safe operating and safe design areas of im drives

8/14/2019 Safe Operating and Safe Design Areas of IM Drives

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 1, NO. 5, SEPT'EMBEIUOCTOBER1995 1121

Safe Operating and Safe Design Areasof Induction Motor Drives

Andrzej M. Trzynadlowski, Senior Member, IEEE

Abstract-An overview of safe operating areas of inductionmotors under various control options is presented. The concept ofsafe design area of a drive system is introduced. A computer aideddesign method is developed to achieve the best match between agiven load and the proposed drive system. Practical examplesof scalar and vector controlled systems illustrate the describedapproach to the optimal design of drive systems with inductionmotors.

I. INTRODUCTION

NDUCTION motors have been for a long time the principal

I orkhorses of industry. Widespread introduction to indus-trial practice of adjustable speed drives, typically based oninvertcr-fed induction motors, can be observed in all developedcountries. New control techniques, particularly those of vectorcontrol, are under intensive development and implementation[ l ] , [2]. Yet, in the avalanche of publications devoted to thecontrol of induction motors, disappointingly little can be foundabout the optimal selection of a motor for a designed drivesystem and optimal matching of the system to the operat-ing conditions of the load. In all considerations concerningdynamically or economically optimal control of drives, themotor is assumed to have already been selected and in theoutlined control strategy its parameters appear as known or

measurable quantities. On the other hand, it is well knownthat enormous reserves of energy and cost savings can beuncovered by retrofitting many existing drive systems so thatthey could be utilized in a more efficient fashion [3].

This paper presents an overview of safe operating areas ofinduction motors under various control options, and introducesthe idea of safe design area of a drive system. A computeraided design method is described that allows a drive designerto achieve the best match between the given load and proposedsystem. The method facilitates a comparative analysis ofavailable motors and control options, so that the optimalstructure of the drive can be determined. In particular, theproposed approach allows answering the following questions:

1) Which of the available motors is best suited fo r the given

2) Which control option results in the most efficient oper-application?

ation of the motor?

Paper IPCSD 95-23, approved by the Industrial Drive s Com mitteeof theIEEE Industry Applications Society for presentation at the 1994IEEE IndustryApplications Society Annual Meeting, Denver, CO,October 2-7. Manuscriptreleased for publication March10, 1995.

The author is with the Departmentof Electrical Engineering, UniversityofNevada, Reno, NV 89557-0153USA.

IEEE Log Number 9412793.

1 ,

- 1 IFig. 1. Steady-state equivalent circuit of inductionmotor.What are the optimal values of the gear ratio betweenmotor and load, and of the controlled flux of the motor?How would possible changes in the design specificationsaffect operation of the designed drive system?What are the safety margins of a given design with re-spect to unforeseen variations in the operating conditionsof the drive, e.g., overloads or supply voltage sags?

11. S A F E OPERATING REASThe variety of the existing control techniques for induction

motors can roughly be classified as speed control and torquecontrol methods. The classic Constant Volts/Hertz (CVH)scalar control and the vector control, based on the field orienta-tion principle, are typical representatives of these two classes,respectively [4]. For an analysis of steady-state operation ofan induction niotor, the classic, per-phase equivalent circuit,shown in Fig. 1, can be used.

Equations can be derived to express the stator voltage andcurrent in terms of the developed torque, T, rotating speed(r/min>, n, and selected flux, A, of the motor using the so-called slip factor, x, defined as

5 w,7, (1 )

where w, denotes the radian frequency of currents in the rotorwinding (slip frequency) while 7, is the time constant of therotor. Now, the safe operating area (SOAR) of a motor canbe defined as such a three-dimensional region in the (n , A, T )space that if the operating point of the motor lies within it,the stator voltage and current, as well as the motor speed andslip factor, do not exceed their allowable values. The voltage,current, and speed constraints are self explanatory. The slip

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1122 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 31 , NO. 5, SEPTEMBEIUOCTOBER 1995

factor limitation, as explained later, is required under most ofthe known control options, except for drive systems with rotorflux control.

The following equations express the stator current, I,, rotorcurrent, I,, stator voltage, V ,,and developed torque, T , of aninduction motor in terms of the three fluxesof the motor, i.e.,stator flux, A,, airgap flux, A,, and rotor flux, A,, supply

radian frequency, w , and slip factor, x . The rotor currentequations, although immaterial for the SOAR determination,will be used for computation of losses in a motor. All theelectric and magnetic quantities are represented by their rmsvalues.

A) In terms of the stator flux:

2 2( U + ? ) + ( $ - o w s )d 1 + ( O x yV, = A, X

T = k i l l :1 + ( o x ) ,

B) In terms of the airgap flux:

C ) In terms of the rotor flux:

T = k 2 A : ~ .

Coefficients appearing in ( 1 ) through (1 3) are

stator time constant,rotor time constant,total leakage factor,rotor leakage factor,inductance coefficient 1 ,inductance coefficient 2,torque coefficient 1, andtorque coefficient 2.

where

R , stator resistance,Rr rotor resistance,L, stator inductance,L , rotor inductance,Lm magnetizing inductance, andp number of poles.

The supply radian frequency, w , can be expressed in termsof the speed, n , of a motor and the slip factor, z, as

7r Xw = - p n + -

60 Tr

Substituting (14) in (4), (8), and (12) allows relating the statorvoltage directly to the motor speed.

Further considerations are limited to the motoring operationof an induction motor since, as seen from (2) through ( 1 3) , thesign of the slip factor does not affect absolute values of themotor currents and torque, while the effect on the stator voltageis minimal. Boundaries of a SOAR can now be determined asfollows

The upper speed limit is taken as the maximum allow-able speed of the motor, nail.The upper limit of the considered flux is taken as therated value of this flux, Rrat, on the assumption thatexceeding this value would result in excessive corelosses and an undesirable level of saturation of themagnetic circuit of the motor.The upper torque limit, calculated from ( 3 , 9), or (13)for each of the allowable ( n , A ) points, corresponds tosuch value of the slip factor that

the stator current, I, , does not exceed its maxi-mum allowable value, I , 9 , a ~ l ,

the stator voltage, V,, does not exceed its rated

a)

b)value,

For motors with stator or airgap flux control, the slipfactor may not exceed certain critical value, z,,it, equal110 for stator flux control and 1 / 0 , for airgap flux control.The corresponding critical value of the developed torque isthe highest possible with a given level of the flux. Vectorcontrolled drive systems with stator or airgap flux orientationlose their stability when forced to operate with a supercriticalvalue of the reference torque [4].

At certain levels of the speed and flux, no allowable torquecan be determined since V, > VJ,ratfor all the permissiblevalues of the slip factor. Clearly, such a situation indicatesthe need for field weakening. The common approach tofield weakening in systems with explicit torque and fluxcontrol consists in adjusting the reference flux in inverseproportion t o the motor speed (vector controlled drives) orsupply frequency (scalar controlled drives) when the speedor frequency is higher than rated. This simple, feedforwardmethod will subsequently be called imposed field weakening.

In certain circumstances, the imposed field weakening un-necessarily reduces the SOAR. An altemate method, usedprimarily in the classic CVH scalar speed control drives,ensures that the stator voltage does not exceed the rated levelby a simple means of limiting the output voltage of the power



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TRZYNADLOWSKI:SAFE OPERATINGAN D SAFE DESIGN AREASOF INDUCTIONMOTORDRIVES 1123

Fig. 2. SOAR of the example motor with stator flux control: No currentoverload permitted.

converter supplying the motor. This can be called naturalfield weakening, for the flux in the field weakening mode

is not controlled, but allowed to assume a value resultingfrom the operating conditions of the motor. The natural fieldweakening is, however, difficult to realize in systems requiringprecise flux control within the whole operating range. Foreach operating point in the field weakening mode, the controlsystem would have to determine such a value of the referenceflux that results in the rated value of the stator voltage.

All the subsequent considerations are illustrated using aspecific, 7.5-kW, 230-V, 6-pole, wye-connected example mo-tor with parameters listed in the Appendix. The maximumallowable speed of the motor, nailr has been assumed at3000 r/min, i.e., at 250% of the rated synchronous speed.

The SOAR of a motor depends on the employed control

strategy, especially in the field weakening mode and, aboveall, on the allowable value of the stator current. This valueis affected by several factors, such as the cooling system,distortion of the current waveform, and duty cycle of the drive.For the following illustrations of the SOAR concept, specificratios of the allowable current to the rated current had beenassumed.

The SOAR of the example motor with the imposed fieldweakening and stator flux control is shown in Fig. 2, while thatwith rotor flux control is shown in Fig. 3. No current overloadis permitted in both cases, i.e., the allowable value of the statorcurrent equals the rated value. The flux coordinates denote theconstant values of flux in the constant-torque mode (no fieldweakening). The left-hand limit of the flux range representsthe rated flux and the black surface of the maximum availabletorque encloses the SOAR. It can be seen that although similar,the SOARs in Figs. 2 and 3 are not identical.

There is practically no difference between SOARs with theimposed and natural field weakening when the stator currentis not permitted to exceed its rated value. If, however, acurrent overload is allowed, e.g., for intermittent operation,then, in comparison with the imposed field weakening, thenatural field weakening results in higher available values ofthe torque at high speeds. The SOAR of the example motorwith a 200% current overload permitted, stator flux control,

F L U X ( W b )-,u.uu

Fig. 3.overload permitted.

SOAR of the example motor with rotor flux control: No current

/l

-,0.00

F L U X (wb)

Fig. 4.field weakening: A 200% current overloa d permitted.

SOAR of the example motor with stator flux control and imposed

and imposed field weakening is shown in Fig. 4, and that withnatural field weakening in Fig. 5 . This example shows thatcertain reserves of the available torque can be uncovered byimproving the techniques of field weakening in drive systemswith explicit flux control. Indeed, in recent years, the issue ofmaximization of the static and dynamic torque has become atopic of intensive studies [5 ] - [9 ] .

DI. SAFE DESIGNAREA

The required operating conditions of a load constitute thestarting point to the design of an electric drive system. Aproperly designed system should involve a motor of thelowest power rating such that it will always operate within itsSOAR. In addition, an effort should be made to minimize thepower consumption of the motor by means of the parametricoptimization of the system. Additional energy savings can berealized by efficiency-optimal control [101, [ 1 11.

For the subsequent considerations, the following assump-tions are made:

1) The load operating area (LOAR), defined as a set ofpossible operating points in the load torque-load speedspace, is specified.



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0 --TI,, , , ,1400 16W la00 ZOO0 2200 2400

LOAD SPEED (rpm)

Fig. 6. LOAR of the example pump drive.

0 0 0 0 0 EXCESSIVE SLIP FACTOR* * e * * EXCESSNE STATOR CURRENT

U F = 9 3 1 %RATED = 32 Wb OcOx, XCESSIVE STATOR VOLTAGE

Fig. 7. SDA plot for the example pump drive.

' '"6,Fig. 8. OF plot for the example pump drive.

to be minimized, the maximum required stator current wasused. The dots in the objective function (OF) plot in Fig. 8 represent individual points of the SDA from Fig. 7 . Zoomingin on the bottom portion of this plot, as shown in Fig. 9,allows pinpointing the ODP. If a direct connection betweenthe motor and the pump is required, i.e., G = 1, another,suboutimal solution can be determined as ODP-I.

.75

Fig. 9. OF plot for the example pump drive: zoom-in.

1125RZYNADLOWSKI, SAFEOPERATING ANDSAFE DESIGNAREAS OF INDUCTION MOTORDRIVES

~~ weakening is required, and the corresponding SDA plot for

ol,, -

LOAD SPEED ( r p m )

Fig. 10. LOAR of the example winder drive.

Example 2: Winder Drive with StatorFlux Orientation: Acontinuously operating winder is to be driven by a vectorcontrolled induction motor with stator field orientation. Theradius of an empty coil is 0.15 m and that of a full coil is0.5 m. The web speed varies from 2 m / s to 5 m / s and theweb tension is to be controlled within the 600 N to 1000 Nrange. The winder LOAR is shown in Fig. 10. If no fieldweakening is assumed, the SD A for the example motor doesnot exist, as illustrated in Fig. 11 . Therefore, another SD Aplot was generated for the imposed field weakening option.This plot is shown in Fig. 12, with the SDA appearing inthe upper right corner. The OF plot, with the maximum powerloss incurred in the motor taken as the objective function to beminimized, is shown in Fig. 13 . The power loss includes corelosses, modeled by an addition of a core loss resistance, R,,in parallel with the magnetizing inductance in the equivalentdiagram in Fig. 1. It is assumed that this resistance is so largethat its inclusion does not affect (2) to (13).

Example 3: Positioning Drive with RotorFlux Orientation:A 70-N . m, 0.8-kgm' load is to be rotated through 50revolutions in time of 3 s. A parabolic speed trajectory is to berealized, resulting in the LOAR shown in Fig. 14 as a paraboliccurve. The driving motor is vector controlled with rotor fluxorientation and a 200% current overload is permitted. No field



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1126 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 31, NO. 5, SEPTEMBEWWTOBER 1995

GEAR RATIOSD A plot for the example winder drive: no field weakening.ig. 11.

O O D O O EXCESSIVE SLIP FACTOR( I****EXCESSIVE STATOR CURRENT

ax03 XCESSIVE STATOR VOLTAGE

in U F - 9 9 1 s

1 P I T F n Fi I M = 0 3? W h

0

\c +7

LOAD SPEED ( rpm)

Fig. 14. LOAK of the example p ositioning drive.

0 * * a * * EXCESSIVE STATOR CU RREM

UF 9 4 8 % ooco3 EXCESSIVE STATOR VOLTAGE1 Z AT t I1 F1 L.X = 0 306 Wb

0 4 0 8 1 2 1 6 2 0 2 4

GEAR RATIOFig. 15. SD A plot fo r the exam ple positionin g drive: rotor flux orientation.

Fig. 12. SD A plot for the example winder drive: imposed field weakening.

. 0.90

Fig. 13. OF plot for the example winder drive.

the example motor is shown in Fig. 15 . The energy loss peroperating cycle of the motor is employed as the objectivefunction to be minimized, and the OF plot is shown in Fig. 16 .As in the drive in Example 1, either a gearing with a certainoptimal ratio can be selected (ODP) or direct coupling of themotor with the load can be used as a slightly less efficient buttechnically sounder solution (ODP-1).

Fig. 16.

Example4: Positioning Drivewith Stator Flux Orientation:The same load as in Example 3 is considered, but the vectorcontrolled motor is oriented along the stator, not rotor, fluxvector. Interestingly, as shown in Fig. 17 , no SDA exists forthe example motor in this case. However, the minimal overlapof the excessive current and excessive voltage areas of theplot indicates a near miss , If the required displacement time



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TRZYNADLOWSKI: SAF E OPERATING A N D SAFE DESIGN AREAS OF INDUCTION MOTOR DRIVES 1127

~ 0 0 0 0 XCESSIVE SLIP FACTOR* * e * * EXCESSIVE STATOR CURRENT

F = 0

RATED = 0 3 2 Wb OOCrJ3EXCESSiVE STATOR VOLTAGE

m2. 4

Fig. 17 . SD A plot for the exam ple positionin g system: stator flux orientation.

O O O D O EXCESSIVE SLIP FACTOR0 UF = 94.7 m * * * * e EXCESSIVE STATOR CURRENT

COCOOEXCESSIVE STATOR VOLTAGERATED FLUX = o,52 Wb

m

2. 5

Fig. 18.relaxed operating conditions.

SDA plot for the exam ple positioning system: stator flux orientation,

is increased by lo%, to 3.3 s, in order to relax the operatingconditions of the drive, the SDA appears as shown in Fig. 18 .The OF plot in Fig. 19 , when compared with that in Fig. 16 for the rotor flux oriented motor, shows that this solution,if acceptable, would result in significant reduction of energyconsumed by the motor.

V. CONCLUSION

For illustration purposes, the design examples presented

have been tailored to fit the example motor. In practice,the SD A and OF plots should be constructed for a varietyof available motors, so that the finally selected machinerepresents a truly optimal choice. Apart from the motorutilization and energy consumption issues, other considerationscan be taken into account, such as the cost, efficiency, or powerfactor of the motor.

In addition to the specific type of motor, the followingfactors are suggested for a comparative analysis:

1) Operating conditionsofthe loud: These can be mademore stringent than initially specified, to increase theutilization factor of the motor or, vice versa, somewhat

0.90

f%

Fig. 19.relaxed operating conditions.

OF plot for the example operating system: stator flux orientation,

relaxed if the SDA plot indicates a near miss and the nextin line motor is significantly larger and more expensive.

In par-ticular, in vector controlled drive systems, orientationalong the stator, airgap, and rotor flux vectors can becomparatively evaluated.

If, for example, supply voltage sags upto 20% are expected, the maximum allowable voltageof the motor can be taken at 80%, instead of loo%,of the rated voltage. If the motor can still drive theload, in spite of the corresponding 36% reduction in thedeveloped torque, it certainly can operate when no sagsare experienced. A similar approach can be used withrespect to other operating conditions.

The proposed method of design of induction motor drivesis flexible and interactive. Development of a self-containedsoftware package linked with motor databases is planned toserve drive engineers as a practical design tool.

2 ) Control methods and field weakening options:

3) Safety margins:

APPENDIXPARAMETERS OF THE EXAMPLEMOTOR

Rated power, PratRated voltage, Vs,ratRated current, Is,ratRated frequency, fratRated speed, n r a tRated stator flux,Rated rotor flux,

No . of poles, pStator connectionStator resistance, R,Stator inductance, L ,Stator time constant, T~

Rotor resistance, R,Rotor inductance, L,Rotor time constant, T~

Rotor leakage factor, ( T ~Total leakage factor, (TMagnetizing inductance, L ,Core loss resistance, R,

7.5 kW230 V23.8 Nph60 Hz1164 r/min0.32 Wblph0.306 Wblph

6WYe0.294 Wph0.0424 Wph0.144 s0.156 Wph0.0417 Hlph0.267 s0.0170.0490.041 Wph7 5 Wph



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1128 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 31. NO. 5, SEETEMBEFUOCTOBER 1995

Inductance coefficient 1, y1 0.983Inductance coefficient 2 , y ~ 1.034Torque coefficient 1, C1Torque coefficient 2, k2

[ I l l J. C. Moreira,T. A. Lip0 andV. Blasko, Simple efficiency maximizerfor adjustable frequency induction motor drive,IEEE Trans. Ind.Applicat., vol. 27, no. 5, pp. 940-946, Sept./Oct. 1991.

[12] A. M. Trzynadlowski, Computer aided preliminary designof electricdrives in key-parameters space,Electr. Mach. and Power Syst.,vol.12, no. 6, pp. 445-457, 1987.

[I31 -, Energy optimizationof a certain classof incremental motiondc drives,IEEE Trans. Ind. Electron., vol. 35, no. I , pp. 60-66, 1988 .

[14] J. C. Brierley, R.E. Colyer, and A. M. Trzynadlowski, The SOARmethod for computer aided design of energy-optimal dc drive sytems, in Conf: Rec. IEEE Ind. Applicat. Soc. Annu. Meeting,1989, pp.464-467.

202 N . m/wb2216 N . m/wb2

ACKNOWLEDGMENT

The author thanks the anonymous reviewers for the thor-ough reviews of the paper, and many useful suggestions.

REFERENCES

J. M. Murphy andF. G. Turnbull,Power Electronic Control of ACDrives. New York: Pergamon, 1988.P. C. Sen, Electric motor drives and control-Past, present, and future,IEEE Trans. Ind Electron.,vol. 37, no.6, pp. 562-575, 1990.MoforMaster Reference Guide,Washington State Energy Office, 1992.A. M. Trzynadlowski,The Field Orientation Principle in ControlofInduction Motors. Norwell,MA: Kluwer, 1994.R. D. Lorenz andS. M. Yang, Efficiency optimizedflux trajectories forclosed cycle operation offield oriented induction machines,in Conf:Rec. IEEE Ind. Applicai. Soc. Annu. Meeting,1988, pp. 457-462.R. D. Lorenz and D. W. Novotny, Saturation effects in field oriented

induction machines,IEEE Trans. Ind. Applicat., vol. 26, no. 2, pp.R. D. orenz andD. B. Lawson,Flux and torque decoupling control forfield weakened operation of field-oriented induction machines,IEEETrans. Ind. Applicat.. vol. 26, no. 2, pp. 290-295, Mar/Ap r. 1990.I. T. Wallace, D. W. Novotny, R. D. Lorenz, and D. M. Divan,Increasing the dynamic torque per ampere capability of inductionmachines, IEEE Truns. Ind. Applicar., vol. 30, no. 1, pp. 146153,Jan./Feb. 1994.-, Verification of enhanced dynam ic torque per a mpere capabilityin saturated induction machines,IEEE Trans. Ind. Applicat., vol. 30,no. 5 , pp. 1193-1201, Sept./Oct. 1994.P. amouri and J.J. Cathey,Loss minimization controlof an inductionmotor drive, IEEE Trans. Ind. Applicat., vol. 27, no. 1, pp. 32-37,Jan./Feb. 1991.

262-268, 1990.

[I51 R. E. Colyer and A. M. Trzynadlowski, Computer-aided selection ooptimal drives for motion control applications, inProc. Int. AegeanCon$ Elec. Mach. and Powe r Electron.,1992, pp. 315-320.

[16] T. F. Lowery and D. W. Petro, Application considerations for PWMinverter-fed low-voltage induction motors,IEEE Trans. Ind. Applicat.,vol. 30, no. 2, pp. 28 62 93 , Mar./Apr. 1994.

Andrzej M. Rzynadlowski (M83-SM86)received the M.S. degree in electrical engineeringIn 1 964, the MS degree in electronics in 1969,and the Ph.D. degree in electrical engineering in1974, from the Technical University of W roclaw,

Poland.From 1966 to 1979, he was a faculty m emberof the Technical University of Wroclaw In thefollowing years, he worked at the University ofSalahuddin, Iraq, the U niversity of Texas, Arlingtonand the University of Wyoming, Laramie Since

1987, he has been with the University of Nevada, Reno, where he is nowProfessor of Electncal Engineering and Assistant Director of Energy Analyand Diagnostic Center.He has authoredor coauthored over 80 publicationsin the areas of power electronics and electric drive systems and has begranted 11 patents. He is the author of The FieM Orientation Principle inControl of Induciion Motors (Norwell, MA: Kluwer, 1994).

Dr Trzynadlowski is a member of the Industrial Drives Committee anthe Industrial Power Converters CommitteeHe was the recipient o f the 1992IEEE Industry Applications Society Myron Zucker Student-Faculty Grant.

safe operating and safe design areas of im drives

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