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374

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,

VOL. 42,

NO. 4, AUGUST 1995

Torque Capability and Control of a Saturated

Induction Motor Over a Wide

Range of Flux Weakening

Horst Grotstollen,

Member, ZEEE, and Josef

Wiesing

Abstract-The 6rst part

of

this paper covers an investigation of

the maximum torque which an induction motor with saturated air

gap inductance

can

generate over its permittedspeed range, when

voltage as well as current are limited. From the investigation

three regions

of

operating speed are identified, based

on

imiting

quantities which determine the maximum obtainable torque.

In each of these regions a different control strategy must be

applied. When maximum torque is not

required,

efficiencycan be

optimized but this strategy should not be applied at low torque

levels when good dynamic performance is required. The second

part illustrates how a modifiedrotor fluxoriented control strategy

is applied

to

achieve full utilization of the torque capability over

the whole speed range. Several measures for improving dynamic

and transient behavior of the drive

in

the flux weakening region

are suggested. Performance of the new control strategy is verified

by experiments.

ZSdlim, iSqlim

VSdlim, VSqlim

Rnom, Rapt

NOMENCLATURE

Components of stator current vector in the

rotor flux oriented frame.

Magnetizing current.

Components of stator voltage vector in the

rotor flux oriented frame.

Electromagnetic torque.

Rotor flux.

Angular speed of motor.

Rotational speed.

Amplitudes of maximum stator current and

maximum stator voltage.

Limits of stator current components.

Limits of stator voltage components.

Nominal value and optimal value of rotor

flux.

Maximum torque (depends on speed).

Maximum mechanical power.

Saturated mutual inductance.

Leakage inductances of stator and rotor

winding.

Resistances of stator and rotor winding.

Number of pole pairs.

Manuscript received March 23, 1994; revised January 6, 1995.

H. Grotstollen is with the Departm ent

of

Electrica l Engineering, University

of

Paderbom, D-33095, Paderbom, Germany.

J. Wiesing was with the Department

of

Electrical Engineering, U niversity

of

Paderbom, D-33095, Paderbom, Germany. He is now with LUST Antriebs-

technik, D-3563

1

Lahnau,

Germany.

IEEE Log Number 9412497.

I.

INTRODUCTION

N

MANY

applications, electrical drives have to deliver

I onstant torque (rated or maximum) at low speeds only,

and a decrease of torque and operation at almost constant

power is acceptable at medium and high speeds. In these cases,

weakening

of

the motor flux is a suitable control method which

results in an economic rating of the power converter and motor.

If the maximum torque and power are required over a wide

range of flux weakening, the following aspects need to be

considered: First, the calculation of the obtainable torque as

well as the design of a control scheme which makes it possible

to reach maximum torque over the whole speed range must

take the nonlinearity of the magnetization curve into account

[l]. Second, the flux weakening region has to be divided

into two parts since the current limit has to be considered

at medium speed only, but not at high speed. Third, when

maximum torque is not required efficiency can be optimized.

Fourth, during transients ringing or overshoot of the currents

can appear due to the limitations existing in the control loops.

Interest in the influence of magnetic saturation on the

performance and control of induction motors as well as the

operation of these motors in the flux weakening region have

increased in recent years: All the phenomena listed above

have been investigated or are at least mentioned by many

authors.

To

achieve satisfactory results, all these phenomena

must be considered simultaneously. Until now, few attempts

were made to achieve this goal.

Many investigations, for example, were devoted to the

influence of the magnetic saturation on the torque capability

[l], [2]and the control [3], [4 ] of the saturated induction motor

when being operated in the basic speed region. In [5],he lower

flux weakening region was considered in addition.

Control of an induction motor with weakened flux has also

been investigated and three methods for establishing the flux

were suggested: a) The flux reference can be set according to a

fixed flux-speed characteristic; or b) it can be calculated from

simplified motor equations, which can be improved through

consideration of additional variables; or c) it can be provided

by a voltage controller, which sets the flux in such a way

that the voltage required by the motor matches the voltage

capability of the inverter [ 6 ] . The strategy c) seems to be

optimal because it is not sensitive to parameter variations.

When this strategy is applied a torque break-off will appear at

high speed. For this reason, different control strategies were

0278-0046/95 04.00 0 1995 IEEE


2/8

GROTSTOLEN

AND WIESING TORQUE CAPABILITY AND CONTROL OF A SATURATED INDUCTION

MOTOR

Fig.

1. Rotor flux oriented model

of

the induction motor

375

1

combined in [7]: In the lower flux weakening region, the

flux reference is provided by a voltage controller while it is

varied inversely to the actual speed when the critical high-

speed region is entered. Until now, this simple flux-speed

characteristic is frequently used [8] even though being not

optimal, especially when the control is related to the rotor flux.

The reason for this is demonstrated in

[9]

where the differences

between the lower and the upper flux weakening regions are

illustrated graphically but where, as in [6]-[8], saturation is

not considered.

The possibility of optimizing efficiency at partial load was

discussed for the basic speed region, and implemented in a

field oriented controller which takes magnetic saturation into

account

[ 5 ) .

In [lo], optimization of either torque or efficiency

or a weighted optimization of both quantities, was suggested

for the unsaturated machine. It is, however, not clear why the

results of the optimization depend on the choice of flux (stator,

air gap, or rotor) by which the model of the motor is oriented.

Last but not least, the mechanisms by which current over-

shoot can occur in the flux weakening region where the

voltage is limited were only investigated systematically in

[

1

11

Various countermeasures

are

employed to minimize

this phenomenon: Either the voltage component of the

d

axis is given priority to assure a good flux control, or both

components of the voltage vector are decreased by the same

ratio to avoid phase errors. For both methods there exist

operating conditions for which the response of the current

control is neither predictible nor satisfactory.

In this paper, all aspects concerning operation of an in-

duction motor in a speed region limited only by mechanical

stress

are considered together and based on this a rotor flux

oriented control strategy is presented refemng to [ l l ] and

[12]:

In Section 11, the torque capability of the saturated

motor is determined for the whole speed range considering

constant limits of current and voltage. At the same time,

control strategies

are

obtained which allow the utilization of

the maximum attainable torque at all speeds. The possibility

and the suitability of optimizing the efficiency at partial load

is discussed in Section JD.

n

Section IV, all basic knowledge

derived earlier is implemented in a rotor flux oriented control

scheme which is applied in combination with a voltage source

PWM inverter. Phenomena which can disturb

the

control are

explained and countermeasures are suggested. In Section V,

the performance of the new control scheme is verified by

experimental results obtained with a 3-kW spindle drive, for

which the maximum speed is more than five times the rated

speed.

11. TORQUEAPABILITY

OF THE

INVERTER-FED

INDUCTION

MOTOR

In contrast with

[lo],

the torque capability and the efficiency

of the drive are assumed to be inherent characteristics of the

power sections which do not depend on the type of inverter or

on the method of investigation. This is why the investigation

of the power section can start from the dynamic model of

the induction motor in

the

rotor flux oriented frame [13] (see


3/8

3 6

IEEE

TRANSACTIONS

ON INDUSTRIAL ELECTRONICS, VOL. 42, NO. 4,

AUGUST

1995

701

.

t

Magnetizing current (A )

2 . 5

5 7.5

10

12.5

15 17.5

20

TABLE

I

DATAOF INVESTIGATED

SPINDLE

RIVE

Unit Parameter

Inverter: dc link voltage

maximum phase voltage (amplitude)

usmax

maximum current (amplitude)

ismax

rated current (amplitude) isnom

maximum

speed

R M ~ ~ ~

stator resistance

Rs

rotor resistance RR

stray inductances Ls = L R ~

mutual inductance (nominal)

Lmnom

Motor:

rated power (data sheet)

300

v

173 V

38 A

3 kW

21 A

SO00 r/min

0.212 R

0.221 R

1.24

mH

30.1 mH

inertia (load included) 0.04 kgm2

ig. 2.

proximative curve)

Mutual inductance

of

investigated motor (measured points and ap-

Fig. 1) which is used afterwards for control. From this model

the well-known steady-state equations are derived and the

stator flux as well as all frequency variables can be eliminated.

This results in the following equations which establish the

components of the stator voltage

V S d ,

usq he torque TM , nd

the rotor flux I + JR as functions of the stator current components

i S d ,

isq and the angular motor speed W M

= 27r

.n M

(3)

R

= Lm i S d .

4)

Notice that all voltage and current quantities are amplitudes,

R s ,

R R .

and L s , , L R ~re the resistances and the stray

inductances of the stator and the rotor winding, and

Pp

is

the number of pole pairs. The mutual inductance L , which

is related to the flux

of

the air gap is assumed to be saturated

and to depend on the magnetizing current

i

by

5 )

The magnetizing current depends on the stator current com-

ponents according to

L , = L , ( i m ) M L , L a e - a a m- Lpe-Pim

.

The current dependent mutual inductance

L ,

=

L m ( i , ) of

the motor investigated is shown in Fig.

2.

In Table I, all the

data of the 3-kW pindle drive to which all results of

this

paper refer are given. Notice that a second exponential term is

used in

(5)

to model the increasing slope of the magnetization

curve

R

=

~ ( i , )

at low currents which causes the almost

linear section of the curve to be offset from the origin. This

measure has proved to be important for modeling operation at

very high speed where flux becomes very small.

100

Rotor flux

(Vs)

Fig . 3. Current limit curve for is =

ismax.

Unsaturated motor:

Lm = L,,,, = 30.1

mH.

Saturated motor: L , according to

7).

and

L,

=

10 mH, La = 6 3

mH,

L p

=

30 mH,

I

= 0.07 1 A-', and

p = 0 . 77A - l ) .

At first, the torque generated when only the current limit is

considered will be investigated: Using the secondary condition

i z d

z q

= 2 = const. where

is

=

ismax

7)

and (3) through (6), the flux and the torque are calculated

that appear when the decomposition of the current into its

d- and q-components is varied. Since the voltage equations

do not need to

be

considered, unique results are achieved

which are independent of speed. In Fig.

3,

the torque of the

investigated drive is plotted as a function

of

the flux. This

is because the flux magnitude will be used as reference for

the suggested flux oriented control scheme. Curves with and

without considering saturation are given to demonstrate the

magnitude of the error which is made when saturation is

ignored. In particular it becomes obvious that under conditions

of saturation an accurate setting of flux is required when

maximum torque must be achieved. Evidently the error which

is made by neglecting saturation depends on the current limit

and will be smaller when the case is = snoms investigated.

In the following text, the torque curve of Fig. 3is referred

to as the current limit curve and the area below this curve

in which the permitted current is not exceeded is called the

permitted operating area.

In the next step the torque is investigated by considering

only the voltage limit established by

v z d

vgq

=

=

const. (8)

lux and torque

of

the motor that would appear when the

maximum voltage is applied are calculated for varying de-


4/8

GROTSTOLLEN AND WIESING: TORQUE CAPABILITY AND CONTROL OF A SATURATED INDUCTION MOTOR

311

Rotor flux

(Vs)

Fig. 4. Borders of operation area defined by voltage and current limit curv es.

Voltage limit curves us

= usmax: 1 1

for

n =

n =

1150 r/min, 1.2

for n = n2 = 1490 r/min,

1.3

for n = ng

= 2500

r/min, 1.4 for

Z = n4 = 5250 r/min,

1.5

for n = n

=

7000 r/min. Current limit cu rve

for is

= ismax):

for

any

speed.

composition of the voltage into its d- and q-components. This

calculation cannot be performed analytically because (1) and

(2) have to

be

considered, and cause the result to depend on

speed. In Fig. 4, a set of five torque-flux characteristics (curves

1.1 through 1.5) are given, which are obtained when the speed

is set to five constant values

721

through

725.

These curves

are referred to as voltage limit curves and mark the upper

border of the possible operating region which the drive cannot

exceed, due to the limitation of the inverter voltage. From

the well-defined peak of each curve the maximum attainable

torque at the related speed without consideration of current

limitation, can be seen. This torque is almost identical to the

well-known breakdown torque of the line-fed induction motor

which is calculated under constant frequency conditions. The

possible operating region is further decreased when the speed

is increasing.

Following these considerations, the true torque capability

of a drive can be determined by considering the voltage and

current limits simultaneously. For this purpose the current

limit curve of the saturated motor is shown again in Fig. 4.

Now, for each speed the area in which operation is permitted

and possible, and the point in this area where the torque

is a maximum can be seen easily. As a consequence, the

maximum torque T M ~ ~nd the corresponding flux JRopt

can be calculated. But in doing so, it becomes obvious that

three speed regions can be identified as follows:

Basic speed region, refer to Fig. 4: At low speeds (for ex-

ample

n l )

he current limit curve 2 or at least the peak of

this curve is situated below the voltage limit curve (curve

l. l) , i.e., inside the possible operating region. Since the

permitted operating area must not be exceeded, the peak

of the current limit curve determines the maximum torque.

Thus the maximum torque 7 ' ~ ~ ~oes not depend on

the actual speed, and it is achieved when the drive is

operated with a flux

JROpt

which is constant and which

is established to be the nominal flux

J R ~ ~ ~

f the motor.

The border of the basic speed region is reached at

speed 122 at which the associated voltage limit curve 1.2

intersects the peak of the current limit curve.

Lower flux weakening region, refer to Fig. 4: At medium

speeds (for example, at speed

123)

an intersection of the

corresponding voltage limit curve (curve 1.3) and the

current limit curve exists as in

the

case for speed 722 But

now the peak of the current limit curve is situated above

the voltage limit curve, i.e., outside the possible operating

region and cannot be attained. Therefore the maximum

torque which is permitted and possible at speed 723 is

achieved when the drive is operated at the intersection

of both limiting curves where the voltage as well as the

current are maximal, and where, consequently, the max-

imum apparent power is applied to the machine. When

the speed varies, the point of maximum torque shifts on

the current limit curve 2 and flux weakening has to be

applied when the speed is increased ( JRopt < JRnom).

A simple strategy to reach maximum torque regardless of

the actual speed is to apply maximum current to the motor

with as much flux generating d-component as permitted

by the limited voltage. An important advantage of this

control strategy is that the result does not depend on

any parameter of the machine nor on

the

actual value

of the maximum inverter voltage nor on the flux (stator

or rotor or air gap flux) by which the reference frame of

the control is oriented.

The upper border of the lower flux weakening region

is reached at speed

n4

where the peak of the voltage limit

curve 1.4 has reached the current limit curve.

Upper flux weakening region, refer to Fig. 5: At high

speeds (for example

725

the peak of the voltage limit

curve (curve 1.5) or even the complete voltage limit

curve is situated below the current limit curve. Conse-

quently, the maximum torque is now determined by the

voltage limit only and appears at the peak of the voltage

limit curve. As another consequence the control strategy

must be changed. Otherwise the break-off phenomenon

mentioned in the introduction appears, due to the fact

that the intersection of the current and the voltage limit

curves, being the setpoint in the lower flux weakening

region is shifted to very low torque values and vanishes

with increasing speed. As a likely method, the flux

reference can

be

established by a flux-speed characteristic

which, as justified in the following, should not

be

the

frequently used hyperbola. But first a particularity should

be mentioned: In the basic speed region and in the lower

flux weakening region, the only differences in quantity

appear when the motor state changes from driving to

braking. In contrast for many drives the upper flux

weakening region does not exist under braking conditions,

and this is the case with the investigated spindle drive.

Experience has shown that this fact can be ignored by the

control without achieving lower torque than under motor

operation. Thus, a discussion of details can be dropped.

In Fig. 6, the optimum flux and the maximum mechanical

power which is related to the maximum torque of the saturated

induction motor are plotted

as

functions of the speed. For

comparison, a first order hyperbola and a straight line are

shown which are the corresponding curves of an equivalent dc

motor. From the power curves essential differences between

both motors can be seen which are caused by three phenomena:

When the drive enters the flux weakening region higher torque


5/8

378

0. 02

O . b 4

0.b6

0. 08

0:: 0. 12

0. 1\4

Rotor flux (Vs)

Fig.

5. Borders of

operating area (extract from Fig.

4).

10000, 0 . 5

2000 4000 6000

Sddb

Rotor Speed

(rpm)

Fig.

6 . Optimal

flux

and

maximum mechanical

power.

and power can be achieved than with an equivalent dc motor

because the decrease of the flux generating current iSd makes

it possible to increase the torque generating current isq.This

phenomenon is reinforced strongly by the magnetic saturation

which enforces a large decrease in the flux generating current

for a small decrease in the flux. At high speeds, however, the

voltage consumption

of

the leakage inductances which does

not exist in dc machines causes a reduction of the current and

the obtainable torque. From the flux curves can

be

seen that

weakening the flux according to a first order hyperbola is not

optimal for an induction motor. The loss of torque and power

will be up to

35%

as

shown in

[ll].

Now, before implementing this knowledge about maximum

torque and how to achieve it in a control, the conditions at

partial load will be discussed briefly.

In.

FLUX

CONTROL T PARTIALOAD

When the drive is operated in the flux weakening region and

when the maximum torque is not required, the operating point

can

be

moved on a horizontal (see dashed line in Fig.

5 )

which

is limited by the voltage limit curve at the right and by the

current limit curve at the left. The possibility of optimizing

the efficiency therefore exists. Efficiency is optimized by

operating the drive at the voltage limit, since the flux is as

high as possible and the required torque is generated with

minimum current amplitude and minimum copper losses. It

should

be

remarked that iron losses and additional losses are

not taken into account. This assumption of negligible losses

is valid because of the following two opposite phenomena:

When speed is increased, iron losses are increased, due to the

frequency increase, at the same time the losses are decreased

due to flux weakening.

IEEE TRANSACTIONS

ON

NDUSTRIAL ELECTRONICS, OL. 42, NO. ,

AUGUST

1995

When efficiency optimization is applied without any limi-

tation, large changes of the required torque will require large

corresponding flux changes. These changes progress slowly

because the flux control is slow by nature and the voltage

is at its limit. For this reason efficiency optimization by flux

variation should

be

limited to the region where the torque and

the current are high and where it is important to minimize the

copper losses.

Iv.

CONTROL

SCHEME

BASED

O N

ROTOR LUX

ORIENTATION

The control strategies derived in Sections II and III were

implemented in the digital control of a spindle drive consisting

of an induction motor and a voltage source PWM inverter. As

a control strategy, rotor flux orientation was combined with

the basic scheme of

[6], 7]

for flux weakening (see Fig.

7).

With regard to the following, only the controller section is

of interest. It consists of two current controllers, the reference

signals for which are delivered by a speed controller (adaption

to variations of flux is made as usual and not shown in detail)

and a flux controller. The flux reference is generated by a

voltage controller (which in fact is controlling the modulation

index). The voltage control has

two

very useful features:

On

the one hand, it tends to increase the flux as ong as the voltage

required by the motor does not exceed the value which is

set by the voltage reference U In this way, it is aimed to

operate at the voltage limit. On the other hand, the flux is

reduced automatically when the voltage required by the motor

becomes too high, i.e., when overmodulation is imminent

or present.

In

this fashion, the voltage requirement of the

motor is adjusted automatically to the voltage capability of the

inverter by variation of the flux in the flux weakening region.

Unfortunately this

task

is related to the poor dynamics of the

flux control and problems can be expected during transients.

The particularities of the control presented here are imple-

mented in the basic scheme, through special handling of the

limitations. Unless otherwise explicitly mentioned, no change

in the control scheme takes place when the drive changes from

driving mode to braking. In this way problems which can arise

from changing the control scheme in the upper flux weakening

region are avoided. Results obtained for braking have proven

to be satisfactory over the whole speed range.

Basic Speed Region

In the basic speed region, the voltage controller tends to

increase the flux reference, and operation with the nomi-

nal flux is ensured by limiting

this

signal at the output of

the voltage controller to the corresponding constant value,

Rlim Rnom- TO achieve satisfactory behavior of the drive,

priority is given to the control of the d-component

of

the

current

as

usual.

This

means that the d-component is limited to

the maximum current

iSdlim = ismax

while the limit of the q

component is calculated from

(7)

while considering the actual

value of the d-component: i sql im

=

Jnith the

spindle drive, no loss of performance was observed when the

actual value of

i S d

was replaced by the constant value

&nom

which is related to the nominal value of the flux

Rnom.

In


6/8

GROTSTOLLEN AND WIESING: TORQUE CAPABILlTY AND CONTROL OF A SATURATED INDUCTION MOTOR

319

Fig.

7. Modified scheme of rotor flux oriented control.

this

way the time-consuming on-line calculation of

i sql im

is

avoided.

Flux

Weakening Region

In the flux weakening region, the voltage control loop is in

action and varies the flux in such a way that the amplitude

of the voltage vector

V S

agrees with its reference value

U;

This mechanism is enabled by the d-priority of the current

control and does not depend on the amplitude of the torque

generating current and the torque. For this reason the flux

is increased and the efficiency is optimized automatically

when the maximum torque is not required. With regard to

the dynamic behavior, the increase of flux should be limited

as discussed above. As a result the limiting flux value is no

longer constant but it is decreased inversely proportional to

With respect to transients, a margin in the inverter output

voltage is indispensible. That is why the reference value of the

voltage control has to be smaller than the available voltage of

the inverter. But with the new control scheme the margin can

be as small as 5

V,

i.e., 3 of the rated voltage and therefore

almost negligible.

In the upper flux weakening region, the control strategy

has to be changed and for this investigation a precalculated

characteristic is used as in [7]. In contrast to [7] a change of the

control scheme with all its related problems is avoided and the

voltage controller is not replaced by a flux-speed characteristic.

Instead, the limit i s l i m of the stator current is reduced to

exactly that speed dependent value which corresponds to

the breakdown point which also forms the maximum torque

operating point. By this measure the current limit curve (curve

2 of Fig. 5) is lowered as far as necessary to make it cross

the voltage limit curve (for example curve

1.5)

at its peak.

The basic control scheme of the lower flux weakening region

can therefore be used without any change; in particular, the

W M n o m

W M

the speed Rlim

= Rnom

p

flux limiting signal which has to limit the region of efficiency

optimization can continue to perform this task. The current

limiting signal is thus implemented as a precalculated current-

speed characteristic i s l i m ( W M ) < ismax f course, the

robustness against parameter variations is now lost as is the

case with any off-line [7] or on-line

[9]

calculated flux-speed

characteristic. In contrast to a flux-speed characteristic, the

implemented current-speed Characteristic does not depend on

the flux used for orientation of the control frame.

Transient Behavior

of

the Voltage and the Current Control

Behavior of the control strategy in the flux weakening region

was improved considerably by

the

handling of two limitations

which determine the operation of the voltage control loop.

a) Optimization of the dynamic behavior of the voltage

control loop is complicated by the extremely unusual

plant. Two parallel loops exist in the control section.

The first loop is formed by the controllers only and

has almost no delay. The second loop includes the

closed flux control loop, which includes the machine,

and therefore has a large delay.

As

a first measure, the

input signal of the voltage controller (the voltage error)

is limited to

5

V.

This

measure prohibits unnecessary

stimulations of the voltage control loop as might be

caused by the q-current control. Such stimulations are

initiated by the speed control and can disturb the voltage

control severly because of its poor dynamic properties.

In addition, the voltage controller is made adaptive. The

gain is varied in proportion to the flux amplitude (not

shown in detail).

b) Current overshoot is avoided under all operating condi-

tions by the use of a new strategy for limiting the voltage

components which are applied to the inverter. The new

strategy results from an investigation into the origin of

the overshoot phenomenon, which is explained referring

to Fig. 1.


7/8

380

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,

VOL.

42,

NO.

4, AUGUST

1995

7.0

-7.0--

-

14.0--

s

-21.0::

-

-35.0..

42.0-

gow

42.0

00

A M :

: :

-

ni

S O

2 8 0

10

-

/

ow

140

00

7.0

1:O

2 0

3 0 4:O

5 0

-15M

Time (s)

(a)

0.7

I

0 1

0 0

~~

1 0

2 0 3 0

4 0

5 0

Time

s)

(b)

Fig.

8. Acceleration from

n~

= 100 r/mh to

n~

= 8000

r / h .

(a)

Reference and actual values

of

s p e e n

and q-current

asq.

b)

Reference

and actual value of

rotor flux

R.

When the speed and the frequency signals are assumed to be

positive and of sufficient amplitude the following conditions

exist, which

are

typical for the flux weakening region: Because

of the high frequency, the d-voltage WSd is determined by

the coupling voltage V,d and therefore the sign of us is

opposite to the sign of the q-current isq.Consequently, when

the motor is driving the load, WSd

< 0

(due to isq

> 0)

and i S d

>

0 (always true) hold which implies that the d-

voltage and the current which it has to control have opposite

signs. Consequently, '1)Sd has to be made more negative,

i.e., the amount of V s d has to be increased, when i S d has

to be decreased. The same requirement exists and must

be

satisfied under all conditions if an increase of

i S d

has to

be

prevented, i.e., if i S d shall be controllable. That

is

why the

voltage component V s d is given priority (V Sdl im

=

usmax .

V S q l i m

= J-

when the motor is driving the load

When the motor is braking, the critical condition of a

current and the controlling voltage having different signs can

appear in the q-axis. At high speeds, voltage component

usq

is determined by UE and so

usq

> 0 holds. Consequently, a

critical state is reached where an increase in

usq

is required,

when the magnitude of isq has to be reduced while

isq

< 0

or

when an increase of the negative current must be prevented.

Thus under braking conditions

MM

. W M < 0 ) voltage

component usq is given priority ( w s q l i m = usmax, 'USdlim

=

( M M . W M > 0).

V. EXPERIMENTAL RESULTS

To demonstrate the operation and the performance of the

new control scheme, the spindle drive was investigated with

an inertial load.

7 0

I

350i42

+

.0015

Time (s)

b)

Fig.

9.

Dynamic response of qcurrent control

at

braking

and

weakening region n ~6OOO dmin) . (a) Voltage components

the

same ratio.

(b) Voltage components reduced with q-priority.

in

the

flux

reduced by

At first, acceleration from 100 r/min to maximum speed was

investigated. In Fig. 8(a),

the

reference and the actual values

of the speed

n M

and the torque generating current component

isq are shown. In Fig. 8(b), the corresponding flux values can

be seen. Notice, that the

flux

is increased when the drive is

no longer accelerating because maximum torque is no longer

required. In this way, efficiency is improved as discussed in

Section III. During the transient a slight oscillation is caused

by the

flux

model in which saturation is not considered.

The improvement achieved by the new method of limiting

the voltage components is demonstrated in Fig. 9. Here the

step response of the q-current control is shown, which appears

when the motor starts braking. An overshoot of the current is

observed when the voltage limitation is performed by reducing

both voltage components by the same ratio (see Fig. 9(a)). The

overshoot is avoided,

as

visible in Fig. 9(b), when priority is

given to the q-component.

Finally, the effectiveness of limiting the voltage error is

demonstrated in Fig. 10. If no limitation is implemented, a

strong ringing of the voltage control happens which can be

observed from the reference value and the actual value of the

flux (see Fig. lO(a)). No ringing appears when the voltage

error is limited to an amount of 5 V (see Fig. 10(b)).

VI.

CONCLUSION

When the torque capability of an induction motor drive

having a wide range of

flux

weakening is investigated, sat-

isfactory results cannot be achieved without considering the

magnetic saturation and without distinguishing three speed

regions in which the maximum torque is determined by

different quantities. The same aspects have to

be

considered

during the design of a control scheme which achieves the


8/8

GROTSTOLLEN AND WIESING: TORQUE CAPABILITY AND CONTROL

OF

A SATURA TED INDUCTION MOTOR 381

006 012 018 0.24

03

0.0

t

Time

(s)

(a)

0

7

006 012

018

024

03

0 0

Time

(s)

(b)

Fig.

10.

Dynamic response of voltage control at acceleration started from

n~

= 100 r/min. (a) Voltage error not limited. (b) Voltage error limited to

5

v.

maximum obtainable torque. Therefore a closed loop flux

control, the reference of which is set by a closed loop voltage

control is a good choice. This control scheme which was

introduced in

[7]

for the lower flux weakening region ensures

utilization

of

the maximum torque and optimization of the

efficiency at partial load automatically. It is also robust against

parameter variations which can, for example, be caused by

saturation. Special handling of the limiting quantities makes it

possible to adapt the control strategy to the particularities of

all speed regions without changing the basic control scheme

and to suppress overshoot and ringing of the control under

all operating conditions. When the drive is in the braking

mode, only two speed regions exist but this does not require

a change of the control strategy. The new control strategies

were tested experimentally on a spindle drive employing a

DSP-based digital control.

I

REFERENCES

[l] R. D. Lorenz and D. W. Novotny, Saturation effects in field oriented

induction machines, IEEE Trans. Ind. Applicar., vol. 26, no. 2, pp.

[2] 0 Ojo and V. Madhani, Steady state performance evaluation

of

saturated field oriented induction motors, in Proc. 1990 IEEE

Ind.

Applicat. Soc. Annu. Meeting,

pp. 55-60.

[3] F. Khater, R. D. Lorenz, D. W. Novotny, and K. Tang, Selection of

flux in field-oriented induction machine controllers with consideration

283-289, 1990.

of magnetic saturation effects, IEEE Trans. Ind. Applicat., vol. IA-23,

pp. 276282, 1987.

[4] P. Vas and M. Alakula, Field oriented contr ol of saturate d induction

machines,

IEEE Trans. Energy C onversion,

vol.

5 ,

no. 1, pp. 218-224,

Mar. 1990.

[5]

J

Fetz and K. Obayashi, High efficiency induction motor drive with

good dynamic performance for electric vehicles, in Proc. I993 Power

Electron. Specialists Con ,

pp. 92 1-927.

[6]

R. Gabriel, W. Leonhard, and

C.

Nordby, Regelung der stromrichterge-

speisten Asynchronmaschine mit einem Mikrorechner, Regelungstech-

nik,

vol. 27, no. 12, pp. 397-386, 1979.

[7] H. Schierling , Selbsteinstellendes und selbstanpass endes Antriebsregel-

system fr die Async hronm aschin e mit Pulswechselrichter, Doctors

thesis, Technische Hocbschule Darmstadt, 1987.

[8] Y.-T Kao and C.-H. Liu, Analysis and design of microprocessor-based

vector-controlled induction motor drives, IEEE Trans. Ind. Electron.,

vol. 39, no. 1 Feb. 1992.

[9] S.-H . Kim,

S.-K.

Sul, and M.-H. Park, Maximum torque control of an

induction machine in

the

field weakening region, in

Proc. 1993 IEEE

Ind. Applicat. Soc. Annu. Meeting, vol. 1, pp. 57C577.

[ lo] 0 Ojo, I. Bhat, and G. Sugita, Steady-state optimization of induction

motor drives operating in the field weakening region, in Proc. 2993

Power Electron. Specialists Con , pp. 979-985.

[ l l ] J Wiesing and H. Grotstollen, Field oriented control of an asyn-

chronous motor with a very wide region of flux weakening, in

Proc.

IEEE Int. Symp. Ind. Electron., vol. 2, pp. 606-610, 1992.

[121 J. Wiesing, Betrieb der feldorientiert geregelten Asynchronmaschine

im Bereich oberhalb der Nenndrehzahl, Doctors thesis, University of

Paderborn, 1994.

[131 W. Leonhard, Control of Electrical Drives. Berlin: Springer-Verlag.

1985.

Horst Grotstolen (M95) received the 1ng.-

grad. from Staatliche Ingenieurschule, Duisburg,

Germany, in 1960, the Dip1.-Ing. from Rheinisch-

Westfaelische Technische Hochschule, Aachen,

Germany, in 1965, and

the

doctorate degrees

in electrical engineering from

the

Technische

Universitaet, Berlin, Germany, in 1972.

He habilitated at the Universitaet Erlangen-

Nuemberg, Germ any, in 1982. From 1965 to 1970,

he joined AEG, where he developed electrical

servo drives in the Frankfurt Research Center, and

investigated drive problems in the Department of Industrial Equipment

in

1970. From 1973 to 1981, he was the Chair for Electrical D rives and Chief

Engineer, University

of

Erlangen-Nuemberg, where he was teaching the

subjects of electrical machines and power electronics.

His

area of research

was

servo

drives with permanent magnet synchronous motors. Since 1981, he

has been a professor in the Department of Electrical Engineering, University

of

Paderborn, Germ any. His current research interests are

in the

digital control

of ac drives and in switch mode power supplies.

Josef

Wiesing was born in 1959 in Delbrueck,

Germ any. He received the Dip1.- Ing. and Dr.-Ing. in

electrical engineering from the University of Pader-

bom, Germany, in 1986 and 1995, respectively.

Since 1991, be has been employed by LUST

Antriebstechnik, Lahnau, Germany, a drive systems

manufacturer.

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