356 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. IA-19, NO.

3, MAY/JUNE 1983

Control Methods for Good Dynamic Performance

Induction Motor Drives Based on Current and
Voltage as Measured Quantities
ROBERT JOETTEN AND GERHARD MAEDER

Abstract-A family of schemes for the control of torque and speed of

the induction machine is described. It has been developed with the
intention of closing the gap between high dynamic performance
drives, requiring measurement of the rotor position or the field, and
the simpler schemes with poor dynamic performance. Dynamic be-
havior and a static accuracy have been achieved which promise a
broad range of applications. This is due also to the relative simplicity
of the equipment and insensitivity to changes in resistance param-
eters. Implementation with a voltage source inverter and a current
source inverter are shown.

I. REVIEW OF THE PREVIOUS STATE OF THE ART

FOR MANY applications of controlled ac drives, mainly
the steady-state behavior is of interest for the user (best
possible utilization of the machine, sufficient static accuracy
of the control). In these cases emphasis is put on simple signal Fig. 1. Rotor current'2, cos 02 l, torque m, versus slip frequency w2
processing and not on high dynamic performance. On the for constant air gap flux.
other hand, the dynamic behavior of the machine is well- lation
known. Control schemes have been developed for which the
only limitation for dynamic performance is how well the =-(0W -Xm (1)
chosen inverter type is able to follow the reference values set
by the control scheme. (where wm = np m' 2np is the number of poles, and wm
Because of the ability of the inverter to change voltage and is the rotor speed in rad/s) among slip frequency, stator fre-
frequency very quickly, a direct or indirect current limitation is quency, and mechanical rotor speed, the straight line approxi-
always necessary. Furthermore, the machine is run only in op- mation of the torque-slip function can be plotted against the
eration modes where the losses are nearly minimal. The classi- mechanical speed, using w, as a parameter, yielding a set of
cal mode is operation with approximately constant field and straight parallel lines.
field weakening only in an upper speed range. The slip frequency is a quantity which is difficult to meas-
ure directly. The common practice to limit it is to measure
Slip Limitation the mechanical speed and add a preset and limited slip accord-
The equations describing the steady-state behavior of the ing to w1 = wdm + w,2 *
machine become extremely simple if the air gap flux is as- If the stator voltage is made proportional to the stator fre-
sumed to be constant. In this case the behavior of the ma- quency, the assumption of constant air gap flux is fulfilled
chine is dependent only on the slip frequency (Fig. 1). only approximately in an upper frequency range and not at all
With the rotor current, the stator current is also determined if the stator frequency approaches zero. Analog computing
by the slip frequency. It has been postulated that the slip fre- schemes to obtain a compensation of the stator voltage drop
quency must be limited to stay within the range between the have been devised.
two extrema of the torque. Control Schemes Without Regard to Dynamic Performance
If this is done, the straight line approximation of the torque
versus slip function is a useful approximation. Using the re- If an inverter is used which easily permits the control of
the amplitude of the stator current, constant air-gap flux can
be maintained by adding a constant magnetizing current com-
Paper IPCSD 82-61, approved by the Industrial Drives Committee ponent
of the IEEE Industry Applications Society for presentation at the 1982 geometrically to the rotor current. The rotor current
International Semiconductor Power Converter Conference, Orlando, is made proportional to the slip frequency. In this way a co-
FL, May 24-27. Manuscript released for publication December 21, ordination of stator current and slip is possible. Thus the
1982.
The authors aie with the Institut fur Stromrichtertechnik und An- scheme shown in Fig. 2 has been realized (speed control, con-
triebsregelung, Schlossgraben 1, Darmstadt, Germany. trol of the amplitude of the stator current, slip-current co-

0093-9994/83/0500-0356$01.00 © 1983 IEEE

JOETTEN AND MAEDER: CONTROL METHODS FOR INDUCTION MOTOR DRIVES 357

Fig. 3. Frequency control with voltage-frequency coordination and

inner current control loop. SL: slope (6v1*) limiter; u1: stator
voltage; lu 1: rectified stator voltage, used as actual value for
Fig. 2. Speed control with inner current control loop and current-slip voltage control. Asterisks denote reference values.
coordination. i1: stator current; other symbols defmed in text.
Asterisks denote reference values. but also of asynchronous drives [3], [5]. The relation between
the torque producing current component and the slip fre-
ordination). The required static accuracy, for the addition of quency contains the inverse of the rotor resistance, which
the frequencies, can be obtained by digital techniques. This varies with the temperature. This led to the proposal to meas-
system is feasible only with tachometer feedback. Settling ure the field of the machine directly or indirectly [6], [7],
times in the range of 500 ms and poor damping are typical which has been termed "field oriented control." To avoid
[4], [12]. If the requirement for static accuracy of the set field measurement with its difficulties, automatic parameter
speed is low, an open loop frequency control with voltage adaption has been developed and used with a rotor position
frequency coordination is sufficient. If a current source in- oriented control [13].
verter (CSI) is used, the voltage frequency coordination is ob- The opinion of the authors is that for high dynamic per-
tained by superimposing a voltage control loop to the current formance ac drives with induction machines a scheme with
control loop [9], [10]. In this case, slip limitation is possible rotor position measurement and automatic parameter adap-
only indirectly by limiting the slope of the stator frequency tion is the best solution. Incremental measurement is sufficient.
change versus time (Fig. 3). A proposal has been made to get If an absolute measurement is provided, e.g., for position con-
an approximate actual value for the slip frequency by compu-
trol, this can be used favorably.
tation from the measurement of the terminal currents and
voltages [8] It is based on the steady-state equations and has
. II. INCENTIVES TO THE NEW DEVELOPMENT
been used for the current-slip coordination [8], [15]. This A handicap for the use of controlled ac drives has been the
method is not feasible at very low speed, as will become clear higher cost of the converting equipment and the complexity of
in the following, and its accuracy is not satisfactory under high the signal processing, compared to dc drives. With the develop-
load. ment of integrated circuits, the complexity of the signal proc-
essing as such is not the main obstacle but the cost and incon-
Control Schemes for High Dynamic Performance venience of the position or even field measurement and the
In order to realize controlled ac drives with a dynamic per- tachometer. In a majority of applications, speed control is re-
formance comparable to that obtainable with a dc drive, the quired; however, requirements for static accuracy and/or dy-
behavior of the machine must be taken into account for the namic performance are less important. Nevertheless, to have a
control. This has led to some consequences. The first was to wide range of applications for a given scheme, a satisfactory
use as signal quantities not the frequencies, but angles which dynamic performance, accuracy, and a large control range are
are the time integrals of frequencies. They are defined by desirable. Torque control is another desirable feature not
Wm ~Ym W2 Y2, cl1 I1
= = = In this context the instantaneous covered by previous simple schemes.
value of the angle between the current phasor and the flux or
III. THE NEW METHODS
electromotive force (EMF) phasor is taken into account.
The differential equations which describe the dynamic be- A. Principles
havior become extremely simple if the absolute value (the Indirect Rotor EMF and Slip Measurement: If the slip fre-
modulus) of the rotor flux linkage (which is a vector) is kept quency were directly measurable, it could be used as a limited
constant. This is contrary to what has been said earlier, in the controlled variable in an inner control loop. An improved
context of Fig. 1, for the steady-state equations. These are method of computing the instantaneous slip was developed,
simpler if the air gap flux is assumed to be constant. The pro- based on the differential equations describing the machine
portionality between the torque producing current compo- behavior in rectangular coordinates. The notation used here
nent and the rotor frequency turned out to be a condition for has been reviewed in recent survey papers [1], [2]. The de-
decoupling the torque producing current and magnetizing cur- tailed derivation of the used equations finally is given in [16]
rent and avoiding electromagnetic transients in the machine. and outlined here in an abbreviated form.
The practical consequences have been the use of rotor po- The basic equations to start with are the state differential
sition measurement for the control not only of synchronous equations in stator fixed rectangular (a, 3) coordinates, with
358 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. IA-19, NO. 3, MAY/JUNE 1983

flux components as state variables and the currents as auxiliary

variables:
4,1lc -
Uici -R, * ila (2a)
4'2cu =- m * 2, -R2 * i2c (2b)
.10 =
ulp -RI il3
-
(2c)
.29 =
Wm '
.2a -R2 i2#- '
(2d)
(In the notation used here the impedance parameters are 2/3
of the normally used phase parameters, and 3/2 for the in-
verse elements, respectively.)
i=(K)- v =(L)-1 .4
=i 1ot, i2a, ilg, i2f)T (3)
Fa I iE
4 = (Ola, 2co, 419, 423)T
d (1ML2 t ML )
Fi^g. 4. Computation of rotor EMF and slip frequency.
(4) in the (ce, 3) frame. Thus for (9) we get
e2 ", ip + e2c ilc
The inner (electromagnetic) torque, expressed in rotor qi
(02 ~co1.R2 -(M/L2) . 2 2 (11)
e2cy ±e213
tities is
The EMF's e2l, e2g, can be deduced from measured stator
mi = np * (i2a * ;29- i2pS*;2> quantities according to (12):
Substituting the currents in (5) by (2b) and (2d) and set
(see (1)) e2aOf= (L21M) * (ul,o-RI i1 c-i cilK, 1 )
-

ci)m = np * Sm W21
=J I (6) e2p (L-21M) (u 1 p R I il g z:', plK, 1)
=: - -
(12)

Xl=Yl, (K1 1 is the element of (K), see (3)).

tu~ ~ ~ ~ ~ (a)
Equations (11) and (12) are the key equations for the slip
where y'1 is the angle between the directions of and the computation from measured stator quantities. It can be shown
42

,Baxis, yields, after some computation, that the approximations (10) are valid even if fast field weaken-
ing is provided.
m = np *W2 (l/R2) * (02a2 + 0202). (7) Fig. 4 shows the corresponding computing scheme. It con-
tains no integrators, and drift problems are avoided. There are
Hence two differentiators, and one might anticipate difficulties due
to the ripple in the input quantities. To the contrary, the dif-
mi R2
(8) ferentiationhas a smoothing effect on the output. The plausible
-

np *2p2)
np 02,-

22 reason for this is that the quantities entering the multipliers

are stator current and rotor EMF. It can be concluded from in-
The inner torque can be expressed by stator currents and rotor spection of the equivalent circuit that the rotor EMF is con-
fluxes, yielding siderably smoothed, compared to the stator voltage or stator
EMF. Thus only the ripple of the stator current enters the
m 2ca * il,'- 2,B * ila multipliers. It contributes to the ripple of the torque and
c2 =-
R2. 2 2 (9) must not be suppressed.
L2 + 2, The method could be tested with a drive with position
The stator current components are measurable. For (42., measurement. Fig. 5 shows the static characteristic of com-
puted slip plotted against real slip. Fig. 6 shows the dynamic
,2p) a useful approximation is obtained if =2202 2
performance of the slip calculation.
2,2 can be made constant, respectively, only changing Also with this method an accuracy problem results if the
slowly. Then we get stator frequency approaches zero, since in (11) the nominator
and denominator then approach zero. Equation (12) shows
4'2at4/2,/@ (10)
that the stator resistance influences the result. The term pro-
portional to the stator resistance is negligible at high frequencies
and important only at very low frequencies. It will be shown
2of -2, can be interpreted as components of the rotor EMF later that the method can be used down to stator frequencies in
Fig. 6.
:_ _7:-f
JOETTEN AND MAEDER: CONTROL METHODS FOR INDUCTION MOTOR DRIVES

T
7,5

i
percent of rated speed.

.:
1
5t -
5:
-0 !::

...-
D--
t1 -
WZ 1l/s]

Fig. 5. Static characteristic of computed slip versus real slip at six

:::

Dynamic performance of slip computation. (a) Real slip. (b)

Computed Slip. Speed reduction: 600 r/min to 75 r/min.

the range of +3-±5 percent of rated frequency. Equation (11)

shows that the rotor resistance also has an influence on the
computed slip frequency. As can be shown, this influence can-
cels with the new control methods described below.
(a)
L{CX2}/L {co } = (1/K1) 1 + /K-
s

with K1 = np,2 l '2 2/(JR2), with J being the inertia. The

closed loop frequency response may be approximated by

LIW2}ILJ2
IL}t2 1+ s *T,

with Ti 10 ms. The inverter needs, besides the frequency, an

input for its terminal voltages or currents and reference values
for these.
Stator Frequency Control: Fig. 7 shows, as an example,
stator frequency regulation as a main control loop and an in-
verter of the voltage source type with voltage control as-
359

induction
machine
Fig. 7. Stator frequency regulation with inner slip control loop and
voltage source inverter. Asterisks denote reference quantities. N:
nominal.
has to be adapted, is obtained as

(14)

(15)

Current Orientation: As has been outlined in the first sec- sumed. Field weakening is provided. The voltage references are
tion, to obtain good dynamic performance and avoid elec- calculated in an (x, y) reference frame which is orientated in
tromagnetic transients, angles should be processed as signal such a way that the rotor flux linkage is always in the y direc-
quantities instead of frequencies. Since the rotor EMF is now tion. Hence the angle used in (6a) is
available- as an instantaneous phasor, it can also be used for
the current orientation. 'Yi = 40,Y) = 40, X).
The argument angle of the rotor flux linkage in stator fixed
coordinates y1 is given by Since the flux is not measured, it is better to say that the
orientation is such that, according to (10), the phasor of the
71 = arctan (e2p/e2ce). (13) rotor EMF is always in the (-x) direction (for wO positive).
The voltage phasor is then transformed into a stator fixed
Thus instead of field orientation, rotor EMF orientation of (a, ,B) frame and finally into three-phase quantities. Thus the
the current phasor can be performed on the basis of (12) if the output of the slip computation is used here also for orienta-
EMF is not zero, respectively, and has some minimal value. tion of the stator voltage at the rotor EMF and not only for
the limitation of the slip.
B. Control Schemes The field reference value is set as a function of the stator
frequency. The purpose of the two multipliers following the
Inner Control Loop for Slip Frequency: Most of the con- stator frequency controller is to adapt the closed loop gain of
trol schemes described in this paragraph have an inner control the main control loop in the field weakening range and to ex-
loop for the slip frequency. Its reference value is the output of tend the limit for the slip frequency in such a way that the full
some superimposed control loop, e.g., torque, speed, stator current can be obtained also in the field weakening range.
frequency regulation. The actuating output of this controller Stator Frequency Control with Slip Compensation: If sta-
is the stator frequency. The actual measured value is the out- tor frequency control is used instead of speed control, the
put of the slip frequency computation. The machine is part of speed is dependent on the load and differs from the stator fre-
this control loop with the input w1 and the output O2C (com- quency by the slip which is used to compensate the load
puted value). The transfer function, to which the controller torque. It is possible to compensate this load dependent drop
360 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. IA-19, NO. 3, MAY/JUNE 1983

Fig. 8. Control scheme for drive with CSI and computation of rotor EMF. Subscript c: computed value. id: direct current
in intermediate dc circuit. Asterisks denote reference values.

by a positive feedback of the computed slip on the input of reversing through the dead zone, the method can be refined
the frequency controller. This positive feedback must be ap- and the rate of change kept at the value as just before enter-
plied with an appropriate time delay to keep the main loop ing the zone. The effect of these measures will be shown in
stable. Section IV.
Speed Control with Tachometer Feedback: High accuracy The additional circuitry for passing the dead zone near
in speed and better dynamic performance can be achieved if zero speed is not shown in Figs. 7 and 8, in order to avoid
tachometer feedback and speed control is provided for the confusing complexity. It should be noted, however, that at
main control loop. In this case in Fig. 7 the reference value of standstill, with cO = 0 and C02 * =0, magnetization of the ma-
the main loop is replaced by the speed reference, its actual chine is ensured, due to input i2y* in Fig. 7 and i1y* in Fig.
value by the tachometer output. 8, respectively.
Torque Control: If the application of the drive requires IV. RESULTS
torque control, e.g., for a coiler drive or in traction applica-
tions in Fig. 7, the speed or stator frequency feedback is A. ExperimentalResuits of a Drive with a Voltage Controlled
omitted. The controlling torque input replaces the output of Source Inverter and VariIous Control Schemes
the frequency- or speed-controller. In this way torque control The following figures show experimental results with t-he
is possible also in the field weakening range. schemes according to Fig. 7. The first figures show the behavior
Example for Control Scheme with a CSI: Fig. 8 shows as with stator frequency control. In the oscillograms, one phase
another example a modification which is adapted to the cur- voltage, one phase current, the slip frequency reference, the
rent source inverter. In this case the mneasurement of the computed slip frequency, the stator frequency, and the rotor
terminal currents can be replaced by measurement of the speed are shown. It can be seen that startup from and braking
intermediate direct current and a coordinate changer (poldr/ to standstill is no problem, (Fig. 9). Fig. 10 shows reversal ofthe
Cartesian) which gets the information for the argument angle drive through the dead band. Fig. 11 shows the closed loop re-
fromn the firing circuit of the inverter. In this case the stator sponse for a step in load torque. The settling time, referred to
current is oriented at the rotor EMF phasor in the (a, ,B) ref- the speed, is in the range of 100-150 ms. For compan'son,
erence frame, a possibility already mentioned in Section Fig. 12 shows the closed loop response to a step in load torque
III-A, and the computed slip is not used in an inner control with slip compensation. The speed error vanishes; however,
loop. In the example stator frequency control is provided, the transient is less damp compared to the case without slip
and optional slip compensation is shown in dashed lines. compensation,
Additional Measures in the Region Near Zero Speed: As
outlined in Section III-A in the region near zero speed, the EMF B. Influence ofParameterR2
and slip computation cannot work properly. The drive must, The rotor resistance enters the voltage reference computa-
however, be able to start from standstill, brake to standstill, tion and the coordinate transformation (x, y) -> (a, ,B). In the
and reverse through zero speed. In the range near zero speed first case it cancels. In the second case its influence is teduced,
(+3-±5 percent), the output of the computation is suppressed, since co, is not obtained as a result of the positive feedback of
and the rate of change of the stator frequency is limrited. It C.Jm but as the actuating output of the slip controller. (For a
remains so until the stator frequency leaves the dead band. In detailed explanation see [166.)
JOETTEN AND MAEDER: CONTROL METHODS FOR INDUCTION MOTOR DRIVES 361

0/~ I 0. A ~~~~
I~~~.I.. .I:
I

Fig. 9. Startup and biaking to standstill, frequency control with VSI. Fig. 11. Generatoric step in torque, frequency control with VSI.

0.33

0,5

LI? . I. 0,5

i k ILtsfil 111 '' "1 r| -" ......'lt .. J§ !.... ,

t(t.) Ji ii§i !§ E 1~~~~~~~~~~~~~11

.to

Fig. 1 0. Reversal from -600 r/min to +600 r/min, freq,uency control Fig. 12. Generatoric step in torque, frequency control with slip com-
with VSI. pensation, VSI.

C. Verification of the Feasibility of the Scheme with the CSI V. CONCLUSION

The feasibility of the scheme shown in Fig. 8 has been tested It has been shown that a controlled drive with an induction
by digital simulation. Fig. 13 shows startup from standstill machine and good dynamic performance is feasible, using as
and reversing through standstill. The time interval where themeasured quantities terminal voltages and currents, respectively,
EMF computation is blocked is marked in the lowest trace. intermediate dc current and terminal voltages only. The dy-
namic performance is satisfactory for most applications and
Furthermore, in this and in the next figure the rotor flux comn-
ponents in the (x, y) frame are shown. Ideally, i2x should bedistinctly better than with previous solutions. The only limita-
zero, 42y should be constant. It can be seen that deviations tion for the application of the described schemes is the case
occur only in the zone where the EMF computation is blocked. where very good dynamic performance and high accuracy is
Fig. 14 shows that these deviations become greater if the pa-required in a region near zero speed. This forbidden range
amounts to 3-5 percent of rated speed. It is no handicap for
rameters R1 is incorrectly set, according to the temperature to
starting, stopping, and reversing.
be expected at full load while the machine is cold. A resistance
error 1:1.5 has been assumed. It is remarkable that deviations Omission of the measurement of the rotor position or of
from the desired values of the flux components are corrected the field, be it directly or indirectly, is an essential simplifica-
very fast if the frequency leavesthe dead zone. tion. Insensitivity to resistance parameter changes is another
 :k_,s'_Xu
362 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. IA-19, NO. 3, MAY/JUNE 1983

id Id 11 "
'dN 'dN
1-
AaN 'iaN 'r-), 7., rl% %--.r
U1a
.:::2 lu \I-f 1-i
1-
-1- --L -L--
-t- r-r, 7 r-
1- ..

IV2 NI I/2NI -

11y21
1-

Wl (t)p WIM07
ZXN qN Ul I
-mj
MiN ArN4
, .. - ,,VW

125 tlms]
Fig. 13. Frequency control with CSI. Startup and reversing with correctly set parameters in computing scheme. mi: inner
torque.

id id
'dN 'dN
JdN JdN
1-

'ia
hloN AlaN
ULa
1- j wftylAl ,_ I f +eA,
UlaN

2x Ay 1_ _ __ ........................ -
N'2NI IW2NI f _

I1NI 1
_ .

Wt4 WiN W1N 025-

mi
miN 1

125 ItIi.s]
Fig. 14. Frequency control with CSI. Startup and reversing with incorrectly set parameters in computing scheme. mi: in-
ner torque.

important advantage compared to previously known schemes. [6] F. Blaschke, "Das Verfahren der Feldorientierung zur Regelung
Signal processing and control have been implemented with der Drehfeldmaschine." Diss. Braunschweig, 1974.
[7] F. Blaschke and K. Boehm, "Verfahren der Felderfassung bei der
analog means and conventional integrated logic. If microproc- Regelung stromrichtergespeister Asynchronmaschinen," presented
essors were used instead [14], simplicity, uniformity, and at the IFAC Symp. Control in Power Electronics and Electrical
adaptability of the control apparatus would yield even greater Drives, Dusseldorf, 1974.
[8] A. Abbondanti and M. B. Brennen, "Variable speed induction
advantages. motor drive uses electronic slip calculator based on motor voltages
and currents," IEEE Trans. Ind. Appl., vol. IA-II, 1975.
[9] W. Landeck and U. Putz, Selbstgefi;hrter Zwischenkreisumrichter
REFERENCES mit eingepragtem Strom fur Drehstrom-Asynchronmotoren. Tech-
nische Mitteilungen AEG-Telefunken, 1977.
[1] R. Joetten, "Stand der Technik bei geregelten Drehstromantrie- [10] A. Abbondanti, "Method of flux control in induction motors driven
ben," VDE-Fachberichte 1978. ("State of the art of controlled a.c. by variable frequency variable voltage supplies," presented at the
drives;" survey paper with references). IEEE/tAS Int. Semiconductor Power Converter Conf., Orlando,
[2] , "Dynamisches Verhalten stromrichtergespeister Asynchron- FL, 1977.
maschinen," ETG-Fachberichte Nr. 5 1979/80. ("Dynamic be- [11] A. C. Plunkett, J. D. D'Atre, and T. A. Lipo, "Synchronous
haviour of asynchronous machines fed by converters," survey control of a static a.c. induction motor drive," presented at the
paper with references). IEEE/1AS Meeting, Los Angeles, CA, 1977.
[3] K. Hasse, "Zur Dynamik drehzahlgeregelter Antriebe mit strom- [12] K. Moll, H. Schulze, and J. Stoschek, Umrichter mit Gleich-
richtergespeisten Asynchron-Kurzschlusslaufermaschinen." Diss. stromzwischenkreis fur Industrieantriebe. BBC-Nachrichten 1978.
Darmstadt 1969. ("Dynamics of speed controlled drives with in- [13] L. J. Garces, "Ein Verfahren zur Parameterkorrektur bei der
duction machines"); Abbr. version in Regelungstechnik, 1972. Drehzahlregelung der umrichtergespeisten Kafigliiufermaschine."
[4] B. Maag, "Characteristics and application of current source slip Diss. Darmstadt, 1979. Abbr. version: "Parameter adaption for the
regulated a.c. induction motor drives," presented at the IEEE-IGA speed controlled static a.c. drive with squirrel cage induction
Conf., Cleveland, OH, 1971. motor," presented at the IEEE-IAS Annu. Conf. Rec., 1979.
[5] R. Joetten, "Signalverarbeitung fir die Regelung umrichterge- [14] R. Gabriel, W. Leonhard, and C- Nordby, "Field oriented control
speister Drehfeldmaschinen," presented at the IFAC Symp. Con- of a standard a.c. motor using microprocessors," presented at the
trol in Power Electronics and Electrical Drives, Dusseldorf, 1974. IEEE-IAS Annu. Conf. Rec., 1979.
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. IA-19, NO. 3, MAY/JUNE 1983 363

[15] J. Holtz, R. Venkataraman, and B. Ramaswami, "Electronic ana- has been a Full Professor at TH Darmstadt. His fields of interest include
log slip calculator for induction motor drives," IEEE Trans. Ind. power electronics, control of drives, and HVDC transmission, especially
Electron. Contr. Instrum., vol. IECI-27, 1980. its converter and system and control aspects.
[16] G. Mader, "Regelung einer Asynchronmaschine unter alleiniger
Verwendung an den Klemmen messbarer Grossen" ("Control of an
induction machine based on only such quantities which are meas-
urable at the terminals"), Diss. Darmstadt, 1981.

Robert Joetten was born in Boerfink, Germany,

in 1920. He received the Dipl.-Ing. and Dr.-Ing. Gerhard Maeder was born in Bad Homburg,
degrees in electrical engineering from Tech- Germany, in 1952. He received the DipI.-Ing.
nische Hochschule Darmstadt, in 1949 and 1953, and Dr.-Ing. degrees in electrical engineering at
respectively. Technische Hochschule Darmstadt, in 1977 and
He served in the Luftwaffe for seven years, 1981, respectively.
including the war. After 1953 he worked for ten He worked as a Teaching and Research Assist-
years as a Development Engineer in the power ant at the same institute. Since the fall of 1981 he
electronics factory of AEG-Telefunken, Berlin. has worked as an independent electrical engineer.
He became Head of the development branch for
controlled plant, especially drives. Since 1963 he

A Comparison of PWM Strategies for Inverter-Fed

Induction Motors
JOHN M. D. MURPHY AND MICHAEL G. EGAN

Abstract-Several sophisticated or "optimum" modulation strate- specific low-order harmonics are suppressed or total harmonic
gies have been suggested for voltage source pulsewidth modulated content is minimized [1] -[3]. These optimized PWM strate-
(PWM) inverters for ac motor control. These modulation strategies gies are extremely difficult to realize with conventional
may suppress specific low-order harmonics or minimize total har-
monic content and have been successfully implemented in practical analog circuitry, but they can be effectively implemented
drive systems. The effectiveness of these PWM techniques in mini- with modern microprocessor-based control techniques [4],
mizing harmonic losses and reducing torque pulsations is investigated [5]. Conventional modulation strategies which have been im-
analytically, and their performance is compared with that of the usual plemented by means of complex analog circuits may now be
sinusoidal or subharmonic PWM approach. The influence of skin more effectively realized using a look-up table accessed by a
effect on rotor 12R copper loss is taken into consideration, and har- microprocessor or digital hardware. In an ac motor drive, the
monic core losses are compared. Peak current is also an. important
factor in inverter design, and the various modulation strategies are modulation strategy which is most appropriate to a particular
again compared on this basis. Fourier analysis techniques are used in portion of the speed range is readily selected. It is, therefore,
order to allow skin effect phenomena to be taken into consideration, of interest to compare the different modulation techniques
and performance criteria are developed to allow comparisons of wave- available with regard to the additional harmonic losses in the
form quality in respect of harmonic copper and iron losses.
motor and the pulsating torques developed.
For the purposes of comparison, it is assumed that a
INTRODUCTION standard 50- or 60-Hz induction motor is fed from a standard
OLTAGE SOURCE pulsewidth modulated (PWM) inver- ac supply network by a frequency converter circuit as shown
Vters for ac motor control have conventionally employed in Fig. 1. The ac supply is rectified_ to a fixed dc voltage
square wave or sinusoidal PWM strategies. In recent years, by the diode bridge rectifier and converted to variable-fre-
more sophisticated techniques have been suggested in which quency ac by the PWM inverter, which also controls the ampli-
tude of the fundamental output voltage. If the inverter gen-
Paper IPCSD 83-5, approved by the Industrial Drives Committee of
erates an unmodulated six-step voltage waveform, motor
the IEEE Industry Applications Society for presentation at the 1982 operation at rated voltage and frequency is possible. Constant-
Industry Applications Society Annual Meeting, San Francisco, CA, torque operation is obtained below base frequency by modu-
October 4-8. Manuscript released for publication January 31, 1983. lating the output voltage waveform from the PWM inverter
The authors are with the Department of Electrical Engineering, Uni-
versity College, eork, Ireland. so that the fundamental component of the output voltage is

0093-9994/83/0500-0363$01.00 ©) 1983 IEEE