Analysis an AC Excited Synchronous Machine in Unbalanced Steady State Operating Condition (Part 1) −Derivation of Basic Equations and Fault Calculations−

Basic characteristics of an AC Excited Synchronous Machine (AESM) in unbalanced steady state operating condition are presented in this paper. As analyses both of an induction machine and a synchronous machine in unbalanced steady state operating condition are developed by using the method of symmetrical coordinates, this paper also applies the above method to the analysis of an AESM along with the two-axis theory. First, the basic equations and the equivalent circuits are derived for unbalanced condition both of the primary circuit and the secondary circuit. These equivalent circuits consist of three components, which are respectively zero-sequence, positive-sequence and negative-sequence. Next the torques for unbalanced operation are obtained. Finally the basic fault calculations in the primary circuit (three-phase short, circuit, line-to-line fault, one-line-to-ground fault and two-lines-to-ground fault) are developed using the above basic equations