[No. 56] Lèse-Majesté

Fig. 1 The IPM — monarch of motorsFig. 1The IPM — monarch of motors

It is easy to imagine the IPM (interior permanent-magnet motor) as the monarch of electric motors.Indeed to question its supremacy could be said to be lèse-majesté.1It reigns supreme in electric vehicle drive systems, and it is found in countless other applications including humble pumps, fans and compressors.Many of the earlier kings and queens of the electric motor business have been overthrown or laid to rest, and some of them have been completely forgotten.

So let’s commit lèse-majesté — not once, but three times!The theme of our confrontation with the monarch is the question of efficient utilization of material, especially magnet material.

A.A significant fraction of the magnet flux is short-circuited through the central webs and the bridges on either side of each magnet.(See Engineer’s Diary No. 12; also Video 15).At first sight this looks like a waste of magnet material, often termed ‘rotor leakage’.It is analysed in more detail in Video 16.(See also Ref. [1], which describes a rotor without the webs and bridges, but which uses a carbon-fibre sleeve to hold the rotor together).

B.It is common in EV drive systems and other IPM applications to weaken the flux, essentially by means of a negative component of d-axis current.This flux-weakening is usually applied at higher reaches of the speed range.It can be explained as follows.The motor generates a back-EMF proportional to the product of speed and magnet flux, while the terminal voltage (supplied by the inverter) is limited by the battery voltage.The result is that the speed is limited unless the total flux can be weakened or reduced.Similar conditions arise also in DC commutator motors and wound-field synchronous AC motors, but in these machines the flux can be weakened efficiently and economically by reducing the field current.In the IPM it requires a component of armature reaction (stator current) oriented by the field-oriented controller to act in a demagnetizing or flux-weakening direction.We can characterize this by saying that we start with expensive rare-earth magnets, and then use the most expensive source of ampere-conductors (the inverter) to weaken them.In the extreme case the magnet operating point is driven down its second-quadrant BH curve towards the onset of partial demagnetization (the ‘knee’ in the demag curve), a condition that is especially severe at higher temperatures.Thus it appears that flux-weakening wastes precious magnet flux, while the most expensive grades of magnet are required if it is to be done safely without partial demagnetization.

C.Only the fundamental space-harmonic component of the magnet flux crossing the air-gap is used in torque production.We know that the magnet flux distribution in the air-gap is not perfectly sinusoidal, so is it not the case that we are wasting all the other harmonics and thereby using the magnet inefficiently?We also know that the stator winding is designed as far as possible to link the fundamental space-harmonic component of the magnet flux, and not the harmonics, so it seems that the winding is also wasteful in that it makes no use of the harmonics.

In a medieval court we would expect to have our heads cut off simply for asking these questions — a clear case of lèse-majesté!But a kindly monarch would ask his or her staff to answer the questions, and even to publish the explanations in Engineer’s Diary!Basically we have three questions that seem to ask whether the IPM wastes precious magnet material.What might the answers be?

A.First, the webs and bridges.In Video 15 we showed that although the webs and bridges do reduce the air-gap flux, they actually contain or divert some of the magnet flux, raising the operating point in the second quadrant of the BH curve and thereby helping to protect the magnet against the likelihood of demagnetization.A carbon-fibre sleeve offers no such protection, while at the same time it increases the working air-gap length significantly.This itself will depress the operating point of the magnet while reducing the flux per pole, so it may be the case that the rotor with webs and bridges actually needs less magnet material than the sleeved rotor.The overall evaluation is complicated because these alternative rotor configurations are not necessarily optimized for the same speed or the same torque, so we have to be careful to define a level playing-field; but at least we can see that there is more to the question than might at first appear.At a more basic level we might argue that the handle of a shopping-basket is a waste of material, because the groceries are in the basket and not suspended from the handle.We could always carry the basket in our arms, or tie it by a length of string around our necks, obviating the need for the handle.In any case the handle is not necessary when the basket is laid down.In engineering there are countless examples of components that appear to have no primary function, but which cannot be eliminated because their function (however indirect it may be) is an indispensable part of the whole system.So it is with the webs and bridges in the IPM.

B.The flux-weakening question.In simple terms, if flux-weakening is applied skilfully (as it usually is), it extends the speed range while maintaining constant power output, without requiring a larger inverter.We can say that the purpose of flux-weakening is to save on power semiconductors.It has little to do with the cost of the magnet, because that is more closely related to the maximum torque, not the maximum power.As for the ‘cost’ of the flux-weakening ampere-conductors obtained from the inverter, we should note that flux-weakening does not necessarily require an increase in current, but only a phase-shift.And although it appears that the DC commutator motor and the wound-field AC synchronous motor have the advantage of independent field control, they also require additional components — brushes and commutator in the former, or brushes and slip-rings or a brushless equivalent in the latter.Both these machines also require separate exciters to supply the field current.All these components consume power.They also take up valuable space in the motor itself.
The process of flux-weakening is in fact rather complex, and in the IPM it is tied up with the topic of reluctance torque which can be claimed to save magnet material to some extent.But we can conclude that the notion that flux-weakening somehow implies a waste of magnet material appears to be false.It may, however, require a higher grade of magnet to withstand demagnetization at higher temperatures under flux-weakening conditions.

C.When we question the logic of relying solely on the fundamental space-harmonic components of not only the magnet flux but also the stator ampere-conductor distribution — and of ‘wasting the harmonics’ — we are going to the very heart of the theory of operation of the AC machine.There isn’t enough space to cover that here!(But see Engineer’s Diary No. 52, and the Blue Book).So let’s just make a couple of points.We can take ourselves back to the early days of brushless DC motors, when it was thought in some circles that a rectangular magnet flux distribution with a concentrated full-pitch winding would produce 4/π times as much torque as would be obtained from the fundamental space-harmonic components, and there was a debate — ‘brushless DC versus brushless AC’ — as to which was better.The question is not as simple as it seems, because it goes to the proportioning of the yokes and pole-arcs, and it even leads to the idea of machines with more than 3 phases (6, 9, or more).It is also intimately connected with the question of torque ripple.But the overwhelming predominance of the sinewave AC motor (particularly at higher power levels) reflects the industry’s long-affirmed conclusion that this is the one that makes the most sense, even though the harmonic effects remain and do cause parasitic nuisance effects.It is axiomatic that AC machines rely on the fundamental space-harmonic components of flux and ampere-conductors to produce their running torque, and that is why we try to design windings with the highest possible winding factor, which expresses the degree to which the winding utilizes the available fundamental flux of the magnet.And if we examine the actual flux distribution in the air-gap of a well-designed IPM — or indeed of any well-designed PM AC motor — we often find that the fundamental space-harmonic component is not significantly less than the total magnet flux.For the winding we can also use the harmonic leakage reactance as a measure of how much voltage is wasted by the winding harmonics, and in the case of the IPM we will generally find that this is small (especially with higher numbers of slots/pole and distributed windings).It is true that the rotor design in the IPM can be tailored to improve the air-gap flux distribution, and particularly to reduce the third-harmonic; but if we really wanted a near-perfect sine-distribution of magnet flux we would need to use a Halbach array that would be more expensive than an IPM rotor.

The idea of lèse-majesté in engineering is really a question of questioning the way we design machines, including questions that may seem silly.Those are often the most fundamental questions, and often the ones that lead to new ideas.

References :

[1] Olsen et al, ‘Permanent magnet motor with wrapping’, WO 2021 / 225902 A1 11-Nov-2021 Tesla Inc.

Note :

1 I’m not sure if I need to explain the term lèse-majesté, but I think readers will laugh if they look it up on the internet.In engineering circles it means questioning authority, often with sardonic humour expressed with a kindly wry smile.

If you have any comment for "An engineer’s diary"

Use this form to share with us your comments. Your precious feedback will be used for our future reference. Note that we will not reply to any questions. We ask for your understanding in advance.
Caution: This entry form is for English only. Please refrain from using multibyte characters such as Japanese, Chinese, and Korean.


Prof. Miller was educated at the universities of Glasgow and Leeds, U.K., and served an industrial apprenticeship with Tube Investments Ltd. He worked for G.E.C. in the U.K. and General Electric in the United States. From 1986-2011 he was professor of electric power engineering at the university of Glasgow, where he founded the Scottish Power Electronics and Electric Drives Consortium. He has published more than 200 papers and 10 books and 10 patents, and he has given many training courses. He has consulted for several industrial companies in Europe, Japan and the United States. He is a Life Fellow of I.E.E.E. and in 2008 he was awarded the Nikola Tesla award.

The Green Book: “Design of Brushless Permanent-Magnet Machines”

The Blue Book: “Design Studies in Electric Machines” (June 30, 2022)