Analysis of Instability in Electrical Machines

While there exist numerous studies of electromechanical instabilities of specific electrical machines in constant or periodic speed operation, a broader perspective is not commonly offered. In contrast, a general machine model is used here to present essential and common features of these stability analyses. Fundamental issues are illuminated at this level of generality before specialization to the details of a specific machine. To begin, Park-transformable machines in constant-speed operation are considered. The local dynamics of these machines are linear and time-invariant. For such machines it is shown that instability may be analyzed in a useful way via systematically obtained reduced-order models. This is illustrated by significantly expanding an earlier study of a hybrid stepping motor. The more general situation in which the linearized models that govern local behavior are periodically varying is considered next. Classical Floquet theory is reviewed to provide the tools needed for stability analysis in this situation.