Brushless Permanent Magnet Motor Drives

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I umotor drivesThe brushless PM DC motor is extremely common in a widevariety of low-power applications such as computers andoffice machinery. As magnet properties improve and controlelectronics become more sophisticated the brushless PMmotor expands i ts application potential to higher power levelsby Tim MillerPermanent magnetsPermanent magnets provide a mo tor with life-long ex citation. The only cost is the initial cost,which is buried in the cost of the motor. Itranges from a few pence for small ferritemotors, to several pounds for rare-earthmoto rs. Broadly speaking, the primarydeterminants of magnet cost are the pow erdensity (o r torque per unit volume ) of themotor; the operating temperature range; andthe severity of the operational duty of themagnet.Power densityFor maximum po wer density the product ofsthe electric and mag netic loadings of themotor m ust be as high as possible. The electricloading is limited not only by thermal factors,but also by the demagnetising effect on themag net. A high electric loading necessitates along magnet leng th in the direction ofmagnetisation, to prevent demagnetisation. talso requires a high coercivity, and this maylead to the more expensive grades of material(such as 2 -17 cobalt-samarium, for example).The m agnetic loading, or air-gap flux, isdirectly proportional to the remanent fluxdensity of the magnet, and is nearlyproportional to i t s pole-face area. A highpow er density thus requires the largestpossible magne t volume (le ngth times polearea) to be fitted to the ro tor (see Fig. 1 . Withferrite magnets the limit on the magne tvolume is often the geometrical limit on thevolume of the rotor itself, and the highestpower densities cannot be o btained with thesemagnets. With rare-earth or other high-energymagnets, the cost of the magnet may be thelimiting factor.The air-gap flux density is limited bysatura tion of the stator teeth . Excessivesaturation absorbs too much ex citation MM F(requiringa dispro portion ate increase inmag net volume ); or causes excessive hea tingdue t o hysteresis and eddy curre nts. For thisreason there is an upper limit to the usableenergy of a permanent magnet. With astraight demagnetisation characteristicthroughout the second quadrant and a recoilPOWER ENGINEERING JOURNAL JANUARY 1988

permeability of unity (see Fig. 21, the maximumenergy prod uct BH),,, is given byIBH),,, = jouleim34PoAssuming that the stator teeth saturate a t1.8T and that the tooth width is half the toothpitch, the maximum air-gap flux density cannotbe much above 0.9T and is usually lower thanthis Therefore, there will be little to gain froma magnet with a remanent flux density aboveabout 1 or 1,2T, implying that the highestusable energy product is about 300kJ/m3(equivalent to 3 5-40 MGOe). At 1OO'C, suchcharacteristics are barely with in th e range ofthe best available neodymium-iron-boron orrare-earth magnets. According to thisargument, which has been made before inconnection with line-start motors,' it is just asimportant t o develop magne t materials with'moderate' properties and low cost as it is todevelop 'super m agnets' regardless of cost. Thelong awa ited m aterial with cobalt-samariumproperties a t ferrite prices is unfortunately st i l lawaited, although progress is being made withneodymium-iron-boron.Operating tempe rature rangeseveral comm on motor magnets at 25 and125C. Because of the deg radatio n in theremanent flux density and in the coerciveforce, the choice of material and the magnetvolume must often be determined withreference to the highest operatingtemp erature . Fortunately brushless mo torshave very low rotor losses. The stator is easilycooled because of the fine slot structure andthe p roximity of the outside air. Consequentlythe magne t can run fairly cool (often below1OOOC), and it is further protected by its ow nthermal mass and that of the rest of the motor,The sho rt-time therma l overload capability ofthe electronic co ntroller would normally be lessthan that of the m otor; providing a furthermargin of protection against magnet over-temperature.Severity of operationalduty

Fig. 2 shows the demagnetisation curves for

Magnets can be demagnetised by fault55


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1A Rotor of brushless PMmotor w i th bondedmagnet r ing for Hal l -effect commutationsensor [Courtesy: WalterJones Co. (Eng ineer s)Ltd.1B Selection of computer-peripheral brushless PMmotors w i th in terna lstators. The permanentmagnets are mounted onthe inside of the rotor huband rotate with i t . The

laser-scanner motor(bottom r ight) is integral lymounted on the dr ivercircuit card [Courtesy:Synektron Corporation,Portland, Oregon, USA1

currents such as short-circuit currentsproduced by inverter faults In brushless motorswith electronic control the problem is generallylimited by the protective measures taken in theinverter and the contro l (In Iine-s tart AC PMmotors the problems are more severe21 Withan over-runnin g load, or where tw o motors arecoupled to a single load, short-circuited turnsor windings can be troublesome because ofdrag torque and p otential overheating of thestator But, by the same token, the dynamicbraking is usually excellent with a short-circuitapplied to the m otor terminals As is often thecase, characteristics that are desirable for oneapplication are undesirable for another Thedesign must accommodate all the factors thatstress the magnet, not only electromagneticbut thermal and m echanical as wellWhy perrnanent-magnet m otors?Because of the natural laws ofelectromagnetic scaling there is an 'excitationpenalty' associated with small motors.6 As thegeometrical size is decreased, the cross-sectional area available for copper conductorsdecreases faster than the need for MMF. Theper-unit copper losses increase and theefficiency decreases. The loss-free excitat ionprovided by permanent magnets is therefore ofincreasing value as the m otor size is reduced.In larger mo tors m agnets can he lp achieve veryhigh efficiency. But in larger motors theexcitation penalty is small and the magnet costbecomes pro hibitive. It is therefore rare to findPM moto rs rated much larger than a fewkilowattsThere is no hard-and -fast power level belowwhich perma nent-ma gnet excitation becomesadvantageous, but it is possible to examine theexcitation penalty in ways which indicateroughly where the breakpoint lies, and why. Fora given level of excitation the choice can bemade betwee n magnets or copper windingsoperating at a current density I (in the copper).

It can be shown that the ratio of magnetvolume V , o the volume V, of copper requiredto produce the same fundamen tal air-gap fluxdensity 6 isV, = /IopreiJB.DV, 8k,6:p2y l ~ y )

where D is the stator diameter; B, is the

remanent flux density of the magnet; p is thenumber of pole pairs; and k is the ratio of 6 tothe m aximum air-gap flux density producedover the pole arc by the magnet when themotor is on no load.precs the relative recoilpermeability of the magnet The parameter y isthe ratio of the actual flux density in themagnet at no load to the remanent fluxdensity, and a value of 0.8 is chosen fori IIust ra on.Consider tw o four-pole m otors with 6,0.7T and k =1.1. The PM mo tor has rare-earthmagnets wit h B, = 03T and pie< 1.05. Theelectrically excited motor has 1= 4A/mm2,givingvm Dv, 1000where D is measured in m illimetres. This meansthat, for m otors le55 than 1 000 mm indiameter, the magn et volume is le55 than thevolume of copper needed for excitation in aseparate field wind ing. Unfortu nately the costper unit volume of high-energy magnets at thislevel is of the order of 25 times that of copper.For the m agnet cost to be less than the cost ofthe copper in a separate field winding, themo tor diameter m ust therefore be le55 than1000125, i e. only 40mm. This result suggeststhat the technical potential of high-energymagnets is offset by their very high cost in allbut the smallest motors. In very small motors asmaller value should be used for the c urrentdensity I with 1= 2.5A/m m2 the diameter forequal cost would be increased from 40mm to64mm (2.5 in). n general, high-ene rgy magnetscan only be justified where there is a specialpremium on efficiency or compactness. Ofcourse, this argume nt is simplistic, and ignoresfactors such as process and m anufacturin gcosts and many others; but it provides a basicphysical understanding of the ap plicationpotential of magnets, and the effects of scale.Motors magnetised with ceramic magnetsmust settle for a lower air-gap flux density.Using values o f J = 4A/mm2; 6, = 0.3T; prec 1;6 = 0.35T, the result isV, 460

For motors of less than 46 0m m statordiameter the m agnet volume indicated is le55than the volume of copper in a separate field

v,=

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windin g Ceramic m agnets are m uch lessexpensive than high-energy magnets, the costper unit volume being of the order of 0.6 timesthat of copper, so that the magne t cost will beless than the cost of field co pper in m otors ofdiameter less than 460/0.6, I e 767mm Inpractice, PM motors as large as this arerelatively uncommon With ferrite magnets theflux density is too low and with rare-earthmagnets the cost is too highIf running costs are taken into account, thecomparison between PM and electricallyexcited motors changes significantly With thepresent cost of raw materials and the presentkWh tariff, the kWh cost of electrical excitationwould outstrip the raw -material cost of thecopper in just a few months, assuming themotor runs a t full excitation 2 4 h per day Evenwhen all the manufacturing costs are addedup, the PM m oto r will eventually pay for itselfin this way How long it takes is a complicatedcalculation beyon d the scope of this articleTorque and speed controlFig. 3 summarises the operation of themo tor. Fig. 3a depicts a three-phase motorwith 12 slots (i.e tw o slots per pole per phase).Fig b shows the current flowing throughphases a and b of the motor, supplied byswitches 1 and 6 in the controller. Fig 3cshows the spatial distribution of air-gap flux atthe instant when the north-pole axis of therotor is 90 ut of alignment with phase a. Theflux linkage of phase a is therefore zero, butthe induced EMF is a maximum This instant isindicated by a vertical line on Fig. 3d, whic h isthe time diagram of the induced voltage andthe corresponding phase current. Although Fig.3 shows a two-pole motor, the relationshipsare identical in motors of any pole number ifthe angles are expressed in electrical degrees.The motor shown in Fig. 3 is an inverted DCmotor w ith the mechanical comm utatorreplaced by the electronic controller. Using the'BLv' and BL? formulas for EMF and force, theinduced voltage E and the torque T can bederived:E = 2NBLrw voltsiphaseand T = 4NBLrlwhere N is the number of turns in series perphase; 6 is the air-gap flux density produced bythe magnet; s the active length; r is the rotorradius; I is the phase current; and w is theangular velocity. In Fig. 3 tw o phases areconducting a t any time, the conduction anglebeing 120 electrical. The cu rrent wav eformcan be mainta ined approximately rectangularby voltage PWM, and there are severalcomme rcially available integrated circuits tha tperform both the commutation and thevoltage PW M; some of these even providefacilities for speed feedback.6The torque and EMF equations are identicalin form to those of the PM commutator motor.Torque is proportional to the product of fluxand current, while EMF is proportional to theproduct of flux and speed. If the phaseresistance and leakage ind uctan ce aresufficiently small, and if other losses are

newton m etres

negligible, the EMF E is equal to the per-phaseterminal voltage Vi2 This results in aspeeditorque Characteristic of the form ofFig 4 Control is effected through pulsewidthmodulation of the voltage, and if a closelyregulated con stant speed is required it maywell be necessary to add a tachogenerator anda speed feedback loop in addition to thepos ition sensor used for com mu tation Fulltorque can be maintained over a wide ranae of 2 Second-quadrantspeed, and the maximum speed is deterrnhedby the driving voltage Vavailable from thecontroller. Since the motor EMF is proportionaldemagnetiSat ion curves~ ~ ~ ~ ~maonet materials:(a) 55C; b )125Co speed, this limit tends to be a sharp one,

1 2

1 0

0 8m

0Alnico 5-7Aln i co 9

/O 4

- 0 2

0

--__I_1.0

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0

5 1 1 3 3 5 5 1 1 3 3 5 56 6 4 4 6 6 4 4 6

b

dsspace diagram

E

C

+a b + C + a b-b C -a -b C -a

switchesconductina

d t ime diagram

Principle of operationof idealised brushless PM and occurs as soon as the PWM duty cyclereaches 1OOO/o,motor: (a) wo-polemoto r schematic;b )electronic controller(freewheel diodesomitted); (c) air-gap fluxdistr ibution at the instantshown in (a); dEMF andideal phase-currentwaveforms

Further increases of speed can then beobtained by advancing the c onduction angle,or by a combination of both these techniques.3Although the motor speed may be increased, itis difficult t o maintain constant power: thetorque tends to fall away rather rapidly.Sinewave-fed motorsanalytical expression describing the increase o fspeed above 'base' speed, the highest speed atwhich maximu m torque can be o btained. Sucha result is more easily obtain ed by simulationor exp eriment. Howevel; such an expressioncan be derived for the synchronous form ofPM mo tor from an analysis of its circlediagra m. The brushless DC motor wi thmagnets mounted on the rotor surface issimilar to a synchronous AC mo tor with no'saliency'. If the stator win ding is distributedand sh ort-pitche d, and if the phase currentsare sinusoidal, then th e m oto r can be analysedusing d,q-axis theory.The limiting torque/speed characteristic ofthe sinewave-fed synchronous moto r is shownin Fig. 5. At speeds below 'base' speed the

It is not possible to formulate a simple

voltage Vcan be increased in proportion to thefrequency, so that maximum current andmaximum torque can always be obtained, eventhou gh the m otor EMF E is increasing At thebase speed the contro ller voltage reaches itsmaximum Now as the supply frequencyincreases the torque decreases until it reacheszero at some frequency k times the frequencya t base speed At this po int it is still possible toget rated current into the motor, but if lossesare neglected it IS entirely in the direct axis andno torque is produced The followingexpression for k illustrates the factors thatcontrol the high-speed operation

e ~ J I e')where e is the per-unit EMF of the motor atbase speed, i.e EIV Neglecting all losses, it canbe shown that e = cos @, the p ower factor atbase speed, and that sin @ = x the per -unitsynchronous reactance. It is characteristic o fthis type of m otor that x, is quite small, givinga high powe r factor a t base speed. In moto rswith ceramic magnets this results from theneed for a long ma gnet length in the directionof magn etisation (to prevent demagnetisation).In motors wit h high-energy magnets x, is smallfor a different reason: it is proportional to theratio of electric loading to magnetic loading,Jand this ratio tends to be qu ite low in suchmotors (correspondingly, he short-circuitcurrent is high ). f the per-unit synchronousreactance (wh ich includes stator leakage) s, forinstance, x, = 0.15, the base-speed powerfactor is 0.99, e = 0.99 per unit and k = 1 I 9,indicating a very lim ited capability to operateabove base speed. In the case of thesynchronous motor, this is the best that can bedone; there is nothing to be gained fromadvancing the phase or duration of the current'pulses', since these a re sinewaves whose phaseis already as far advanced as is possible wit hthe available driving voltage.Other forms of pe rmanent-ma gnet AC andbrushless motors are possible besides thesurface-magnet motor, and some o f these havemagnetic saliency with a significant differencebetween the d- and q-axis reactances. In thesemotors there is an appreciable reluctancetorque; and correspondingly the air-gap flux isnot fixed solely by the magnet, but can becontrolled to some extent by the m agnitude ofthe stator current and i t s phase relative to theroto r pos ition.'O The speed range above basespeed is then wider. A different type of motorwith similar properties is shown in Fig. 6.Thismotor, which is similar to an inductor-typemachine, has permanent magnets a t each endof the rotor, but there is a significantcomponent of reluctance torque, which helpsto provide a wider range at constant powerabove base speed. The perm ane nt magnets inthis m achine can be replaced by a simple fieldcoil, which permits full control of the air-gapflux. The price paid for these operationaladvantages is a longer rotor, but in manyapplications this may be acceptable.In these hy brid motors the reluctance andPM torque s can only be satisfactorily combined

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if the supply is sinusoidal and the windingsmore or less sinusoidally distributed. If themagnets are completely removed ordemagnetised the resulting motor is a cagelesssynchronous reluctance motor?OSlotless motorsA pure synchronous machine produces notorque ripple, and the same is true of the idealbrushless DC mo tor w ith perfectlyconcen trated windings, rectangular air-gap fluxdistribution, and rectangular currentwaveforms. But neither of these machines canbe realised perfectly in practice, and there isalways a certain amount of torque ripple.Torque ripple in PM motors is a parasitic effectassociated with departures from the idealstructure and the ideal control Thesedepartures are inevitable in any practical motor.In the last three or four years the availabilityof extremely high-energy neodymium-iron-boron magnets has re-awakened interest in theslotless motor, in which the stator teeth arecompletely removed and the resulting space ispartially filled with additional copper. At leastone such motor is manu factured commercially.The slotless construction permits an increase inrotor diameter with in the same frame size, oralternatively an increase in electric loadingwithout a corresponding increase in currentdensity. The magnetic flux density at the statorwinding is inevitably lessened, but the effect isnot so drastic as might be expected. For amotor w ith an iron stator yoke and an ironrotor body the m agnetic field and its harmoniccomp onents can be calculated by the methodsof Reference 5. Considering the fundamentalradial compone nt of 5 the value is greatest atthe rotor surface (radius r ) and falls off w ithincreasing radius to its smallest value just insidethe stator yoke (radius R) . The ratio betweenthe values of th e fundam ental radialcomponent at these two radii is given by

2 r i R ) p[ I + (r/Rj2p1

b = - ~ ~~Consider a rotor of 40mm diameter with ahigh-energy magnet of remanent flux density1.2T and thickness 5 mm (Fig 7 ). f the radialthickness of the stator wind ing is 5mm(including the air gap), then, for a four-polemagnet, b = 0.78. The magn et flux density willbe about half the remanent flux density withthese proportions, so that the radial fluxdensity in the stator w inding varies from about0.6T near the bore to 0.47T just inside thestator yoke, giving a mean value of about0.53 T (fundamental).Given that the electricloading may be increased relative to that of aslotted stator, the power density should beroughly the same and possibly a little higher,since the stator-tooth iron losses areelim inate d. This machine may we ll accep t lessexpensive grades of lamination steel becauseof the absence of slotting and the relativelylow flux density in the stato r yoke Thereactance is also lessened by the elimination ofslot-leakage effects, and the risk ofdemagnetisation is decreased.In this type of motor the maximum usable

I tincreasing

torqueO

magnet energy is obviously higher than in aconventional slotted motor; indeed theconcep t would not be viable a t all withoutmagnets of high remanence and coercivity.Once the s tator teeth are removed, theconduc tors are n o longer constrained to lieparallel to the axis. They may be skewed by asmall amount to reduce torque ripple (which salready reduced by the elimination of co ggingeffects against the stator teet h). A furtherpossibility is a completely helical winding suchas that proposed for superconducting ACgenerators, or as used in very small PMcomm utator motors. Because the helicalwinding has no end turns, its utilisation ofcopper is higher than the severe skew mig htsuggest, and it should permit the design of avery compact motor.

4 Speedltorquecharacteristic of id ealbrushless m otor. If~ ~ ~ ~ ~ ~ ~ ~ e ~ , ~renegligib le, the cu rve isstra ight

Conclusionof exciting small motors W ithout them thebrushless DC motor would have to rely on awound rotor, or purely on reluctance torque Inboth cases, the perfo rmance would suffer andthe control would tend to become morecomplex for the same operational flexibilityEase of speed control, bidirectional operation,good dynam ic braking and a simplecommutation strateqy are amonq the

Permanent magnets are the natural means

5 ldeal ised speed/torquecurve of synchronous PMmotorattractive features of these drive; As thecontroller costs become relatively less, and asapplication requirements for controllability and

speed , per unit

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Brushless variable-reluctance motor (V RM)with permanent-magnetexci tation: a) otor;(b) complete motor[Courtesy: MagneticsResearch Int ernational,Fairfield, Iow a, USA]

low maintenance increase, the brushless PMmotor is certain to expand its applications overa wide range of industrial, aerospace andcommercial areasAcknowledgmentsThe author gratefully acknowledges manyinformative discussions with former colleaguesat GE (USA)and. more recentlv. with several UKassociates of the Glasgow Unbersity SPEEDprogramm e Thanks are due also to M r TNicol, Technical Director of Walter Jones & Co(Engineers) Ltd, to M r Fred Reiter, Chie fDesigner a t Magnetics Research Internationalof Fairfield, Iowa, USA, and t o Dr Robert LI ofSynektron Corporation, Portland, Oregon, USA7 Slotless-stator brushlessPM motor

u agnetic steel (stator laminated)stator windin g

magnet

The views expressed in this article are those ofthe author and not of any commercialcompanyReferences1 RICHTER, E , MILLER, T J E , NEUMANN, T Wand HUDSON, T L 'The ferrite permanentmagnet AC motor a technical and economicassessment: IEEE Trans, 1985, IA-21,pp 644 6502 MILLER, T J E 'Synchronization of line startpermanent-magnet AC motors', ibid, 1984,PAS-I 03 pp 1822 18283 JAHNS, T M 'Torque production in PMsynchronous motor drives with rectangularcurrent excitation', ibid, 1984, IA-20,pp 803 8134 MILLER, T J E , and HUGHES, A 'Compa rativedesign and performance analysis of air-coredand iron cored synchronous machines: Proc

IEE, 1977,124, pp 127 1325 HUGHES, A , and MILLER, T J E Analysis offields and inductances in air cored and ironcored synchronous machines: ibid, 1977, 124,

6 MILLER, T J E 'Small mo tor drives expand theirtechnology horizons: Power Engng J , 1987, 1,pp 283 2897 MILLER, T J E 'Brushless reluctance motordrives: ibid, 1987, 1, pp 325 3318 CHIRA, A , and FUKAO, T A close d loop controlof super-high speed reluctance motor for quicktorque response' IEEE Industry A pplicationsSociety Annual Meeting, Atlanta, USA, Oct1987impleme ntation of hysteresis-controlled inverteron a PM synchronous machine: IEEE Trans,

10 JAHNS, T M I KLIMAN, G B , and NEUMANN,T W 'Interior permanent magnet synchronousmotors for adjustable-speed drives: ibid, 1986,

1 1 ROSS, J H UK Patent 1 395 152, 1971

pp 121-126

9 LAJOIE-MAZENC, M I et a/ 'Study and

1985, IA-21, pp 408-41 3

IA-22, pp 738 747

EE 1988Tim Miller is Titular Professor in Po wer Electronics,The University, Glasgo w G I 2 8QQ, UK He is an IEEMember

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Brushless Permanent Magnet Motor Drives