Unbalanced Operations of AC Machines

In this paper, unbalanced operations of induction and synchronous machines are discussed. The current-voltage differential equations, referred to the moving reference axes α and ß, are derived directly from the general equations of armature reaction and induced voltage. Kron's tensor transformation is used to develop a reciprocal system representing the actual machine under unbalanced operations. As an illustration, the line-to-line short-circuit case of a synchronous machine is solved in detail. An approximate solution for the differential equation with variable coefficients is proposed.