The use of 3 phase synchronous machines (motor or generator) is becoming more widespread with the introduction of variable frequency drives, which allow the machines to be used very effectively as low maintenance alternatives to brushed DC commutator motors. However, mathematical modeling of these machines is often difficult to understand. Many textbooks on electro-mechanical machines introduce the synchronous machine using a phasor model of the voltages induced in the armature and the applied voltage. This yields some neat results of output torque as a function of the torque angle but fails to provide much insight into how this torque comes about. Furthermore, the method assumes that the resistance of the armature windings is negligible compared with armature reactance. The method falls apart when resistance must be included. Even when armature resistance is small, there is no insight into how efficiency is compromised by copper losses in the armature. The approach described in this paper is based on the same theory, which is usually used to explain the operation of DC commutator machines. This approach provides direct insight into how torque is developed. Losses introduced by armature resistance are included so reasonable efficiency estimates can be made. Meanwhile the neat results of the simple phasor model can be obtained as a special cases by setting armature resistance to zero.

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