drives can be applied to the BDFM