application characteristics of permanent magnet synchronous and brushless dc motors for servo drives

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986 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 2 1 , NO. 5, EPTEMBERIOCTOBER 1991

Application Characteristics of PermanentM agnet Synchronous and Brushlessdc M otors for Servo DrivesPragasen Pillay, Member, IEEE, and Ramu Krishnan, Member, IEEE

Abstract-The permanent magnet synchronous motorPMSM) and the brushless dc motor BDCM) have many simi-larities; they both have permanent magnet s on the rotor andrequire alternating stator currents to produce constant torque.The difference in these two machines is that the PMSM and theBDCM has sinusoidal and trapezoidal back emfs, respectively.This means these two machines have different operating charac-teristics and control requirements. For application considera-tions, these two motor drives have to be differentiated on thebasis of kn own engineering criteria. Some of the criteria used toassess these two machines include power de nsity, torque per unitcurrent, speed range, feedback devices, inverter rating, coggingtorque, ripple torque, and parameter sensitivity. Guidelines forthe appropriate machine to be used fo r a given ap plication aregiven based on the results of the criteria listed above.

NOMENCLATURE

v d * qV

' r' e

a, b , and c phase back emfs, Vpeak value of back emf, Va, b , and c phase currents, Ad and q axis stator currents, Apeak value of current, Avector sum of d and q axis currents, Astator d , q inductances, Hderivative operatornumber of pole pairsstator resistance, aelectric torque, N-mload torque, N-mtotal motor torque, N-md and q axis stator voltagesdc bus voltage, Vstator d, q reactances,angle between magnet flux and is radrotor speed, rad/ssynchronous speed, rad/smutual flux linkage between rotor and stator dueto magnet, Wb-turn

Paper IPCSD 91-24, approved by the Industrial Drives Committee of theIEEE Industry Applications Society for presentation at the 1987 IndustryApplications Society Annual Meeting, Atlanta, GA, October 18-23.Manuscript released for publication February 26, 1991,P. Pillay is with the Department of Electrical Engineering, University ofNew Orleans, Lakefront, LA 70148.R. Krishnan is with the Electrical Engineering Department, VirginiaPolytechnic Institute and State University, Blacksburg, VA 24061.IEEE Log Number 9100932.

h d , hqhnle r

stator d and q axis flux linkage, Wb-turnair gap flux linkage, Wb-turnangle between stator phase A and the rotor, radsuperscript indicating reference valueI, INTRODUCTION

HE PERMANENT magnet synchronous motor (PMSM)T nd the brushless dc motor (BDCM) have many similari-ties [l] , [2]; they both have a permanent magnet (PM) on therotor and require alternating stator currents to produce con-stant torque. The difference in these two machines is thatthe PMSM and the BDCM have sinusoidal and trapezoidalback emfs, respectively. This means these two machineshave different operating characteristics and requirements.Although some of the fundamental differences [11- 5] be-tween these two machines are known, no guidelines exist tohelp the application engineer to compare and contrast thesetwo servo drives for a given application. The aim of thispaper is to compare and present the application characteris-tics of these two motor drives. Selection criteria for compar-ing and contrasting different motor drives have already beenpresented [l]. This paper uses these criteria to compare andassess the characteristics of the PMSM and BDCM drives forservo applications. Some of the criteria used include powerdensity, torque per current rating, speed range, feedbackdevices, inverter rating, cogging and ripple torques, andparameter sensitivity. Guidelines are developed to select theappropriate machine to be used for a given application basedon the results of the comparison criteria listed above. Anattempt is made to present the results on a normalized basisas far as possible so that the applicability of the results areessentially independent of the particular motor rating.There are a variety of ac servo drives on the market[1]-[5] competing with both the dc brush machine and otherac servo drives. The selection process of a servo drive for aparticular application in the fractional to 30-hp range canbe represented by Fig. 1. From Fig. 1, it is clear that thefirst decision to be made is whether to use a dc brush or abrushless servo.The reasons for choosing brushless servo motor drivesover the brush type dc motor drives are well known andinclude robustness, higher torque and speed bandwidths, andlower maintenance. The mechanical commutator and brushesof the dc motor also enforce severe limitations on its maxi-mum speed and overcurrent capabilities. Assuming that it hasbeen decided to use a brushless servo motor drive. the next

0093-9994/91/0900-0986$01.00 991 IEEE

QXA IEEE TRANSACTIONS ON INDUSTRY APPL ICATIONS, VOL. 2 1 , N O . 5,SEPTEMBERIOCTOBER 1991



PILLAY AND KRISHNAN: APPLICATION CHARACTERISTICS OF dc MOTORS FOR SERVO DRIVES 987

APPLICATION

DC BRUSH BRUSHLESS

AC MOTORS SWITCHED RELUCTANCE

i 7PERMANENT MAGNET INDUCTIONf-11PMSM BDCM

Fig. 1 Motor selection procedure.

decision to make is whether to use an ac or a switchedreluctance motor. The switched reluctance motor is inher-ently a pulsating torque machine, although some work hasbeen done in an attempt to reduce the torque ripple. Hence, ifa reasonably smooth output torque is required, an inductionor permanent magnet machine is to be preferred over theswitched reluctance motor. The next decision to be made,then, is whether to use an induction or a PM motor.The permanent magnet motor drives have the followingadvantages over the induction motor (IM) drive [1]-[lo]:

The rare earth and neodymium boron PM machine hasa lower inertia when compared with an IM because ofthe absence of a rotor cage; this makes for a fasterresponse for a given electric torque. In other words,the torque to inertia ratio of these PM machines ishigher.The PM machine has a higher efficiency than aninduction machine. This is primarily because there arenegligible rotor losses in permanent magnet machines;the rotor losses in the IM, however, can be consider-able, depending on the operating slip. This discussionis applicable to constant flux operation.The IM requires a source of magnetizing current forexcitation. The PM machine already has the excitationin the form of the rotor magnet.The need for magnetizing current and the fact that theIM has a lower efficiency necessitates a larger ratedrectifier and inverter for the IM than for a PM ma-chine of the same output capacity.The PM machine is smaller in size than an inductionmotor of the same capacity. Hence, it is advantageousto use PM machines, especially where space is aserious limitation. In addition, the permanent magnetmachine weight less. In other words, the power den-sity of permanent magnet machines is higher.The rotor losses in a PM machine are negligiblecompared with those in the induction motor. A prob-lem that has been encountered in the machine toolsindustry is the transferal of these rotor losses in theform of heat to the machine tools and work pieces,thus affecting the machining operation. This problemis avoided in permanent magnet machines.

The induction motor drive has the following advantagesover permanent magnet motor drives [2]:Larger field weakening range and ease of control inthat regionlower cogging torquesless expensive feedback transducers such as an incre-mental rotor position encoder for the IM instead of anabsolute position encoder that is required by the per-manent magnet motor driveslower costmuch higher rotor operating temperatures that areallowed in induction motors than in PM motors.

Depending on the application, a choice is made between anIM or ac PM motor drive if the dc brush and switchedreluctance servos are excluded. If the choice is narrowed toan ac permanent magnet motor drive, then there are hardlyany guidelines to differentiate he available permanent magnetmotor drives, namely, the PMSM drive and the BDCMdrive. This paper concerns itself mainly with this aspect ofthe problem.The paper is organized as follows: The similarities anddifferences between the PMSM and BDCM and the drivestrategy are discussed in Section 11. Power density, torque toinertia ratio, speed range, torque per unit current, braking,parameter sensitivity, and other criteria are used to compareand contrast the PM motor drives in Section 111. Conclusionsare given in Section IV.

11. DESCRIPTIONF THE PMSM AND BDCMSimilarities Between the PMSM and BDCM

The PMSM owes its origin to the replacement of theexciter of the wound rotor synchronous machine, whichincluded a field coil, brushes, and slip rings with a permanentmagnet. A distinguishing feature of the PMSM is that itgenerates a sinusoidal back emf just like an induction motoror wound rotor synchronous motor; in fact, the stator of thePMSM is quite similar to that of the induction machine.The BDCM owes its origin to an attempt to invert thebrush dc machine to remove the need for the commutator andbrush gear. The commutator in the brush dc machine con-verts the input dc current into approximately rectangularshaped currents of variable frequency. By applying this rect-angular-shaped current directly to the stator of the BDCMand transferring the field excitation to the rotor in the form ofa permanent magnet, an inversion of the brush dc machinehas taken place with the advantage that the new invertedmachine does not have a mechanical commutator and brushgear, hen& the name brushless dc machine.The magnets in the PMSM or the BDCM can be eitherburied or surface mounted. In the surface-mounted machine,two variations can exist. The magnets can be inset into therotor or project from the surface of the rotor. These ma-chines will be referred to as buried, inset, and projecting PMmachines, respectively.Buried PM machines are more difficult to construct thaneither the inset or projecting surface-mounted machines. In



~

988 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS VOL. 2 1 , NO. 5 , SEPTEMBERIOCTOBER 1991

addition, an epoxy glue is used to fix the magnets to the rotorsurface in the inset and projecting surface-mountedmachines.This implies that the mechanical strength of the surfacemounted machines is only as good as that of the epoxy glue,assuming no retaining sleeve is used; hence, buried PMmachines are more robust and tend to be used for high-speedapplications. In addition, the direct and quadrature axis in-ductances of the projecting surface-mounted PM machinesare approximately equal. This is because the length of theairgap is equal to that of the magnet, which has a permeabil-ity approximately that of air. This results in the direct andquadrature axis reluctances and, hence, inductances beingapproximately equal. The opposite is true, however, in theburied PM machine. Here, the quadrature axis inductancecan be much larger than that of the direct axis since, althoughthe length of the airgap is the same, the space occupied bythe magnet in the direct axis is occupied by iron (and not air)in the quadrature axis. The difference between the quadratureand direct axis inductances in inset PM machines lies be-tween that of the buried and projecting surface-mountedmachines. This means that in addition to the electric torque, areluctance torque exists in buried and inset PM machines.This torque can be used to increase the torque/current ratingas discussed later.Although most machines on the market are of the radialfield design, recent research [2] indicates that the axial fieldhas some advantages over the conventional radial field de-signs, especially in terms of power density and torque-to-in-ertia ratio.Differences Between the PMSM and BDCM

The PMSM has a sinusoidal back emf, whereas the BDCMhas a trapezoidal back emf [ 5 ] . Both have a permanentmagnet rotor, but the difference is in the winding arrange-ment of the stator and shaping of the magnets. Sinusoidalstator currents are needed to produce a steady torque in thePMSM, whereas rectangular-shaped currents are needed toproduce a steady torque in the BDCM, as is shown in Fig. 2.It is this difference that has numerous ramifications both inthe behavior of the motor drive and in the structure of thecontrol algorithms and circuitry.Permanent magnet motor drive scheme: There are anumber of similarities in the overall drive scheme of thePMSM and the BDCM. Fig. 3shows a schematic that isessentially applicable to either drive system. A speed servo isshown. The error between the reference and actual speeds isused to obtain the torque reference, which in turn is used toobtain the stator current reference. Rotor position feedback isneeded in both drives to convert the stator current referenceinto phase current references. The position informationneeded for each drive is somewhat different, and this concept

will be elaborated on in the next section. Hysteresis or rampcomparison [ l l ] current controllers can then be used tomaintain the actual currents flowing into the machine as closeas possible to the references during constant torque opera-tion. Current feedback is used in order to achieve this. Theactual logic of the current controllers have been presented[16]. The configuration of the entire power electronic stage

ack e mf o f t h e b r u s h l e s s D m o t o r

I C d r r e T c waveform r e q u i r e d f o r c o n s t a n t t o r q u eFig. 2. Block emf and current waveform of the brushless dc motor.

including the current controllers and base drive amplifiers areessentially the same for both machines. Significant differ-ences are in the position feedback device and the manner inwhich this is used to obtain the phase currents from the statorcurrent vector.

111. APPLICATIONHARACTERISTICSF TH E PMSMAND BDCMThe characteristics of these two machines are comparedand determined with the aid of well-known selection criteriadeveloped in [l]. The criteria include the following:

costpower densitytorque to inertia ratiospeed rangetorque per unit currentbrakingcogging and ripple torqueschoice of feedback devicesparameter sensitivityrectifier/inverter ratinglosses and thermal capability.

Ultimately, it is the cost that plays a crucial role indeciding on a particular drive. However, the cost is only afair comparison if the engineering performance of the drivesunder consideration are comparable. Some of the engineeringcharacteristics that should be considered are examined in thefollowing sections.Power Density

In certain high-performance applications like robotics andaerospace actuators, it is preferable to have as low a weightas possible for a given output power. The power density islimited by the heat dissipation capability of the machine,which in turn is determined by the stator surface area. In PMmachines, most of the losses are developed in the stator interms of copper, eddy currents, and hysteresis losses. Rotorlosses are assumed negligible. Hence, for a given frame size,the motor that develops lower losses will be capable of ahigher power density. Assume in the first case that the eddycurrents and hysteresis losses of the PMSM and the BDCM




-

TI TZ T3 T4 TS ThFig. 3 . PMSM or BDCM drive system.

are equal. Then, the relative power densities would be deter-mined by the copper losses. The power output of these twomachines is compared based on the equality of copper losses.In the PMSM, sinusoidal currents of low harmonic contentare obtainable from hysteresis or PWM current controllerssuch that the copper losses are essentially determined by thefundamental component of current. If the peak current is I,,then the RMS current is Zpl/d2, and the machine copperlosses are given by 3 Z p l /J2)2R,, where R , is the phase-Aresistance.In the case of the BDCM that requires trapezoidal cur-rents for constant torque, the losses are given by 3 J21p2J3)2R,, where Zp 2 is the peak of the trapezoidal current.Hence, assuming that the core losses of the two machines areequal and the power density is determined by the copperlosses

3(zpl t '2)2R, = 3(J21p2J 3 ) 2 R , 1 )( 2 )( 3 )

Zpl J2 = J2Zp2 / J3I,, = 2 Z p 2 J 3 = 1 . 1 5 Z p 2 .

Now the ratio of the BDCM output power to the PMSMoutput power is given by2EpZp2 (3EpZPl J2 J2 = 4EpJ3Zpl 6EpZpl= 1.15 ( 4 )that is, the BDCM is capable of supplying 15%more powerthan the PMSM from the same frame size, that is, the powerdensity can be 15 larger, provided the core losses areequal.Torque to Inertia Ratio

Since it is possible to get 15 more power out of theBDCM, it is also possible to obtain 15%more electric torque

if they have the same rated speeds. If their rotor inertias areequal, then the torque-to-inertia ratio of the BDCM can be asmuch as 15%higher than the PMSM. It should be noted thatthe PMSM and BDCM have a higher torque-to-inertia ratiothan the induction motor [2].Speed Range

Servo drives operate in the constant torque mode of opera-tion from zero to rated speed and in the constant power modeof operation from rated to maximum speed. In the constanttorque region, the air gap flux is held constant, whereas inthe constant power region, the air gap flux is weakened byapplying a stator flux in opposition to the rotor magnet flux.This is also known as armature reaction and is illustrated inFig. 4.During constant flux operation, is is maintained at 90 tothe rotor flux as shown in Fig. 4. In the flux-weakeningmode, is is maintained at an angle greater than 90 from therotor flux. This allows a component of stator current id tocreate a stator flux that opposes the rotor flux, and hence,air-gap flux weakening is obtained.The magnitude of is ,which is the vector sum of the directand quadrature axis stator currents, has a fixed continuousrating during steady-state operation. This can be exceeded forshort periods of time during transients. If a higher speedrange is required, a larger negative i d is needed in order toreduce the air-gap flux and i should be lowered in order toensure that the continuous rating of is is not exceeded. Thespeed capability of a permanent magnet motor drive whenthis method of flux weakening is used can be determinedfrom the two axis equations as follows [14]:

(0.636V/X,)2 = i i ( X d ( i d W ~ A , ~ / X , ) / X , ) ~5 )



990 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 21, NO. 5 SEPTEMBERIOCTOBER 1991

b)flux-weakening operation.Fig. 4. Vector diagram of the PMSM during a) constant flux and b )

O0 270 540'a)

where V is the dc bus voltage, X ,, X , are the stator d, qaxis reactances, i d , i, are the stator d, q axis currents, w e isthe inverter frequency, and Xu, is the mutual flux linkagebetween the rotor and stator due to the magnet. By settingi, = 0 and i d equal to the continuous current rating of themachine, the inverter frequency and, hence, motor speed canthen be determined. Since the motor is locked in at thesynchronous speed, the actual maximum motor speed is givenby w e / P ,where is the number of pole pairs. For typicalPM motor parameters, it has been found that [15] around 1.5times rated speed can be attained. In practice, it would bedifficult to force i s to operate at 180 to the magnet flux, andthe practical maximum speed would be less than that obtainedin ( 5 ) .The above discussion applies equally well to the PMSMand the BDCM. The practical limitation on the maximumspeed is obtained when the back emf of each machine be-comes equal to that of the dc bus. Because of the differencein the waveshape of the back emf of the PMSM and theBDCM, the voltdrop that is available to force current flow isdifferent in each machine in a given period, as shown in Fig.5.Fig. 5(a) shows the desired current relative to the backemf in order to obtain the maximum speed in the PMSM. Atthis operating point, the peak of the back emf is equal to thatof dc bus. In the BDCM, on the other hand, current can onlybe forced into the motor when the back emf is less than thedc bus voltage, as shown in Fig. 5(b). Assuming that theforced current is rectangular in shape, with a peak equal tothe rated value of the BDCM, it is possible to find thefundamental component of this current, which becomes i d in(5) with i = 0. Comparing a PMSM and a BDCM with thesame parameters, but taking into account the current wave-forms shown in Fig. 5 , from 5 ) , it can be shown that

@eP / w e B = ( - d i d B ) / ( uf - L d i d P ) = 1*46 ( 6 )for the motor parameters given in Appendix I. o e p nd oe Bare the maximum PMSM and BDCM synchronous speeds,

I b)a) PMSM back emf and current waveforms and b) BDCMig. 5 . waveforms during flux-weakening operation.whereas i d , and i d B are the direct axis currents of thePMSM and BDCM, respectively. Therefore, the speed rangeof a PMSM would be higher than that of a BDCM of thesame parameters. The speed range of a permanent-magnetmachine therefore depends on the motor parameters, itscurrent rating, the back emf waveform, and the maximumoutput voltage from the inverter.Torque Per Unit Current

Very often, servo motor drives are operated to produce themaximum torque per unit current out of the machine. This isdone because by minimizing the input current for a giventorque, the copper, inverter, and rectifier losses are mini-mized. In addition, lower current ratings of the inverter andrectifier are needed for a given output; this reduces theoverall cost of the system.The torque-angle curve of a PM machine is shown in Fig.6 . The total motor torque consists of electric and reluctancetorque components. The electric torque is produced as aresult of the interaction of the stator current with the airgapflux while the reluctance torque is produced as a result ofreluctance variation due to rotor saliency. As shown in thevector diagram of Fig. 4, the d axis is chosen to be alignedalong the magnet axis. The permeability of the magnet in thed axis is approximately that of air. If the length of the airgapon the quadrature axis is equal to that of the magnet plus airgap on the direct axis, then there is no appreciable reluctancedifference between the d and q axes. Hence, the reluctancetorque is approximately zero, and the total motor torque isequal to the electric torque only, where the maximum isproduced at a 6 of 90 i.e., when is is perpendicular to therotor flux. This is normally true of projecting surface-mountedmachines. In buried permanent-magnet machines, however,the reluctance variation between the d and q axes can be



PILLAY AN D KRISHNAN: APPLICATION CHARACTERISTICS OF dc MOTORS FOR SERVO DRIVES 99

significant, with the d axis reluctance normally being largerthan that of the q axis. This is so because whereas in themagnetic circuit on the q axis there is only iron, a part of themagnetic circuit on the d axis consists of the magnet, whichhas a permeability approximately that of air. This increasesthe d-axis reluctance, hence, reducing its inductance. Thisleads to the reluctance torque being of a negative sign to thatof a wound rotor salient pole synchronous motor as shown inFig. 6 . This means that maximum torque is produced at anangle greater than 90 . If a 6 of 90 is chosen for the buriedor inset machines, the reluctance torque is forced to be zero,and maximum torque/amp operation would not be attained.Hence, a buried PMSM is capable of producing a higheroutput torque/amp when compared with a surface-mountedmachine that has the same magnitude of electric torque. Theburied permanent-magnet motor is , however, more difficultand expensive to manufacture.In order to determine the improvement in total torquecapability of a PM machine by the addition of the reluctanceto the electric torque, the following procedure is adopted.The equation for the total torque produced by a PM machineis as follows:

The equation for the electric torque only, which is producedat an angle of 90 , isT, = 3P(Xafi ,sin6)/2. (8)

Hence, the ratio of the total to the electric torque isT f / T , = 1 + (Ld- L,) i ,sin26/(2Xafsin6) . (9)

Since L, is always less than or equal to L,, this ratio isalways greater than or equal to 1 if 6 is greater than or equalto 90 and less than 180 . Defining the ratio of the quadra-ture to direct axis inductances as K q d , graph of T, T, as afunction of K,, is given in Fig. 7.Values of K q d up to 2.5have been practically realized in buried permanent-magnetmachines, whereas this value is approximately 1 for surface-mounted machines. Hence, the range of K,, considered isfrom 1 to 3 . From the graph, it is clear that for a K,, of 3,the total torque produced from the motor can be 40% largerthan the electric torque alone. This value of K q d would existonly in buried PM machines, whereas for inset PM surface-mounted machines, the total torque can be 10-15% largerthan the electric torque. It should be remembered that thisimprovement in the torque is a result only of changing thelocation of the stator current vector from 90 to a valuelarger than 90 with the magnitude of the current vectorremaining constant. The actual angle that provides this maxi-mum torque can be obtained by finding the first derivative of7) and setting it to zero to obtain

COS 6 = - X - J ( X 2+ 0 . 5 )= X a f / ( 4 ( ~ ,- ~ q ) i s ) * (10)

Hence, for maximum torque per ampere rating, and given thequadrature-to-direct axis inductance ratio, the torque en-hancement and the angular position of the stator current

I t o t a laU0Y

L0

0r e l u c t a n c e

Fig. 6. Torque angle curve of the PMSM.

23

KqdFig. 7 . Ratio of total torque over electric torque as a function of inductanceratio.

vector can be determined from the above equations andgraphs.When comparing a PMSM and a BDCM that have thesame peak value of back emf, the torque/(unit peak current)is higher in the BDCM by a factor of 1.33. It is assumed herethat the peak of the sinusoidal current of the PMSM equalsthe peak of the rectangular current of the BDCM. The factorof 1.33 comes from finding the fundamental component ofthe rectangular current waveform of the BDCM since it is theproduct of the fundamental component of current and thefundamental component of the back emf that develops thesteady torque in the BDCM.Braking

Since both the PMSM and the BDCM have permanent-magnet excitation, braking in inherently easier than withdrives that face the possibility of loss of excitation due to apower supply failure. Hence, all the advantages and disad-vantages that apply to the PMSM also apply to the BDCM.In both the PMSM and the BDCM, braking can be achievedby adding a resistor in series with a transistor, which areconnected just before the inverter power circuit. Duringmotoring operation, this transistor is off, thus disconnectingthe resistor from the supply. During braking, the rectifier isturned off, and the braking transistor is turned on in conjunc-tion with the inverter power transistors. The trapped energyin the motor forces a current to flow through the motor coilsand through the braking resistor. Braking is achieved by thedissipation of heat in the braking resistor.



992 IEEE TRANSACTIOb

Cogging and Ripple TorquesCogging and ripple torques are unwanted pulsating torquesthat are produced by essentially different phenomena. In apermanent-magnet machine, the teeth in the stator can pro-duce a reluctance torque variation as the rotor rotates. Thisreluctance torque that depends on the rotor position and

exists in the absence of any armature current is coggingtorque. Hence, cogging is space dependent. Ripple torque isa consequence of armature current commutation and harmon-ics that do not produce constant torque. Hence, ripple torqueis essentially independent of cogging, and either can exist inthe absence of the other.A design criterion for the minimization of cogging torquehas been established [13]. If the reluctance as seen from therotor is constant, then cogging torque would be negligible. Itis well known [13] that skewing of the stator slots or rotormagnet by one slot pitch reduces cogging to 1-2% (peak toaverage) of the rated torque [5]. Hence, there is no signifi-cant difference between the cogging torque of the PMSM andthe BDCM.The phase current waveforms of the PMSM and the BDCMare intrinsically different, as was discussed previously. Asinusoidal current is needed for the PMSM, whereas a rect-angular current is needed for the BDCM to produce constanttorque. Although it is possible to source a sinusoidal currentinto the PMSM, it is impossible to source a rectangularcurrent into the BDCM because the inductance of the BDCMresists rapid current transitions. Therefore, the input currentinto the BDCM is trapezoidal rather than rectangular due tothe finite rise time. In addition, a finite time is needed for theactual current to reach zero from its maximum value in theBDCM. This forces the actual current to have a trapezoidalshape rather than the desired rectangular shape needed forconstant torque. It is this deviation that causes the BDCM toexhibit commutation torque ripples that are absent in thePMSM drive. At high speeds, these ripples would be filteredout by the rotor inertia, but at low speeds, they can affect theperformance of the drive severely. In particular, the accuracyand repeatability of position servo performance would deteri-orate. It should be noted that in addition to the currentdeviating from the desired rectangular shape, the actualcurrent oscillates around the reference value at a high fre-quency, depending on the size of the hysteresis bands in ahysteresis current controller or the switching frequency of aramp comparison controller. The net effect of this high-frequency current oscillation is to produce a high-frequencyoscillation in the torque, the magnitude of which would belower than that produced by the commutation of the current.This high-frequency torque oscillation is also present in thePMSM since a hysteresis or ramp comparison current con-troller is also needed here to maintain the current flowing intothe motor as close to sinusoids as possible. In practice, thesetorque oscillations are small and of sufficiently high fre-quency that they are easily damped out by the rotor inertia.Figs. 8and 9 show the starting torque of the PMSM andBDCM, respectively. Both are subject to the high-frequencytorque pulsations due to the hysteresis or ramp comparison

IS ON INDUSTRY APPLICATIONS VOL. 21 , NO. 5 , SEPTEMBERIOCTOBER 1991

I

Fig. 8 . Start-up torque of a PMSM.

I I I I.m d.os d.10 d.16 d.21 d . p 6.31 d 37 0 42T IME I S E C I + 1 0 ~Fig. 9. Start-up torque of a BDCM.

current controllers. These can be reduced by using smallerhysteresis windows or a higher PWM switching frequency.However, the torque pulsations in Fig. 11due to the commu-tation of the phase currents are clearly evident and are muchlarger than that produced as a result of the current controlleraction.This phenomenon has been observed by others [5]. It istherefore preferable to use the BDCM for lower performancespeed servos and position servos of low resolution, whereasthe PMSM should be used for high-performance speed andposition servo applications like robotics. This is a significantadvantage of the PMSM over the BDCM.Choice of Feedback Devices

The fact that the PMSM requires sinusoidal currents whilethe BDCM requires rectangular currents leads to differencesin the feedback devices necessary for the proper operation ofthese machines. The current conduction pattern in the BDCMis as follows: Each phase conducts for 120 and then remainsnonconducting for 60 . Current transitions occur every elec-trical 60 ; therefore, it is only necessary to detect thesepoints on the periphery of the motor to commutate thecurrents. Hence, rotor position detectors are needed only




every electrical 60 ; in addition, only two phases conduct atany given time. The PMSM, however, requires sinusoidalcurrents, the magnitudes of which depend on the instanta-neous rotor position. All three phases conduct simultane-ously, and a continuous rotor position feedback is needed. Ifthe PMSM is being used as a position servo, then the angularposition encoder used for rotor position feedback can be usedfor commutation purposes as well, and there is no advantageof the BDCM over the PMSM in this regard. However, forspeed servos, the high-resolution rotor position transducer isstill necessary in the PMSM, whereas the low-resolutiontransducer would suffice in the BDCM. This makes theBDCM preferable for speed servos, provided the commuta-tion induced torque ripple is tolerable.Two current transducers would suffice in either drive sincein the BDCM, the current in one conducting phase is thenegative of the other, whereas in the PMSM, the sum of thethree phase currents must equal zero. Hence, the third phasecurrent can always be inferred from the other two phases.Parameter Sensitivity

Parameter changes in all electrical machines occur due tochanges in temperature, current level, and operating fre-quency [181. In permanent-magnet machines, an increase intemperature results in a partial loss of flux density of thepermanent magnets and an increase in stator resistance. If thepermanent-magnet machines are rated at the maximum oper-ating temperature, then at ambient temperature, higher thanrated output would be obtainable due to the increase in fluxdensity relative to the rated conditions. Conversely, if themachine is rated at ambient temperature, the output at ele-vated temperatures would be reduced.Higher-than-rated current values saturate the machine in-ductances. The saturation of the leakage inductances wouldcause a reduction in their value, thus allowing a greaterpotential difference between the dc bus and the back emf and,hence, providing greater current control.Changes in machine parameters (notably stator resistance)due to increase in frequency is a secondary effect and can betaken into account at the system design stage for properperformance. The majority of permanent-magnet machinesare surface mounted [171. Hence, the reluctance torque termin (7) is essentially zero, and the motor torque is produced bythe interaction of the magnet flux and stator current vector.During current source operation, i s is controlled, but themagnet flux can change due to changes in temperature. Thisis true of both the PMSM and the BDCM, and hence, eachmachine is equally sensitive to parameter changes in themagnet flux due to temperature changes. Depending on thetype of magnet, a 100 increase in the temperature canproduce a 2 to 20% loss in magnet flux for samarium cobaltand ferrite magnets, respectively. Since the PMSM is capableof a higher speed range than the BDCM, it tends to be usedfor high-speed applications. It may then become desirable touse a buried magnet configuration to make the machine moremechanically robust. In this case, the reluctance torque termin (7) is not negligible and saturation of the machine induc-tances can affect the total output torque. The degree of

parameter sensitivity that can be experienced in a buriedPMSM is studied next [14].Parameter sensitivity effects in a servo drive can be studiedwith the speed loop open (torque servo) or with the speedloop closed (speed servo). By expressing the actual machinevariable with parameter change over the original unchangedvariable, normalized curves are generated that give an indica-tion of how other machines of different power ratings wouldbehave. The ambient or unsaturated value of a variable issuperscripted with a *. This is referred to as a referencevalue.Saturation on the q axis of the machine is represented bydefining the variable P , where /3 is the ratio of the saturatedq-axis inductance to the unsaturated value. Similarly, thereduction of magnet flux linkage as temperature increases isrepresented by defining the variable Y to be the ratio of themagnet flux at elevated temperature to the value at ambient.P can range from 0.7 to 1.0, indicating as much as a 30%reduction in the q-axis reactance, particularly for machineswith a cage rotor, whereas for low-performance magnets likeferrite, Y can be as low as 0.75, indicating a 25% loss inmagnet flux. Hence, the range of P chosen is 0.6 to 1.0 andthat of Y is 0.7 to 1.0. This study in parameter sensitivity iscarried out at the maximum torquelunit current point, whichcan be calculated from (10).Fig. 10shows the ratio of the actual torque to the referencevalue as a function of a , with varying between 0.6 and 1.For a given value of a , a larger /3 results in a larger value ofthe ratio between the actual and reference torques. In fact, achange in /3 of 0.2 produces approximately a 0 .1 p.u. changein T,/ T; for a given a. This is because an increase in thesaturation (lower P results in a lower reluctance torquecomponent. The stator current magnitude is held at 1 p.u. inthis study.Fig. 11shows the same results as Fig. 10but with the xaxis as /3 and with Y varying between 0.7 and 1. This isdone so that the application engineer need not have to backcalculate these values from Fig. 10.Fig. 12shows the effectsof different stator current magnitudes on T,1T,*. At highercurrents, the reduction in T, T: is lower for a given a . Thisis because the reluctance torque increases as a square of thecurrent, whereas the electric torque increases only linearly.Hence, the effect of the reduction of magnet flux with tem-perature is less on the total motor torque at higher currentlevels.In a closed-loop speed servo, the speed controller ensuresthat the actual motor torque equals that of the load. However,due to parameter changes, the reference torque will have tobe different from the actual value, the difference being depen-dent on the load torque. As P reduces, higher values of thereference torque is needed. This is because the reluctancetorque contribution to the total motor torque is reduced as /3reduces. Similarly, the electric torque is reduced as a re-duces, again demanding a larger reference torque for a givenload torque.Rectifier1 nverter Rating

For the inverter circuit given in Fig. 3 , the reverse block-ing capability of the transistors is not of particular importance



994 IEEE TRANSACTIONS ON INDUSTRY A PPLICATIONS, VOL. 21, NO. 5 , SEPTEMBERIOCTOBER 1991

0.9..

0 . 8 -

0.7-

0.67-

0 . 6 4 0 . 7 0 . 8 0 ; 9 1 .o

CL

Fig. 10. Torque reduction as a function of flux-reduction coefficient.

T-

:0.6 0 . 8 .o5

Fig. 11. Torque reduction as a function of the saturation coefficient.

even during freewheeling or braking. The inverter deviceratings that are of interest are the forward voltage blockingand the current rating. Generally, current ratings of interestare the continuous and the pulsed values. When the com-manded torque of the servo is much larger than the actualvalue, i.e., during startup, the peak current rating of themotor can be demanded for extended periods of time. TheBDCM requires a trapezoidal current, and the continuousrating of the inverter should be the peak of this waveform.On the other hand, the PMSM requires sinusoidal currents.However, for a zero speed command, dc currents flow in thePMSM (which can also be considered to be the ac of zerofrequency). Hence, the continuous rating of the inverter mustbe the peak of the sinusoid. Current control in a current-regu-lated inverter is only maintained if there is sufficient voltagedifferential between the dc bus and the back emf of the

0.7 0.8 0 . 9 .oFig. 12. Torque reduction as a function of the flux-reduction coefficient.

machine. Let a given inverter have a continuous currentrating of I,,, and suppose it can tolerate a maximum backemf of E p for proper current control. Then, when driving aPMSM, the maximum possible output is3E , I, / J 2 J 2 = 3E, Zp 1 2 .

If it drives a BDCM, then the output is 2 E,, Zp.Therefore, agiven current-regulated inverter (ramp comparison or hys-teresis), with a continuous current rating of I,, can drive aBDCM of 33% higher power output than a PMSM. Thisvalue would be reduced somewhat by the increased corelosses of BDCM, as will be discussed in the next section.The rectifier must be capable of holding the dc bus voltagewithin limits while the inverter is supplying its peak currentcapability. Since in this section the comparison was done onthe basis of the inverter supplying the same peak current, therating of the rectifier is the same whether a BDCM or aPMSM is used.Losses and Thermal Capability

The electrical losses in a PM machine takes two forms:copper and core. Copper losses are fairly easy to compute,given the stator resistance and the magnitude and shape of thestator current. Core losses are much more difficult to calcu-late because they are dependent on the molecular characteris-tics of the steel, whether the magnetization is pulsating orrotating, and is quite heavily dependent on the ability of themanufacturer to prevent burrs that form short circuits be-tween adjacent laminations. The core losses can be dividedinto hysteresis and eddy currents. For sinusoidal excitation,the hysteresis loss is given by

Ph = K , B x W l k g (12)where x lies between 0.5 and 2.3 and is normally around 2.The eddy current loss is given by

P, = K , B 2 . (13)In the PMSM, the flux density is sinusoidal, whereas in theBDCM, it is trapezoidal. Each of the harmonics of the flux


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PILLAY AND KRISHNAN: APPLICATION CHARACTERISTICS OF dc MOTORS FOR S E R V O DRIVES

density of the BDCM contributes to the eddy as well as thehysteresis losses of the BDCM. A Fourier analysis of the fluxdensity of the BDCM reveals that it can be decomposed intothe following series:~ ( x ) 4 [ s i n ( ~ ) s i n ( x )+ s i n ( 3 ~ ) s i n ( 3 ~ ) / 3 *+ s i n ( 5 H ) s i n ( 5 ~ ) / 5 ~ s i n ( 7 H ) s i n ( 7 ~ ) / 7 ~* - . ] H T

(14)where H is the angle between the positive zero crossing andthe beginning of the peak flux density as is shown in Fig. 2. Let the fundamental component of the flux density of theBDCM be equal to that of the PMSM. The harmonics of theflux density of the BDCM therefore contribute additionalcore losses. The ratio of the eddy current loss in the BDCMto the PMSM is given by dividing (14) by its fundamentalcomponent, which, after some algebraic manipulation, isgiven by1+ (sin ( 3 ~ ) / 3 s i n H ) ) ~ (sin 5 ~ ) / 5in ( H ) ) ~

+(sin 7H) /7 in ( H ) ) 2 . (15)whereas the ratio of the hysteresis loss in the BDCM to thatin the PMSM is given by

(sin ( 3 ~ ) / s i n ~ ) ) ~ / 3 ~(sin ( 5 ~ ) / s i n ~ ) ) ~ / 5 3(sin ( 7 H ) sin (H))2/73 + . . (16)

Clearly these equations depend on the value of H , whichimplies the electrical angle for which the flux density isconstant. A graph of the core losses as a function of H isgiven in Fig. 13. Decreasing H , which means increasing theduration that the flux density is constant, increases both theeddy current and hysteresis losses with the increase in theeddy currents being a lot more substantial. This increasedcore loss of the B D e M when compared with the PMSM is anadvantage of the PMSM over the BDCM.IV. CONCLUSIONS

Well-known engineering selection criteria have been usedto determine the application characteristics of the PMSM andthe BDCM. From the results of these criteria, the followingconclusions can be drawn.If the copper losses of the PMSM and the BDCM areequal, then the BDCM is capable of a 15% higher powerdensity. The contribution of the higher harmonics to the totalcore losses is significant in the BDCM, and equality of thetotal core losses therefore demands a significantly ower losscontribution from the fundamental component of the fluxdensity of the BDCM. These core losses increase drasticallywith an increase in the angle for which the flux densityremains constant in the BDCM. Therefore, low core lossesdemand as small a constant portion of the flux density curveas permissible.The ripple torque of the BDCM is higher than that of thePMSM. The ripple torque in the PMSM is due only to theripple in the currents. These ripple torques are of high

995

10 20 30 40 S O o

Fig. 13. Ratio of core losses of the BDCM to PMSM.

frequency and are easily damped out by the rotor. In additionto these ripples, the BDCM has a commutation ripple thatdepends on the speed of the machine. This makes the BDCMless suitable for high-performance position applications.Buried permanent-magnet machines are capable of a highertorque per unit current than surface-mounted machines. Thisis due to the contribution of the reluctance torque. Withproper design, a 40 % increase is possible. The BDCM has ahigher torque per unit peak current than the PMSM, assum-ing both are operating in the constant torque mode of opera-tion. For this reason, and because of the possibility of thehigher power density of the BDCM when compared with thePMSM, the BDCM is to be preferred where weight or spaceis a constraint.Continuous rotor position feedback is needed by the PMSMfor proper operation, whereas the BDCM requires rotorposition feedback information only every 60 . This is anadvantage of the BDCM over the PMSM for speed servos. Ina position servo, the rotor position feedback can be be usedfor current commutation by the PMSM, and this advantage ofthe BDCM over the PMSM disappears.

An inverter with a given continuous current and voltagerating could theoretically drive a BDCM of 33% higherpower rating than could a PMSM. However, the increasedcore losses of the BDCM would reduce this value.The PMSM is capable of a higher speed range than aBDCM of the same parameters. This is due to a higherrestriction placed on the BDCM to the flow of current whenthe back emf equals the dc bus voltage. The PMSM istherefore to be preferred i flux-weakening operation is to beimplemented.Buried PM machines are more sensitive to parameterchanges than surface-mounted machines because of the ab-sence of the reluctance torque term in surface-mounted ma-chines. The surface-mounted PMSM is just as sensitive toparameter changes in the magnet flux as the BDCM.

APPENDIXMOTOR ARAMETERS

RS = 0.175 ClL , = 2.53 mH


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996 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 21, NO. 5, SEPTEMBERIOCTOBER 1991

L , = 6.38 mHha,. = 0.058 Wb4 poles.

APPENDIX1MACHINE ODELv = Ria ph, o,hd

[I61 P. Pillay and R . Krishna n, M odeling, analysis and simulation of ahigh performance, vector controlled, permanent magnet synchronousmotor drive, in Proc. IEEE IAS Ann. Mtg., 1987.T. M. Jahns, G. B. Kliman, and T. W. Neumann, Interior perma-nent magnet synchronous motors for adjustable-speed drives, inProc. IEEE IAS Ann. Mtg., 1985, p. 814-823.R. K rishnan and F. C. Doran , Study of parameter sensitivity in highperformance inverter fed induction motor drive systems, in Proc.IEEE IAS Ann. Mtg., 1984, pp. 510-524.R. Krishnan and P. Pillay, Param eter sensitivity in vector controlledac motor drives, in Proc. 1987 IEEE IECON.

[17]

[18]

I191

REFERENCESR. Krishnan, Selection criteria for servo motor drives, in Proc.IEEE IAS Ann. Mtg., 1986, pp. 301-308.R. Krishnan and A. J. Beutler, Performance and design of an axialfield permanent magnet synchronous motor servo drive, in Proc.IEEE IAS Ann. Mtg., 1985, pp. 634-640.T. M. Jahns, Torque production in permanent magnet motor driveswith rectangular current excitation, IEEE Trans. Industry A ppli-cations, vol. IA-20, no. 4, pp. 803-813, July/A ug. 1984.A. Weschta, Design considerations and performance of brushlesspermanent magnet servo motors, in Proc IEEE IAS Ann. Mtg.,G. Pfaff, A. Weschta, and A. Wick, Design and experimentalresults of a brushless ac servo-drive, in Proc. IEEE IAS Ann.J. Mazurkiewicz, Analysis of new compact brushless vs. pancakemotors, in Proc. Motorcon Conf., 1983, pp. 521-531.D. Pauly, G. Pfaff, and A. Weschta, Brushless servo drives withpermanent magnet motors or squirrel cage induction motors-A com-parison, in Proc. IEEE IAS Ann. Mtg., 1984, pp. 503-509.P. Zimmerman, Electronically commutated dc feed drives, Proc.Motorcon Conf. , 1982, pp. 69-86.M. B rown and D. M oore, Brushless dc or inverter motor drives: Acomparison of attributes, in Proc. Motorcon Conf., 1982, pp.E . K. Persson, Brushless dc motors-A review of the state of theart , in Proc. Motorcon Conf., 1981, pp. 1-16.S . Meshkat and E. K. Persson, Optimum current vector control of abrushless servo amplifier using m icroprocessors, in Proc. IEEEIAS Ann. Mtg., 1984, pp. 451-457.J A. W agner, Numerical analysis of cogging torque in a brushlessdc motor, in Proc. IEEE IAS Ann. Mtg., 1975, pp. 669-674.H. Le-Huy, R. Perret, and R. Feuillet, Minimization of torqueripple in brushless dc motor drives, in Proc. IEEE IAS Ann.T. M. Jahns, Flux weakening regime operation of an interiorpermanent magnet synchronous motor drive, in Proc. IEEE IASA n n . Mtg., 1986, pp. 814-823.T. Sebastian and G. R. Slemon, Operating limits of inverter-drivenpermanent magnet motor drives, in Proc. IEEE IAS Ann. Mtg.,

1983, pp. 469-475.

Mtg., 1982, p. 692-697.

111- 123.

Mtg., 1985, pp. 790-797.

1987, p. 800-805.

Pragasen Pillay SW-M87) received the Bache-lors, Masters, and Ph.D degrees, all in electricalengineering. The P h.D was obtained in 1987 at theVirginia Polytechnic Institute and State U niversity,Blacksburg, funded by a F ulbright scholarship. Hethen joined the University of New castle upon Ty ne,England. Since August 1990, he has been at theUniversity of New Orleans, D epartment of Electri-cal Engineering, Lakefront, LA.Dr. Pillay is a member of the Industry Applica-tions. Power Eneineerinp. and Industrial Electron-ics Societies of the IEEE. H e serves on the Kdustrial Drives, ElectricMachines and Education Committees of the IAS. He is a mem ber of the IEE,

England, a Chartered Electrical Engineer, and is a member of the GreekHonor Society, Phi-Kappa-Phi. He is a past recipient of an IEEE prize paperaward. He organized a tutorial course on permanent magnet motor drives atthe 1989 IAS Annual Meeting; a revised version will be presented at the1991 IAS Annual Meeting. His research interests are in modeling, control,and design of electric machines and electric motor drive systems.

Ramu Krishnan S81-M82) received the B.E .,M.E., and Ph.D. degrees in electrical engineering.He taught for seven years in India. He was StaffEngineer and Principal Investigator of ac servodrive projects at Gould Research Center, RollingMeadows, IL, between 1982 and 1985. SinceSeptember 1985, he has been an Associate Profes-sor in the Electrical Engineering Department atVirginia Polytechnic Institute and State University,Blacksburg. His teaching and research interestsare in high-pe rforma nce vector-controlled vari-able-speed drive s, switched-reluctance motor d rives, electrical machine de-sign, and static power conversion. He has published more than 50 papers onthese topics. He has developed a graduate program in electric motor drivesand machine design at Virginia Polytechnic.Dr. Krishnan is a recipient of four IEEE-IAS awards for his papers, bothpresented and published. He has been Associate Editor of the IEEE TRANS-

ACTIONS ON INDUSTRIALLECTRONICSince June 1987. He is a member ofthe IAS Machine Tools, Robotics, and Factory Automation Committees.

application characteristics of permanent magnet synchronous and brushless dc motors for servo drives

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