D, Q Reference Frames for the Simulation of Induction Motors

Induction motors are being used more than ever before in industry and individual machines of up to 10 MW in size are no longer a rarity. During start-up and other severe motor operations the induction motor draws large currents, produces voltage dips, oscillatory torque and can even generate harmonics in the power system [1 4]. It is therefore important to be able to model the induction motor in order to predict these phenomena. Various models have been developed, and the d,q or two-axis model for the study of transient behaviour has been well tested and proven to be reliable and accurate. It has been shown [1] that the speed of rotation of the d,q axes can be arbitrary although there are three preferred speeds or reference frames as follows: (a) the stationary reference frame when the d,q axes do not rotate; (b) the synchronously rotating reference frame when the d,q axes rotate at synchronousspeed; (c) the rotor reference frame when the d,q axes rotate at rotor speed. Most authors [2 -4] use one or other of these reference frames without giving specific reasons for their choice. Whilst either the stationary [3] or the synchronously rotating [2]