Tensorial Analysis and Equivalent Circuit of a Variable-Ratio Frequency Changer

When two power systems with different frequencies are connected together through an asynchronous tie, the transient behavior of the tie under a sudden change of load on either side becomes of great importance. The paper derives by the tensorial method the steady-state equivalent circuit and the transient equations of a variable-ratio frequency-changer set consisting of an ohmic-drop exciter, regulating machine, and induction machine, when an unbalanced load is applied suddenly to the stator side of the induction machine. A companion paper by Carter, Maginniss, and Rothe gives the results of the solution of the equations by the a-c network analyzer and the differential analyzer.