Rotating-Field Theory and General Analysis of Synchronous and Induction Machines

The two-reaction theory of synchronous machines as developed by Blondel, Doherty, Nickle, Park and others is well known. The present paper attempts to develop the rotating-field theory of synchronous and induction machines as an important alternative to the two-reaction theory. The general analysis includes analysis of rotating machines under steady-state, transient-state and hunting conditions. Rotating reference frames are introduced. The new components, known as the forward and backward components, or f and b components, are then simply correlated to the direct and quadrature components, or d and q components. By use of the f and b components, it is shown that any external network and transmission line with lumped or distributed constants can be connected to a synchronous machine. This forms the basis of interconnection between synchronous and induction machines. A steady-state vector diagram of a salient-pole synchronous machine is given. Transient solution of short-circuit current and torque follows. An equivalent circuit for the same machine with direct- and quadrature-axis excitation is derived, and a 6-terminal network is developed for transient studies. The induction machine is similarly analysed with respect to its own rotor or with respect to a synchronously rotating reference frame. Interconnection of synchronous and induction machines is then possible for steady-state as well as transient studies. The hunting circuit involving one synchronous machine and a load is developed, based on Kron´s uniformly rotating reference frame instead of the Blondel-Park reference frame. Hunting circuits for two rotating machines are developed, based on simple relations in absolute differential calculus. A number of instantaneous torque expressions are developed from the tensorial point of view. New expressions are given in terms of armature currents and flux linkages or their components.