The Magnetic Model approach to Electrical Machines

Its principal advantages are firstly its simplicity. The conventional electrical 'd-q-' model for a salient-pole synchronous machine, for instance, involves 10 electric variables, being 5 coil voltages and 5 coil currents. They are related by a 5x5 inductance matrix. Whereas the magnetic model has only two variables: a complex mmf representing the coil currents, and a complex flux that determines the coil voltages. From these the mechanical torque is obtained.

The other main advantage is that since the complex mmf and flux are space vectors, they are readily visualizable in physical terms. This is invaluable for beginning students who normally accompany the mathematics without problem, but are often at a loss to grasp what is ”really going on”.

A sudden short-circuit on a synchronous machine on the electric approach involves inverting the 5x5 inductance matrix, with laborious mathematics. On the magnetic model the results – including all the torque components – can be written down by inspection with no mathematics at all.

Due to its simplicity, the magnetic model allows quantitative analysis in cases normally only treated descriptively in texts of this level. The dynamic braking of induction machines; the shaded-pole motor; the asynchronous start of a salient-pole synchronous motor with its half-speed 'kink'; and so on. The inclusion of a rotor eddy-current factor in the conventional induction machine model allows the IEC design class torque/speed characteristics to be reproduced, otherwise impossible. A novel mathematical technique enables both axes of a salient-pole device to be treated in a single circuit.

Attention is paid to the practical aspects of design and testing, often neglected in comparable texts. There are ample worked examples – in principle one for each theoretical point – that with different numeral values can serve as a basis for student exercises.

Jeremy Fiennes, MSc, is a Professor at Federal University of Bahia, Brazil. He earned a First Class Honours in Engineering at Cambridge University, and an MSc at Imperial College, London under Prof. E.R. Laithwaite, the originator of the Magnetic Equivalent idea, and published foundational research on it in the IEE Journal. He has extensive practical experience as an erection and commissioning engineer at Machinenfabrik Oerlikon in Zurich, Switzerland, and later at ASEA in Västerås, Sweden. His further academic appointments include Kingston University, London and the Federal University of Paraiba, Brazil.