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876 M. F. Rahman et al.

Substituting the expressions for i

and i

into Eqs. (33.35)

and (33.36),



−



(33.54)



−



(33.55)

Substituting λ

and λ

from Eqs. (33.54) and (33.55) into

the torque equation of Eq. (33.41),

T =



−λ



(33.56)

It is clear from Eq. (33.53) that the rotor ﬂux

determined by i

, subject to a time delay T

which is the

rotor time constant (L

). The Current i

, according to

Eq. (33.56), controls the developed torque T without delay.

Currents i

and i

are orthogonal to each other and are called

the ﬂux- and torque-producing currents, respectively. This

correspondence between the ﬂux- and torque-producing cur-

rents is subject to maintaining the conditions in Eqs. (33.50)

and (33.51). Normally, i

would remain ﬁxed for operation

up to the base speed. Thereafter, it is reduced in order to

weaken the rotor ﬂux so that the motor may be driven with a

constant-power-like characteristic.

Based on how the rotor ﬂux is detected and regulated, two

methods of control are available. One is the more popular

indirect rotor ﬂux oriented control (IFOC) method and the

other is the direct vector control method; both are described

hereafter.

−

∗

∫

Speed

Controller

Current

Controllers

−

−1

1+(L

ref

∗

FIGURE 33.28 Indirect rotor ﬂux oriented vector control scheme.

33.3.4.2 Indirect Rotor Flux Oriented (IFOC) Vector

Control

In the indirect scheme, the relationship between the slip fre-

quency and current i

given by Eq. (33.52) is used to relate

the compensated speed error ω

−ω

to i

. The i

, in turn, is

used to develop to the demanded torque T

∗

according to the

Eq. (33.56). The rotor ﬂux is maintained at the base value for

operation below speed, and it may be reduced to a lower value

for ﬁeld weakening above base speed. The orthogonal relation-

ship between the torque-producing stator current i

and the

ﬂux-producing stator current i

is maintained at all times by

generating the stator current references in the synchronously

rotating dq reference frame, using sine and cosine functions of

angle θ

. This angle is obtained as indicated in Fig. 33.28.

The compensated speed error produces the current refer-

ence i

∗

according to Eq. (33.56). The current reference i

∗

also gives the slip speed ω

, according to Eq. (33.53). The slip

speed ω

is added to the rotor speed ω, to obtain the stator fre-

quency ω

. This frequency is integrated with respect to time

to produce the required angle θ

of the stator mmf relative

to the rotor ﬂux vector. This angle is used to transform the

stator currents to the dq reference frame. Two independent

current controllers are used to regulate the i

and i

currents

to their reference values. The compensated i

and i

errors

are then inverse transformed into the stator a–b–c reference

frame for obtaining switching signals for the inverter via PWM

or hysteresis comparators.

It is clear that this scheme uses a feedforward scheme, or

a machine model, in which the current reference for i

also determined by the rotor time constant T

. This is also

indicated in Fig. 33.28. The rotor time constant T

cannot be

expected to remain constant for all conditions of operation.

33 Motor Drives 877

1500 rev/min

4 Amp

1.8 s

FIGURE 33.29 Speed and current responses of an induction motor

drive under the IFOC scheme of Fig. 33.28.

Its considerable variation with operating conditions means

that the slip speed ω

, which directly affects the developed

torque and the rotor ﬂux vector position, may vary widely.

Many rotor time-constant identiﬁcation schemes have been

developed in recent years to overcome the problem.

The mandatory requirement for a rotor-speed sensor is

also a signiﬁcant drawback, because its presence reduces

the reliability of the IFOC drive. Consequently, sensorless

schemes of identifying the rotor ﬂux position have also drawn

considerable interest in recent years.

Figure 33.29 shows the transient response of an induction

motor under the IFOC drive scheme of Fig. 33.28. In this case,

the drive accelerates a large inertia load from standstill to the

base speed of 1500 rev/min. It is clear that the overcurrent

transients of Fig. 33.21 are eliminated, while the motor accel-

erates under a constant torque (implied by the constant rate at

which the speed increases) and settles at the ﬁnal speed with

little over- or under-shoot in speed. Clearly, rotor and airgap

ﬂuxes remain constant at all times.

33.3.4.3 Direct Vector Control with Airgap Flux

Sensing

In the direct scheme, use is made of the airgap ﬂux linkages

in the stator d- and q-axes, which are then compensated for

the respective leakage ﬂuxes in order to determine the rotor

ﬂux linkages in the stator reference frame. The airgap ﬂux

linkages are measured by installing quadrature ﬂux sensors in

the airgap, as indicated in Fig. 33.30.

FIGURE 33.30 Quadrature sensors for airgap ﬂux for direct vector

control.

By returning to Eqs. (33.32)–(33.40) in the stator reference

frame and using some simpliﬁcations, it can be shown that

−L

(33.57)

−L

(33.58)

where the superscript s stands for the stator reference frame.

Since the rotor ﬂux rotates at a synchronous speed with respect

to the stator reference frame, the angle θ

used for the co-

ordinate transformations in Fig. 33.27 can be obtained from

cos θ

(33.59)

and sin θ

(33.60)

where













The control of torque via i

and the rotor ﬂux via i

, subject

to satisfying conditions (33.50) and (33.51), remain as indi-

cated in Fig. 33.28, according to the basic principle of vector

control.

The requirement of airgap ﬂux sensors is rather restrictive.

Such ﬁttings also reduce reliability. Even though this method

of control offers better low-speed performance than the IFOC,

this restriction has practically precluded the adoption of this

scheme. In an alternative method, the d- and q-axes stator ﬂux

linkages of the motor may be computed from integrating the

stator input voltages.

33.4 Synchronous Motor Drives

33.4.1 Introduction

Variable-speed synchronous motors have been widely used

in very large-capacity (>MW) pumping and centrifuge-

type applications using naturally commutated current-source

878 M. F. Rahman et al.

thyristor converters. At the low-power end, the current-source

SPWM inverter-driven synchronous motors have become very

popular in recent years in the form of permanent-magnet

brushless dc and ac synchronous motor drives in servo-type

applications. There are certain features of three-phase syn-

chronous motors that have allowed them, especially the lower

capacity motors, to be controlled with high dynamic perfor-

mance using cheaper control hardware than is required for

the induction motor of similar capacity. Since the average

speed of the synchronous motor is precisely related to the

supply frequency, which can be precisely controlled, multi-

motor drives with a ﬁxed speed ratio among them are also

good candidates for synchronous motor drives. This section

begins with the performance of the variable-speed nonsalient-

pole and salient-pole synchronous motor drive using the

steady-state equivalent circuit followed by the dynamics of the

vector-controlled synchronous motor drive.

33.4.2 Steady-state Equivalent-circuit

Representation of the Motor

Some of the operating characteristics of variable-frequency

voltage- and current-source driven synchronous motors can

be readily obtained from their steady-state equivalent repre-

sentation, as was the case with the scalar controls of induction

motor drives. Assuming balanced, sinusoidal distribution of

stator and rotor mmfs and an uniform airgap (nonsalient-

pole motor), the per phase equivalent circuit of Fig. 33.31

represents the motor at a constant speed.

The representation in Fig. 33.31 is in terms of the RMS volt-

age V applied to the motor phase winding which consists of

the phase resistance R, synchronous reactance X

(in /phase),

and the per phase induced voltage E

. The back-emf E

devel-

ops in the stator phase winding as a result of rotor excitation

supplied from an external dc source via slip rings or by per-

manent magnets in the rotor. The phasor E

has an arbitrary

jIXs jIXs

jIXs

q-axis

d-axis

(a) (b) (c)

FIGURE 33.32 Phasor diagrams of synchronous motors: (a) under-excited nonsalientpole motor; (b) overexcited nonsalient-pole motor; and

= jwL

V∠0° E

∠d°

∼

FIGURE 33.31 Equivalent circuit of a nonsalient pole motor.

phase angle δ with respect to the input voltage V . This is the

load angle of the motor.

Unlike the induction motor, a synchronous motor may

derive part or all of its excitation from the rotor via rotor

excitation. For small synchronous motors that are used in

the brushless dc and ac servo applications, this excitation is

derived from permanent magnets in the rotor. This is read-

ily and economically obtained with the modern permanent

magnets, thus dispensing with the slip-ring-brush assembly.

The i

R losses in the rotor windings with the external excita-

tion are also eliminated. These magnets also allow considerable

reduction in space requirement for the rotor excitation. For

large synchronous motors, this excitation is supplied more

economically from an external dc source via slip rings or via

an exciter.

The phasor diagrams of Fig. 33.32 may be used to ana-

lyze characteristics of the nonsalient-pole synchronous motor

drive. Since the rotor magnetic ﬁeld may be such that the

motor may develop a back-emf that is smaller or larger than

the ac supply voltage to the stator windings, the motor may

accordingly be under- or overexcited, respectively. The overex-

cited motor will normally operate at a leading power factor,

as is the case in Fig. 33.32b. This is desirable in high-power

applications.

33 Motor Drives 879

In the phasor diagrams of Fig. 33.32c, the stator current I

has been resolved into two components I

and I

, which are

current phasors responsible for developing mmfs in the rotor

d- and q-axes. These representations are in the stator reference

frame, and hence are sinusoidal quantities at the frequency of

the stator supply.

If the voltage drop across the stator resistance is neglected,

which may be acceptable when the stator frequency is near the

base frequency or higher, the developed torque T of the motor

can be found from the phasor relationships of Fig. 33.32. Thus

T =

sin δ =

ωL

sin δ =

3PK

sin δ Nm

(33.61)

for the nonsalient-pole motor (also for the sine wave PM ac

motor with rotor magnets at the surface of the rotor) and

T =



ωL

sin δ +



−L

ωL



sin 2δ



= 3P



sin δ +

2ω



−L



sin 2δ



(33.62)

for the salient-pole motor (also for the interior-magnet motor

in which the rotor magnets are buried inside the rotor). Here

the ﬂux constant of the motor, K

, is the ratio of the RMS

value of the phase voltage E

induced in the stator only due

to the rotor excitation and speed. Note that for a given rotor

excitation, the ratio K

= E

/ω remains constant at all speed.

33.4.3 Performance with Voltage-source Drive

Equations (33.61) and (33.62) imply that if the motor is driven

from a voltage-source supply and if the input voltage to fre-

quency ratio, V–f, is kept constant, the motor will develop

the same maximum torque at all speeds. For the nonsalient-

pole motor, this maximum torque will occur for a load angle

δ = 90

◦

. For the salient-pole motor, this will occur for a

load angle which is also inﬂuenced by the relative values of

and L

At low speed, where the supply voltage V is small, the

voltage drop in the stator resistance may become signiﬁcant

compared to E

. This may lead to a signiﬁcant drop in the

maximum available torque, as given by the torque Eqs. (33.63)

and (33.64), which are derived from the phasor diagrams of

Fig. 33.32. The stator per phase resistance R is now included

in the analysis. The developed torque is then given by

T =

3PE

λX

sin δ +R



cos δ −

λE



(

λX

)

Nm (33.63)

for the nonsalient-pole motor and

T =







R+VE

λX

sinδ+



−X



sin2δ−VRE

cosδ

+λ







(33.64)

for the salient-pole motor where the subscript o refers to

the base quantities and λ refers to the per unit input

frequency f

Equations (33.63) and (33.64) indicate that the maximum

torque that the motor can develop diminishes at low speed

because of the voltage drop across the stator resistance R.

This drop in maximum available torque at low speed can be

avoided by boosting the input voltage at low speed, as indi-

cated in Fig. 33.33a. This voltage boosting is similar to the

IR compensation applied to a variable-frequency induction

motor drive.

Figure 33.33 indicates an open-loop V–f inverter drive

scheme, similar to the scheme for an induction motor drive

in which the RMS stator input voltage is made proportional

to frequency. The speed reference is passed through a ﬁrst-

order ﬁlter, as shown in Fig. 33.33a, so that a large and abrupt

change in the input frequency command to the inverter is

avoided. The ﬁltered speed reference is translated into a pro-

portional frequency reference f

. The voltage reference V

also proportional to frequency reference, but with a zero fre-

quency bias. The variable RMS input voltage V

to the motor

may be obtained from an inverter by SPWM methods or from

a cycloconverter with phase angle control.

1+T

Speed

reference

(a)

max

(b)

max3

max

max3

max2

max1

max2

FIGURE 33.33 (a) V–f controller for an open-loop inverter drive and

(b) T–ω characteristics with a limited maximum δ for constant-power

operation.

880 M. F. Rahman et al.

The available input voltage V

is normally limited by the

available dc-link voltage to the inverter or the ac supply voltage

to a cycloconverter. This limit is normally arranged to occur

at base speed. Above this speed, the stator ﬂux drops leading

to ﬁeld weakening and constant-power-like operation, as indi-

cated in Fig. 33.33b. In some control scheme, the maximum

load angle δ is not allowed to exceed a certain limiting value

max

. By selecting δ

max

, constant-power operation at various

power levels is possible.

33.4.4 Characteristics under Current-source

Inverter (CSI) Drive

A CSI-driven synchronous motor drive generally gives higher

dynamic response. It also gives better reliability because of the

automatic current-limiting feature. In a variable-speed appli-

cation, the synchronous motor is normally driven from a stiff

current source. A rotor position sensor is used to place the

phase current phasor I of each phase at a suitable angle with

respect to the back-emf phasor (E

) of the same phase. The

rotor position sensor is thus mandatory.

Two converter schemes have generally been used. In one

scheme, as indicated in Fig. 33.34, a large dc-link reactor

(inductor) makes the current source to the inverter stiff. The

scheme is suitable for large synchronous motors for which

thyristor switches are used in the inverter. A current loop may

also be established by sensing the dc-link current and by using

a closed-loop current controller that continuously regulates

the ﬁring angle of the controllable rectiﬁer in order to supply

the inverter with the desired dc-link current. It can be shown

that the motor-developed torque is proportional to the level

of the dc-link current.

Current

controller

−T

DC Link

Inductor

DCLlink

ref

DCLink

Converter

Switching

Circuit

−

FIGURE 33.34 Schematic of a current-source inverter (CSI) driven

synchronous motor.

60°120°

FIGURE 33.35 Current waveforms in the dc-link current-source-driven

motor.

The inverter drives the motor with quasi-squarewave cur-

rent waveforms as indicated in Fig. 33.35. The current wave-

forms are switched according to the measured rotor position

information, such that the current waveform in each phase has

a ﬁxed angular displacement, γ, with respect to the induced

emf of the corresponding phase. Because of this, the drive

is sometimes referred to as self-controlled. The angular dis-

placement of these current waveforms (or their fundamental

components) with the respective back-emf waveforms is indi-

cated in Fig. 33.35. Because of the large dc-link inductor, the

phase currents may be considered to remain essentially con-

stant between the switching intervals. The quasi-square current

waveforms contain many harmonics, and are responsible for

large torque pulsations that may become troublesome at low

speed.

In the forgoing scheme, the motor can be reversed eas-

ily by reversing the sequence of switching of the inverter.

It can also be braked regeneratively by increasing the ﬁring

angle of the input rectiﬁer beyond 90

◦

while maintaining the

dc-link current at the desired braking level until braking is no

longer required. The rectiﬁer now returns the energy of the

overhauling load to the ac mains regeneratively.

In another scheme, which is preferred for lower capacity

drives for which higher dynamic response is frequently sought,

phase currents are regulated within the inverter. The inverter

typically employs gate turn-off switches, such as the IGBT, and

pulse-width modulation techniques, as indicated in Fig. 33.36.

Motor currents are sensed and used to close independent

current controllers for each phase. Normally, two current

controllers sufﬁce for a balanced star-connected motor. Three-

phase sinusoidal ac currents are supplied to the motor, the

33 Motor Drives 881

−DC-Link

+DC-Link

≈

−

Look

Table

Variable-

Amplitude

Sinusoidal

Current

Reference

Generation

AC supply

aref

bref

cref

aref

bref

cref

Motor

FIGURE 33.36 Control scheme of the SPWM current-source drive.

amplitude and phase angle of which can be independently con-

trolled as required. The references for the current controllers

are obtained from a three-phase current reference generator

that is addressed by the feedback of the rotor position. The

rotor position is continuously measured by a high-resolution

encoder. In this way, the current references, and hence the

actual stator currents are synchronized to the rotor.

33.4.5 Brushless DC Operation of the CSI-driven

Motor

The torque characteristic of the CSI drive scheme of the fore-

going section can be easily analyzed using the phasor diagrams

shown earlier, if the harmonics in the motor current waveform

are neglected or if the motor current waveforms are indeed

sinusoidal as in the second scheme described earlier. In the

following analysis, it is assumed that the supply current wave-

forms are sinusoidal. It is also assumed that the phase angle

of these current sources with respect to the induced voltage in

each phase can be arbitrarily chosen.

The phase back-emf and the current waveforms and the

phasor diagram of the nonsalient-pole motor are shown in

Fig. 33.37. The phase angle γ between the E

and I phasors and

the RMS value (or amplitude) of I are determined according

to the desired torque and power factor considerations. The

developed torque is found from the phasor diagram to be

T =

I cos γ

= K φI cos γ Nm (33.65)

If the angle γ = 0

◦

is chosen, the familiar dc-motor-like

torque characteristic is obtained. It should be noted from the

forgoing that the developed torque at any speed is independent

of R since a high-gain (stiff) current-source drive is used. Note

also that the ratio E

/ω at any operating speed is proportional

to the amplitude of the stator ﬂux linkage, λ

, due to rotor

excitation. For ﬁxed rotor excitation this ratio is a constant.

Equation (33.65) indicates that the developed torque of a

nonsalient-pole synchronous motor can be controlled by con-

trolling the amplitude of the rotor ﬁeld (ﬁeld control), or

more conveniently, by controlling the amplitude of the stator

phase current. The highest torque per ampere characteristic is

achieved when γ = 0

◦

. Note that the operation with a ﬁxed γ

angle is key to this dc-motor-like torque characteristic.

33.4.5.1 Operation with Field Weakening

If the stator impedance drop is neglected, the maximum E

is largely determined by the dc-link voltage and E

= Kλ

implies that speed ω can be increased by decreasing λ

. Conse-

quently, the operation above base speed is normally achieved

with ﬁeld weakening. In this speed range, because of the

limited dc-link voltage, the rotor ﬁeld must be weakened; oth-

erwise, the amplitude of the phase-induced emf will exceed the

dc-link voltage and current control will not be effective. Field

weakening is a means of keeping this voltage at the rated level

for speeds higher than the base speed.

The ﬂux linkage due to the rotor excitation, λ

, can be

adjusted when a variable rotor supply is available. This may

also be achieved by demagnetizing the rotor mmf by using

882 M. F. Rahman et al.

(a) (b)

q-axis

d-axis

FIGURE 33.37 Phasor relationships of CSI-driven motor: (a) back-emf and current waveforms and (b) the phasor diagram.

q-axis

d-axis

FIGURE 33.38 Field weakening using stator mmf.

the mmf produced by the stator currents. For motors with

permanent-magnet excitation, the latter is the only means

of weakening the λ

. Referring to the phasor diagram of

Fig. 33.38, if I is made to lead E

, the d-axis component of

I, i.e. I

, will lead E

by 90

◦

. The mmf due to I

then opposes

the rotor d-axis mmf. The net rotor ﬂux linkage along the

q-axis is then given by



= λ

(33.66)

where I

is negative when I leads E

. If the airgap is small,

the d-axis component of the armature current may reduce the

rotor ﬂux to the required extent.

33.4.6 Operating Modes

A synchronous motor may be driven with a view to achieving

various operating characteristics, such as power factor com-

pensation, maximum torque per ampere characteristic, and

ﬁeld weakening. The power factor at which a synchronous

motor operates is an important issue, especially for a large

drive. A large angle θ between the input voltage and current

phasors of the motor results in a poor overall power factor.

Operation of the synchronous motor with a CSI which deliv-

ers the stator current waveforms with phase angle with respect

to the respective phase back-emf waveforms that allows inter-

esting power factor compensation possibilities. Consider the

following three cases.

33.4.6.1 Case 1: Operation with I Lagging E

In this case, the motor is under-excited and I lags E

,byan

angle γ, as indicated in Fig. 33.39. The overall power factor in

this case is lagging, since I lags V by an angle θ. The power-

factor angle θ is larger than γ. Note that I

now magnetizes

the rotor ﬁeld.

33.4.6.2 Case 2: I is in phase with E

; Maximum

Torque per Ampere Operation (γ = 0

◦

)

If γ = 0

◦

is used, the motor input current i

is in phase with

the back-emf e

, as indicated in the waveforms of Fig. 33.40a.

From Eq. (33.65), the developed torque is given by

T = K φI (33.67)

Thus, for a ﬁxed rotor excitation, the developed torque is

the highest that can be achieved per ampere of stator current

I. In other words, if γ = 0

◦

is chosen, the drive operates with

its maximum torque per ampere characteristic. From the pha-

sor diagram of Fig. 33.40b, it is clear that the input current I

phasor now lags the voltage V phasor at the motor terminals.

(see the phasor diagram in the ﬁgure). Note that the level of

,which is determined by the level of excitation, also deter-

mines the angle θ to some extent. Clearly, when maximum

torque per ampere characteristic is required, a power factor

less than unity has to be accepted.

33 Motor Drives 883

(

)(

)

FIGURE 33.39 (a) Phase back-emf and current waveforms and (b) the phasor diagram with I lagging E

(a) (b)

γ = 0

I = I

d-axis

g = 0°

FIGURE 33.40 (a) Phase back-emf and current waveforms and (b) phasor diagram for I in phase with E

33.4.6.3 Case 3: Operation with I Leading E

If I is chosen to lead E

, the overall power factor can be

higher, including unity, as is indicated in Fig. 33.41. Note that

the motor now operates with less than maximum torque per

ampere characteristic. Note also that the d-axis component of

I now tends to demagnetize the rotor and that the operation

with ﬁeld weakening is implied.

With a CSI-driven motor, the amplitude and the angle of

the phase current relative to the back-emf can be selected

according to one of the desirable operating characteristics

mentioned above. Additionally, other operational limits such

as the inverter/motor current limit, the maximum stator volt-

age limit, and the maximum power limit can also be addressed.

The amplitude of the stator current I clearly determines the

developed torque of the motor. Consequently, the error of

the speed controller is used to determine the amplitude of I.

The overall control system with an inner torque loop can be

described by Fig. 33.42.

33.4.7 Vector Controls

The foregoing controls were based on the steady-state equiva-

lent circuit of the motor. Even though the torque Eq. (33.65)

for a current-source drive evokes vector-control-like relation-

ships, they do not address the dynamics of the current controls

as is possible in an orthogonal reference frame. Using an

orthogonal set of reference attached to the rotor, a simple

set of decoupled, dc-motor-like torque control relationships

is readily obtained. Following the transformation technique

used in Section 33.3.4, the stator voltage equations of a

synchronous motor with ﬁxed rotor excitation in the rotor

reference frame are







R +pL

ωL

−ωL

R +pL









ωλ



(33.68)

T =



+(L

−L



(33.69)

884 M. F. Rahman et al.

I leading

FIGURE 33.41 Back-emf and current waveforms and phasor diagram for I leading E

aref

bref

cref

Motor

Look

Table

Current

Profiler

−

ref

FIGURE 33.42 Structure of a speed-control system with a CSI-driven synchronous motor.

where all the quantities in lower case represent instantaneous

quantities in the rotor dq-frame. The λ

is the ﬂux linkage per

phase due to the rotor excitation, ω is the electrical angular

velocity in rad/sec, and P is the number of pole pairs. Here,

p is the time derivative operator d/dt. Assuming the magnetic

linearity, the stator ﬂux linkages are

= L

+λ

= L

(33.70)

Note that the Eq. (33.68) can be written down directly from

Eq. (33.31), taking into account the ﬁxed rotor excitation so

that the third and fourth rows and columns of Eq. (33.31) may

be dropped. Since the reference frame now rotates at the speed

of the rotor, ω

= ω. The induced back-emf due to the ﬁxed

rotor excitation occurs in the rotor q-axis and is included in

Eq. (33.68), as a separate term. Similarly, the torque expression

of Eq. (33.69) may also be written down from Eq. (33.41),

using the ﬂux linkages of Eq. (33.70).

Equations (33.67)–(33.69) are for a salient-pole motor for

which L

= L

. For a nonsalient-pole motor, L

is equal to L

and the developed torque is proportional to i

only. In either

case, the inner torque loop consist of two separate current

loops; one for i

and the other for i

, as indicated in Fig. 33.43.

The i

current loop generally derives its reference signal from

the output of the speed controller and constitutes the inner

torque loop. The reference for the i

current loop is normally

speciﬁed by the extent of ﬁeld weakening for which a neg-

ative i

reference is used. Otherwise, the d−axis current is

maintained at zero. Note that for large synchronous motors

with variable external excitation, ﬁeld weakening is normally

applied through adjustment of the rotor excitation, using a

spillover signal from the output of the speed controller.

From Eq. (33.68), it is clear that the couplings of q- and

d-axes voltages exist through the d- and q-axes currents,

respectively, and the back-emf. During dynamic operation,

such coupling effects become undesirable. The coupling effects

of d- and q-axes currents and the back-emf into q- and d-axes

voltages, respectively, can be removed by the feedforward

terms shown in the shaded part of the block the diagram of

Fig. 33.44 which also shows the two current-control loops. The

two outputs v

∗

and v

∗

from the decoupled current controllers

are transformed to the stator reference frame before being sub-

jected to pulse-width modulators or hysteresis comparators.

Note that the current references i

∗

and i

∗

are obtained with

33 Motor Drives 885

d-axis

current

controller

q-axis

current

controller

Inverse

d -q

transformation

d -q

transformation

Inverter

−

FIGURE 33.43 Inner torque loop of a vector-controlled synchronous motor drive.

−

(t)

d-axis current controller

+ wL

−wL

q-axis current controller

FIGURE 33.44 The d- and q-axis decoupling compensation.

due regard for the desired operating and limiting conditions

as described in Section 33.4.5.

Under this type of control, which is exercised in the rotor

reference frame, the d- and q-axes currents are separately regu-

lated. The purpose of the q-axis current controller is primarily

to control the developed torque, especially for the nonsalient-

pole motor. For this motor, the d-axis current is normally

maintained at zero, when the motor is operated below the

base speed. The d-axis current may be used to weaken the

airgap ﬂux so that the motor operates with a constant power-

like characteristic. It should be noted that the ﬁeld weakening

may also be carried out more directly by adjusting the rotor

excitation current by using a spillover signal from the speed

controller, when the base speed is exceeded.

The dynamic response of the drive under the vector control

scheme indicated in Fig. 33.44 is the highest possible with a

CSI drive. It should also be noted that the dq currents in the

rotor reference frame vary only the mechanical dynamics of

the rotor. In fact, they are dc quantities when the motor runs

at a constant speed. Consequently, the following error (or lag)

associated with tracking a sinusoidally time varying current

reference, which is the case when current control is exercised

in the stator a–b–c reference frame, can be reduced easily by

using an integral-type current controllers.

33.5 Permanent-magnet AC

Synchronous Motor Drives

33.5.1 Introduction

Since the introduction of samarium cobalt and neodymium–

iron–boron magnetic materials in the 1970s and 1980s, syn-

chronous motors with permanent-magnet excitation in the

rotor have been displacing the dc motor in many high-

performance applications. The trend is more noticeable in

applications requiring high-performance motors of up to a few

kilowatts. In low- to medium-power applications, the superior

dynamics, smaller size, and higher efﬁciency of motors with

PM excitation in the rotor, compared to all other motors, are

well known. Prior to this development, the ferrite and alnico

magnets were routinely used in small servomotors, with the

magnetic excitation in the outer stator. Such motors need a

brush-commutator assembly to supply power to the armature,

that is a problem. Nevertheless, interesting low-inertia, low-

armature inductance designs are possible that are desirable

for servo applications. One such design is the pancake iron-

less armature with the commutator-brush assembly directly

located on the printed armature. These shortcomings of the

commutator-brush are now avoided by locating the magnets