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Field orientation in a synchronous machine with a smooth rotor

In this animation the stator (three phase symmetrical winding, phase width , terminals 1U, 1V and 1W) is fed by a controllable (in phase, frequency and amplitude) three phase current and the rotor (smooth rotor, distributed winding, phase width , terminals + and -) is fed by a DC current. The rotor speed follows from the stator frequency: with the number of pole pairs ( in the animation). is assumed so that the motor torque is always equal to the load torque : (i.e. only steady state conditions are animated). Red and pink waveforms are the current densities and (A/m) of stator and rotor respectively. It is assumed that the phase conductors are spread very finely/thin over the phase width (), so that the current density is a constant over a phase width. The black waveforms (dashed line) and (dash-dot line) are the accompanying mmfs (Aw) produced by the current densities and respectively (where and symmetry requirements allow to locate the neutral point where ). Please see also: https://www.geogebra.org/m/azhgwttv and https://www.geogebra.org/m/tny9ykfg. The solid black line is the total mmf of rotor and stator, . The torque resulting from a rotating fundamental field layer and rotating fundamental current layer can be calculated with . In this animation the saturation of the magnetic circuit is neglected so that the air-gap induction in each point of the armature circumference follows directly from the local total mmf of rotor and stator: with and the air gap length. The torques and (produced by the fundamental functions) are given by (Nm): and with some (machine) constant. In the animation the torques are then given in relation to the maximum attainable torque in the animation (pu). Field orientation can be achieved when:
  • the fundamental parts of and are in phase, or
  • the fundamental parts of and are in phase
Indeed, for field orientation the torque of the rotor or stator (action = reaction) is maximum for some given stator and rotor current magnitudes. Animation and equations are based on the book Electrical Machines and Drives by Jan A. Melkebeek (ISBN 978-3-319-72729-5). Please download the .ggb file and open with the Geogebra Classic 5 application (see https://www.geogebra.org/download) if the animation is too slow in your browser. Any and all feedback is welcome and can be sent to timon.dewispelaere@kuleuven.be.