Vector Theory of Circuits Involving Synchronous Machines

It has been shown in previous publications that calculations of the performance of a synchronous machine may be simplified by the use of two scalar impedance operators which apply separately to the component of armature current which magnetizes in the axis of the poles, and to the component which magnetizes in the axis of the interpolar space. The present paper describes a method of combining these two scalar operators into a single vector operator which applies directly to the total current. With the new operator it becomes possible to write out the complete equations which apply to various numbers of interconnected machines, under various operating conditions, as readily as would be possible if each machine was replaced by a fixed source of voltage operating through a constant value of impedance. The effect is to simplify and thus to extend the scope of synchronous machine analysis. It is believed that the theory developed will be of value to engineers who are working on problems such as stability, hunting, and other problems of this general character which involve detailed analysis of the operation of two or more interconnected synchronous machines under transient conditions.