A faulted phase in a fault-tolerant permanent-magnet brushless machine can result in significant torque ripple. However, this can be minimized by using an appropriate optimal torque control strategy. Inevitably, however, this results in significant time harmonics in the phase current waveforms, which when combined with inherently large space harmonics, can result in a significant eddy-current loss in the permanent magnets on the rotor. This paper describes the optimal torque control strategy which has been adopted, and discusses its effect on the eddy-current loss in the permanent magnets of four-, five-, and six-phase fault-tolerant machines

Atallah, K.

Ede, J.A.

Howe, D.

Wang, J.B.

English

White Rose Research Online

This is a repository copy of Effect of optimal torque control on rotor loss of fault-tolerant permanent-magnet brushless machines .White Rose Research Online URL for this paper:http://eprints.whiterose.ac.uk/831/Article:Ede, J.A., Atallah, K., Wang, J.B. et al. (1 more author) (2002) Effect of optimal torque control on rotor loss of fault-tolerant permanent-magnet brushless machines. IEEE Transactions on Magnetics, 38 (5 (par). pp. 3291-3293. ISSN 0018-9464 https://doi.org/10.1109/TMAG.2002.802294eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. IEEE TRANSACTIONS ON MAGNETICS, VOL. 38, NO. 5, SEPTEMBER 2002 3291Effect of Optimal Torque Control on RotorLoss of Fault-Tolerant Permanent-MagnetBrushless MachinesJason D. Ede, Kais Atallah, Jiabin Wang, and David HoweAbstract—A faulted phase in fault-tolerant permanent-magnetbrushless machine can result in significant torque ripple. However,this can be minimized by using an appropriate optimal torquecontrol strategy. Inevitably, however, this results in significant timeharmonics in the phase current waveforms, which when combinedwith inherently large space harmonics, can result in a significanteddy-current loss in the permanent magnets on the rotor. Thispaper describes the optimal torque control strategy which hasbeen adopted, and discusses its effect on the eddy-current loss inthe permanent magnets of four-, five-, and six-phase fault-tolerantmachines.Index Terms—Brushless machines, eddy currents, losses.I. INTRODUCTIONFAULT-TOLERANT permanent-magnet brushless acmachine designs differ significantly from conventionalbrushless machines, in that their phase windings are essentiallyisolated magnetically, thermally and physically. Thus, theirfault-tolerance is significantly higher, a major consideration forsafety-critical aerospace applications, such as fuel pumps [1]and flight control surface actuators [2], as well as applicationsin other sectors. However, in such fault-tolerant machines,the stator magnetomotive force (MMF) has fewer poles thanthe rotor permanent magnets. Therefore, torque is producedby the interaction of the rotor permanent magnets with ahigher order stator MMF harmonic. The fundamental andlower order MMF harmonics can then give rise to significantrotor eddy currents, which can be minimized by employingmultiple magnet segments per pole [3]. Further, a faultedphase, open-circuit, or short-circuit can result in a large torqueripple, which can be minimized by adopting an appropriatetorque control strategy [4], [5]. However, this often results insignificant time harmonics in the phase current waveforms.When combined with the inherently large lower order statorMMF space harmonics, this can result in a significant increasein the rotor eddy-current loss.The paper will describe the optimal torque control strategy,which the authors have adopted for fault-tolerant brushlessmachines, and its effect on the eddy-current loss in sur-face-mounted rotor permanent magnets, of representative four-,five-, and six-phase machine designs (Fig. 1).Manuscript received February 14, 2002.The authors are with the Department of Electronic and Electrical Engi-neering, University of Sheffield, Sheffield S1 3JD, U.K. (e-mail: k.atallah@sheffield.ac.uk.Digital Object Identifier 10.1109/TMAG.2002.802294.(a) (b) (c)Fig. 1. Fault-tolerant permanent-magnet brushless machines. (a) Four-phase.(b) Five-phase. (c) Six-phase.II. OPTIMAL TORQUECONTROLA fault on one phase of a fault-tolerant brushless machinean result in a large torque ripple, which depends on the type offault,viz.open-circuit or short-circuit, and the output torque.Optimal torque control aims at achieving a ripple-free electro-magnetic torque under both healthy and faulted conditions withminimum stator copper loss. For a healthy-phase machineconstant. (1)For an -phase machine in which phaseis faultedconstant. (2)In both cases, the copper loss is required to be as low as pos-sible, i.e.,minimum (3)where is the phase winding resistance, and andare the instantaneous ratio of the phase electromotive force(EMF) to the rotor speed and the instantaneous phase current,r spectively. is the instantaneous torque developed bythe faulted phase. Thusfor an open-circuit faultfor a short-circuit fault(4)where is the short-circuit current in phase. Therequired current waveforms in the healthy phases are ob-tained by minimizing the augmented objective functionwith a Lagrange multiplier . Thus(5)0018-9464/02$17.00 © 2002 IEEE3292 IEEE TRANSACTIONS ON MAGNETICS, VOL. 38, NO. 5, SEPTEMBER 2002Fig. 2. Back-EMF waveforms.where, for an -phase machine with a faulted phase .The function must satisfyand (6)Again, for a machine with a faulted phase. Therefore,from (5) and (6), the instantaneous phase current waveforms inthe healthy phases are given by(7)where , for a machine with faulted phase. Further, inpractice the magnitude of the instantaneous phase current is usu-ally subject to a current limit . Depending on the demandedoutput electromagnetic torque and the fault condition, the in-stantaneous current demands ofphases could exceed the cur-rent limit. In this case, the process of determining the optimalinstantaneous currents may take several iterations. Therefore, ifthe instantaneous current demand of phaseexceeds the currentlimit, its current is clamped to(8)where “ ” applies if the current demand of phaseis positive,and “ ” applies if it is negative. The torque contribution fromthe phases is then given by(9)where “ ” applies if the current demand of phaseis posi-tive, and “ ” applies if it is negative. The remaining phases aretreated as a separate subset, and their current demands are deter-mined by the same optimization method so as to satisfy the newtorque demand . The new current demandsare then given by(10)Again, the new current demands are checked to ensurethat none exceeds the specified current limit. If, however, thecurrent demand of one or more phases from the new subset ex-ceeds the current limit, the process is repeated until all the cur-rent demands satisfy the current limit constraint.Fig. 2 shows the back-EMF waveforms of the four-, five-,and six-phase machines shown in Fig. 1, whilst Fig. 3 showsthe phase current waveforms, which are required to produceripple-free rated electromagnetic torque with minimum copperFig. 3. Phase current waveforms. (As a per unit of the peak short-circuitcurrent).Fig. 4. Optimal phase current waveforms of four-phase machine when phase4 is short-circuited. (As a per unit of the peak short-circuit current).Fig. 5. Optimal phase current waveforms of five-phase machine when phase5 is short-circuited. (As a per unit of the peak short-circuit current).loss, when the machines are healthy. The associated copperlosses are 0.96, 0.94, and 0.83 pu of the copper losses, whichwould result without optimal torque control (sinusoidal phasecurrent waveforms). Figs. 4–6 show the phase current wave-forms, which result in a ripple-free rated electromagnetic torquewith minimum copper loss when a phase is short-circuited, forthe four-, five-, and six-phase machines, respectively. It can beseen that for all machines the required peak phase current wouldexceed the peak short-circuit current, being1.5 times thepeak short-circuit current in the case of the four-phase machine.Further, Fig. 7 shows the variation of the copper loss with themean electromagnetic torque when a phase is short-circuited,EDE et al.: EFFECT OF OPTIMAL TORQUE CONTROL ON ROTOR LOSS 3293Fig. 6. Optimal phase current waveforms of six-phase machine when phase 6is short-circuited. (As a per unit of the peak short-circuit current).Fig. 7. Effect of optimal torque control on copper loss. (As a per unit of copperloss without optimal torque control).TABLE IEDDY-CURRENT LOSS INROTORPERMANENT MAGNETS OF THEFOUR-PHASEMACHINE. (RATED ELECTROMAGNETIC TORQUE)from which it can be seen that whilst the torque-ripple witha short-circuited phase winding can be eliminated by optimaltorque control, this can result in a significant increase in statorwinding copper loss. However, it should also be noted that theincrease in copper loss should not compromise the thermalrating of the machines, since it is only about 0.05 pu at the ratedelectromagnetic torque, for the four-phase machine, whichexhibits the highest increase in copper loss.III. EDDY-CURRENTLOSS INROTORPERMANENT MAGNETSAs will be evident, optimal torque control can result in rel-atively large time harmonics in the stator phase current wave-forms, which when combined with stator MMF space harmonicscould lead to a significant eddy-current loss in the rotor mountedpermanent magnets. The four-, five-, and six-phase machinesTABLE IIEDDY-CURRENT LOSS INROTOR PERMANENT MAGNETS OF THEFIVE-PHASEMACHINE. (RATED ELECTROMAGNETIC TORQUE).TABLE IIIEDDY-CURRENT LOSS INROTOR PERMANENT MAGNETS OF THESIX-PHASEMACHINE. (RATED ELECTROMAGNETIC TORQUE)are equipped with sintered SmCo permanent magnets, whichhave a relatively large electrical conductivity. The eddy-currentloss in the magnets has been deduced from a series of two–di-mensional (2-D) time-stepped, moving boundary, finite-elementanalyses, assuming the permanent magnets to be electricallyconducting but to have zero remanence. Thus, they do not ac-count for the eddy-current loss component, which would resultfrom the variation of the magnet working point, due to the ef-fect of stator slotting. Tables I-III show the effect of the typeof fault and the stator current waveform/control strategy on theeddy-current loss of the permanent magnets, for the four-, five-,and six-phase machines, respectively. It can be seen that theeddy-current loss in the permanent magnets is influenced signif-icantly by both the type of fault and the torque control strategy.IV. CONCLUSIONAn optimal torque control strategy for fault-tolerant perma-nent-magnet brushless machines has been presented. It has beenshown that the adoption of a torque control strategy to minimizetorque ripple under open-circuit and short-circuit fault condi-tions may lead to a significant increase in the eddy-current lossin the permanent magnets of such machines.REFERENCES[1] B. C. Mecrow, A. G. Jack, J. A. Haylock, and J. Coles, “Fault-tolerantpermanent magnet machine drives,” inIEE Proc. Elect. Power Applicat.,vol. 143, 1996, pp. 437–442.[2] K. Atallah and D. Howe, “Modular permanent magnet brushlessmachines for aerospace and automotive applications,” inProc. 20thInt. Workshop Rare-Earth Magnets and Their Applicat., Sendai, Japan,2000, pp. 1039–1048.[3] K. Atallah, D. Howe, P. H. Mellor, and D. A. Stone, “Rotor loss in per-manent magnet brushless ac machines,”IEEE Trans. Indust. Applicat.,vol. 36, pp. 1612–1617, Nov.-Dec. 2000.[4] T. Gobalarathnam, H. A. Toliyat, and J. C. Moreira, “Multi-phase fault-tolerant brushless DC motor drives,” inConf. Rec. IEEE Indust. Ap-plicat. Conf., 2000, pp. 1683–1688.[5] C. D. French, P. P. Acarnley, and A. G. Jack, “Optimal torque control ofpermanent magnet motors,” inProc. Int. Conf. Elect. Mach. ICEM’94,pp. 720–725.

Effect of optimal torque control on rotor loss of fault-tolerant permanent-magnet brushless machines

This is a repository copy of Effect of optimal torque control on rotor loss of fault-tolerant 
permanent-magnet brushless machines .
White Rose Research Online URL for this paper:
http://eprints.whiterose.ac.uk/831/
Article:
Ede, J.A., Atallah, K., Wang, J.B. et al. (1 more author) (2002) Effect of optimal torque 
control on rotor loss of fault-tolerant permanent-magnet brushless machines. IEEE 
Transactions on Magnetics, 38 (5 (par). pp. 3291-3293. ISSN 0018-9464 
https://doi.org/10.1109/TMAG.2002.802294
eprints@whiterose.ac.uk
https://eprints.whiterose.ac.uk/
Reuse 
Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright 
exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy 
solely for the purpose of non-commercial research or private study within the limits of fair dealing. The 
publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White 
Rose Research Online record for this item. Where records identify the publisher as the copyright holder, 
users can verify any specific terms of use on the publisher’s website. 
Takedown 
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emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. 
IEEE TRANSACTIONS ON MAGNETICS, VOL. 38, NO. 5, SEPTEMBER 2002 3291
Effect of Optimal Torque Control on Rotor
Loss of Fault-Tolerant Permanent-Magnet
Brushless Machines
Jason D. Ede, Kais Atallah, Jiabin Wang, and David Howe
Abstract—A faulted phase in fault-tolerant permanent-magnet
brushless machine can result in significant torque ripple. However,
this can be minimized by using an appropriate optimal torque
control strategy. Inevitably, however, this results in significant time
harmonics in the phase current waveforms, which when combined
with inherently large space harmonics, can result in a significant
eddy-current loss in the permanent magnets on the rotor. This
paper describes the optimal torque control strategy which has
been adopted, and discusses its effect on the eddy-current loss in
the permanent magnets of four-, five-, and six-phase fault-tolerant
machines.
Index Terms—Brushless machines, eddy currents, losses.
I. INTRODUCTION
FAULT-TOLERANT permanent-magnet brushless acmachine designs differ significantly from conventional
brushless machines, in that their phase windings are essentially
isolated magnetically, thermally and physically. Thus, their
fault-tolerance is significantly higher, a major consideration for
safety-critical aerospace applications, such as fuel pumps [1]
and flight control surface actuators [2], as well as applications
in other sectors. However, in such fault-tolerant machines,
the stator magnetomotive force (MMF) has fewer poles than
the rotor permanent magnets. Therefore, torque is produced
by the interaction of the rotor permanent magnets with a
higher order stator MMF harmonic. The fundamental and
lower order MMF harmonics can then give rise to significant
rotor eddy currents, which can be minimized by employing
multiple magnet segments per pole [3]. Further, a faulted
phase, open-circuit, or short-circuit can result in a large torque
ripple, which can be minimized by adopting an appropriate
torque control strategy [4], [5]. However, this often results in
significant time harmonics in the phase current waveforms.
When combined with the inherently large lower order stator
MMF space harmonics, this can result in a significant increase
in the rotor eddy-current loss.
The paper will describe the optimal torque control strategy,
which the authors have adopted for fault-tolerant brushless
machines, and its effect on the eddy-current loss in sur-
face-mounted rotor permanent magnets, of representative four-,
five-, and six-phase machine designs (Fig. 1).
Manuscript received February 14, 2002.
The authors are with the Department of Electronic and Electrical Engi-
neering, University of Sheffield, Sheffield S1 3JD, U.K. (e-mail: k.atallah@
sheffield.ac.uk.
Digital Object Identifier 10.1109/TMAG.2002.802294.
(a) (b) (c)
Fig. 1. Fault-tolerant permanent-magnet brushless machines. (a) Four-phase.
(b) Five-phase. (c) Six-phase.
II. OPTIMAL TORQUECONTROL
A fault on one phase of a fault-tolerant brushless machine
an result in a large torque ripple, which depends on the type of
fault,viz.open-circuit or short-circuit, and the output torque.
Optimal torque control aims at achieving a ripple-free electro-
magnetic torque under both healthy and faulted conditions with
minimum stator copper loss. For a healthy-phase machine
constant. (1)
For an -phase machine in which phaseis faulted
constant. (2)
In both cases, the copper loss is required to be as low as pos-
sible, i.e.,
minimum (3)
where is the phase winding resistance, and and
are the instantaneous ratio of the phase electromotive force
(EMF) to the rotor speed and the instantaneous phase current,
r spectively. is the instantaneous torque developed by
the faulted phase. Thus
for an open-circuit fault
for a short-circuit fault
(4)
where is the short-circuit current in phase. The
required current waveforms in the healthy phases are ob-
tained by minimizing the augmented objective function
with a Lagrange multiplier . Thus
(5)
0018-9464/02$17.00 © 2002 IEEE
3292 IEEE TRANSACTIONS ON MAGNETICS, VOL. 38, NO. 5, SEPTEMBER 2002
Fig. 2. Back-EMF waveforms.
where, for an -phase machine with a faulted phase .
The function must satisfy
and (6)
Again, for a machine with a faulted phase. Therefore,
from (5) and (6), the instantaneous phase current waveforms in
the healthy phases are given by
(7)
where , for a machine with faulted phase. Further, in
practice the magnitude of the instantaneous phase current is usu-
ally subject to a current limit . Depending on the demanded
output electromagnetic torque and the fault condition, the in-
stantaneous current demands ofphases could exceed the cur-
rent limit. In this case, the process of determining the optimal
instantaneous currents may take several iterations. Therefore, if
the instantaneous current demand of phaseexceeds the current
limit, its current is clamped to
(8)
where “ ” applies if the current demand of phaseis positive,
and “ ” applies if it is negative. The torque contribution from
the phases is then given by
(9)
where “ ” applies if the current demand of phaseis posi-
tive, and “ ” applies if it is negative. The remaining phases are
treated as a separate subset, and their current demands are deter-
mined by the same optimization method so as to satisfy the new
torque demand . The new current demands
are then given by
(10)
Again, the new current demands are checked to ensure
that none exceeds the specified current limit. If, however, the
current demand of one or more phases from the new subset ex-
ceeds the current limit, the process is repeated until all the cur-
rent demands satisfy the current limit constraint.
Fig. 2 shows the back-EMF waveforms of the four-, five-,
and six-phase machines shown in Fig. 1, whilst Fig. 3 shows
the phase current waveforms, which are required to produce
ripple-free rated electromagnetic torque with minimum copper
Fig. 3. Phase current waveforms. (As a per unit of the peak short-circuit
current).
Fig. 4. Optimal phase current waveforms of four-phase machine when phase
4 is short-circuited. (As a per unit of the peak short-circuit current).
Fig. 5. Optimal phase current waveforms of five-phase machine when phase
5 is short-circuited. (As a per unit of the peak short-circuit current).
loss, when the machines are healthy. The associated copper
losses are 0.96, 0.94, and 0.83 pu of the copper losses, which
would result without optimal torque control (sinusoidal phase
current waveforms). Figs. 4–6 show the phase current wave-
forms, which result in a ripple-free rated electromagnetic torque
with minimum copper loss when a phase is short-circuited, for
the four-, five-, and six-phase machines, respectively. It can be
seen that for all machines the required peak phase current would
exceed the peak short-circuit current, being1.5 times the
peak short-circuit current in the case of the four-phase machine.
Further, Fig. 7 shows the variation of the copper loss with the
mean electromagnetic torque when a phase is short-circuited,
EDE et al.: EFFECT OF OPTIMAL TORQUE CONTROL ON ROTOR LOSS 3293
Fig. 6. Optimal phase current waveforms of six-phase machine when phase 6
is short-circuited. (As a per unit of the peak short-circuit current).
Fig. 7. Effect of optimal torque control on copper loss. (As a per unit of copper
loss without optimal torque control).
TABLE I
EDDY-CURRENT LOSS INROTORPERMANENT MAGNETS OF THEFOUR-PHASE
MACHINE. (RATED ELECTROMAGNETIC TORQUE)
from which it can be seen that whilst the torque-ripple with
a short-circuited phase winding can be eliminated by optimal
torque control, this can result in a significant increase in stator
winding copper loss. However, it should also be noted that the
increase in copper loss should not compromise the thermal
rating of the machines, since it is only about 0.05 pu at the rated
electromagnetic torque, for the four-phase machine, which
exhibits the highest increase in copper loss.
III. EDDY-CURRENTLOSS INROTORPERMANENT MAGNETS
As will be evident, optimal torque control can result in rel-
atively large time harmonics in the stator phase current wave-
forms, which when combined with stator MMF space harmonics
could lead to a significant eddy-current loss in the rotor mounted
permanent magnets. The four-, five-, and six-phase machines
TABLE II
EDDY-CURRENT LOSS INROTOR PERMANENT MAGNETS OF THEFIVE-PHASE
MACHINE. (RATED ELECTROMAGNETIC TORQUE).
TABLE III
EDDY-CURRENT LOSS INROTOR PERMANENT MAGNETS OF THESIX-PHASE
MACHINE. (RATED ELECTROMAGNETIC TORQUE)
are equipped with sintered SmCo permanent magnets, which
have a relatively large electrical conductivity. The eddy-current
loss in the magnets has been deduced from a series of two–di-
mensional (2-D) time-stepped, moving boundary, finite-element
analyses, assuming the permanent magnets to be electrically
conducting but to have zero remanence. Thus, they do not ac-
count for the eddy-current loss component, which would result
from the variation of the magnet working point, due to the ef-
fect of stator slotting. Tables I-III show the effect of the type
of fault and the stator current waveform/control strategy on the
eddy-current loss of the permanent magnets, for the four-, five-,
and six-phase machines, respectively. It can be seen that the
eddy-current loss in the permanent magnets is influenced signif-
icantly by both the type of fault and the torque control strategy.
IV. CONCLUSION
An optimal torque control strategy for fault-tolerant perma-
nent-magnet brushless machines has been presented. It has been
shown that the adoption of a torque control strategy to minimize
torque ripple under open-circuit and short-circuit fault condi-
tions may lead to a significant increase in the eddy-current loss
in the permanent magnets of such machines.
REFERENCES
[1] B. C. Mecrow, A. G. Jack, J. A. Haylock, and J. Coles, “Fault-tolerant
permanent magnet machine drives,” inIEE Proc. Elect. Power Applicat.,
vol. 143, 1996, pp. 437–442.
[2] K. Atallah and D. Howe, “Modular permanent magnet brushless
machines for aerospace and automotive applications,” inProc. 20th
Int. Workshop Rare-Earth Magnets and Their Applicat., Sendai, Japan,
2000, pp. 1039–1048.
[3] K. Atallah, D. Howe, P. H. Mellor, and D. A. Stone, “Rotor loss in per-
manent magnet brushless ac machines,”IEEE Trans. Indust. Applicat.,
vol. 36, pp. 1612–1617, Nov.-Dec. 2000.
[4] T. Gobalarathnam, H. A. Toliyat, and J. C. Moreira, “Multi-phase fault-
tolerant brushless DC motor drives,” inConf. Rec. IEEE Indust. Ap-
plicat. Conf., 2000, pp. 1683–1688.
[5] C. D. French, P. P. Acarnley, and A. G. Jack, “Optimal torque control of
permanent magnet motors,” inProc. Int. Conf. Elect. Mach. ICEM’94,
pp. 720–725.


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Effect of optimal torque control on rotor loss of fault-tolerant permanent-magnet brushless machines

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