A New Approach to the Calculation of Synchronous Machine Reactances - Part I [includes discussion]

In Part I of this paper, the 2-reaction theory of synchronous machinesl is used to derive the torque equation at any slip s of the unexcited synchronous motor with one equivalent damper-winding circuit in each axis. It is then shown that this synchronous motor torque equation reduces in the special case of uniform air gap and continuous damper to the torque equation of the induction motor as developed from its equivalent circuit.2 A paramount criterion for the correctness of any resistance or reactance equations derived for synchronous machines is their reducibility in the special case of uniform air gap and continuous damper to those commonly known for the squirrel-cage induction motor.2,3 Equations in terms of dimensions and physical constants are derived in this paper from basic theory of coupled circuits. Also it is shown that all of these equations reduce in the previously mentioned special case of uniform air gap and continuous damper to those universally given2,3 for the squirrel-cage induction motor. These equations are then inserted in the definitions of transient and subtransient reactances obtained by operational calculus methods.4 The nomenclature of this paper will be found in Appendix I. In a later paper, comparison will be made of calculated transient and subtransient reactances based on the equations given here with those given by test and reference,5 and the discrepancies will be discussed. Also, numerical samples of calculations of the different reactances will be given, using information based on the present paper.