Inverter Driven Synchronous

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Inverter-D riven Synchronous

Motors for Constant Power

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nverter-driven synchronous motors (SMs) are

widely used in high-performance variable-speed

I

rive systems. The typical schematic of an SM

drive system is shown in Fig. 1. The armature current

vector of an SM is decided according to the command

(torque or speed) and the current-regulated voltage-

source pulse width modulated (PWM) inverter

drivesSMso that the instantaneous armature currents

follow their commanded values. The stator and wind-

ing of SMs are the same asa standard induction motor,

but the rotor configuration is different depending on

the type of machine. Therefore, SMs can be modeled

by the same d-q reference frame circuit and generally

analyzed, where the machine parameters in the d-q

equivalent circuit depend on the rotor configuration.

Several rotor configurations of SMs have been

reported for high-performance drives

[

1-61, Fig. 2

shows the typical rotor cross-sections of SMs. SMs

can be classified according to the torque production

(excitation torque and/or reluctance torque) and

the machine parameters (per unit open circuit volt-

age

Eo,

per unit d and q-axis reactances Xd, Xq):

SPM ( E o 0, Xd = X,): the surface projecting

permanent magnet synchronous motor

(SPM) shown in Fig. 2(a), in which the mag-

nets are projected from the surface of the

rotor, is a non-salient pole machine (Xd= X,),

and as a result only the magnet torque is

produced.

SynRM ( E o

=

0, Xd

Xd

(Motor

2,

# 3 ,

# 4

and 7), the

operating limits exist, but the maximum torque

Ti

derived by substituting

(7)

and (8) nto ( 3 ) ,and the

output power at low speeds are larger than that in

the case of

Eo =

Xd. Therefore, SMs have to be

designed

so

that t he machine parameters satisfy the

condition ofEo2

Xd ,

which corresponds to the area

below the curve (c) in Fig.

3.

If the large constant

power speed region is desired, the motor design

with

Eo

= X d

is required. This

is

possible in PM

motors , for example the axially-laminated IPM

motor with

Eo

Xd is reported in

147.

In case of an

ideal SynRM, in which a saliency ratio

p ( =

X,/Xd)

is infinity and the machine parameters are

E o

= Xd

=

0 and X, = & as derived from

( 2 5 ) ,

he maxi-

mum torque is l i h n the constant torque region,

and the maximum output power

is 1 O

at infinity

speed. But, such design is impossible, and as

a

result the power capability of SynRM cannot ex-

ceeds that of the optimal designed PM motor.

The maximum operating speed 0 n the PM

1

o5 1 ~ , i , , , , i , ~ , , i , , , , , , , , ~ ~ ~ i r j

\ '

Maximum operating speed wc pu)

Fzg

5 Operatzng charactertsttcs as a unction of maxzmum

operurzng speed W

E Industry Applications Magozine Novernher/Deremher 1996

motor with

E o

2Xddepends only on Eo-Xdas given

by

(15).

From Fig.

4,

t can be found that Motors

2, 3

and

#4,

in which

Eo

- X d

is

the same

(We

is

the same) have almost the same output power

versus speed characteristics even if they have differ-

ent machine parameters. Therefore, it can be con-

cluded that the output power versus speed

characteristics depend only on the parameter of

E o

-

Xd( =

1/0,

in per uni t form. It is very interesting

that the several combinations of machine parame-

ters such as

E o ,

Xd>and X,, which depend on the

rotor configuration, can be selected to achieve the

desired output characteristics.

Fig. 5 shows the operating Characteristics as a

function of the maximum operating speed

(=

l I ( E o - X d ) ) ,

where

amp

s the speed producing the

maximum output power. The power factor be-

comes unity and the output power becomes

1.0

when

w

=

amp.

he constant power speed region

K,pr

and

amp

ncrease almost linearly as ncreases.

On the other hand, the maximum torque

Ti

de-

creases extremely in the range of 0 10 and

reaches

0.71-0.72

when

Ci),

becomes infinity

(Eo-

X d

= 0),

which

is

almost the same value as the ideal

SynRM with an infinity saliency ratio. From Fig.

5 ,

Kcpr

can be expressed by (26) as a function of

We.

Kip?

0.7Wc

-1 ( 2 6 )

If the machine parameters of

E o

and Xd are

given, the maximum torque in t he constant torque

region Ti ) nd the constant power speed region

can be found according to Fig.

5

and

(26).

In order to produce the largest torque

Ti,

the

condition

of = 1.0

is

opt imum , where the ideal

machine parameters are

Eo =

1 O

Xd

= X,

= 0,

and

Ti

s

1.0;

however, this

is

impossible. Therefore,

the machine design with large

E o

and small Xdand

X, is desired

for

a

high-torque machine. On the

other hand, the optimum value

of E o

- Xd has to be

designed for

a

wide constant power operation.

From ( 2 6 ) , he optimum value of EO

xd

can be

found according to the desired constant power

speed

region.

0.7

KP+ 1

Eo-Xdf-

(27)

As shown in the previous chapter, there are

many combinations of machine parameters even if

the value of

Eo -

Xd and the output power versus

speed characteristics are the same. Fig. 6shows the

combinations of machine parameters and the con-

tent rat io of excitation torque

Te

to the total torque

Ti

for

0 = 5 ,

10,

20,

and infinity. The relation-

ships between Xd and

Eo

is linear, which is given


6/7

by

Xd

= Eo -l /oc. , as well as the saliency ratio

increases as E o decreases and the relationship be-

tween

X,

and Eo

is

almost independent of the value

of

0

except for large

Eo

region. The reluctance

torque becomes dominant

as

compared with the

excitation torque as

E o

decreases

( E o < 0 .5 ) .

The

right end of the curves in this figure corresponds

to

SPM

(p = 1) and the other corresponds to

Hybrids (p > 1). The motor with

p

=

2-5

corre-

sponds to the configuration shown in Fig. 2(b)-(d),

and the motor with saliency ratio over

5

corre-

sponds to Fig.

2

(e)-(g).

Now we turn to design of PM motors for wide

constant power operation. In order to obtain the

large constant power speed region,

Xd

has to be

increased as both

Eo

and

CO,

increase. In this case, if

the permanent magnet material

is

the same, the

large volume and thickness of permanent magnet

is required for the large magnet flux-linkage; as a

result the equivalent air-gap length in the d-axis,

including the permanent magnet thickness, in-

creases because the permanent magnet permeabil-

ity is very close to

Po;

thus

l i d

decreases. This is

contrary to the requirement of the opt imum design

for a large constant power speed region. Therefore,

the design with large

Eo

and large

Xd

s difficult.

If high remanence permanent magnets such as

rare-earth cobalt and neodymium-iron-boron are

used, the thickness of the permanent magnet can

be reduced, and as a result Xdniay increase. I t seems

that this design can apply to the

IPM

motor with

the rotor shown in Fig. 2(c), and the constant power

speed region from

2

to

4

may be obtained

E7-91.

If

d s

designed as low as possible, a high X,

and a large saliency ratio are rrquired. This may be

possible if the rotor is axially laminated, in which

case a saliency ratio up to 10 may be obtainable

11-61.In

this case, the low

E o is also

required; as

a

result, the low cost and low remanence permanent

magnets such as ferrite magnets are available,

where the irreversible demagnetization has to be

minded, and the constant power speed region over

5

is obtainable {3,

41.

The PRl motors with small

E o

have an advantage that the overexcitation

threshold speed

(=

l /Eo)

becomes large. The opera-

tion over the overexcitation threshold speed, in

which the motor back-EMF exceeds the dc source

voltage, may cause problems at the unexpected

situation (wrong switching

of

inverter, interrup-

tion)

[7}

The design of PM motors including the design

of rotor configuration, the selection of permanent

magnet materials, and their dimensions has to be

carried out

so

as to satisfy the desired output char-

acteristics such as the rated torque, the rated power,

the base speed, the constant power speed region,

and

so

on, according t o t he applications. The results

of examinations in th is article

as

shown in Figs.

5 ,

6,

and

(27)

will be useful for this procedure.

Fig. 6 .

Combinations

of

machine parameters an d content

rutio of

excitation torque.

U)

D- and q-axir reactances.

h i

Saliency

ratio and content ratio of excitation torque

t o

total torque

in

constant torque

region.

Fig. 7 .

Outpu t power versur .speed characteristicsoJprototype P M

INOtOrJ .

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41

fEf Industry Applicutions Muguzine November December

1996


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as the speed increases; however, both charac-

teristics are almost the same in the practical

operating region (constant torque region and

constant power region). Fig.

7

shows the

ability of the examinations in this article.

References

111 T Sebastian and

G R

Slemon, Operat ing Limits of

Inverter-Driven Permanent Magnet Motor Drives,

IEEE Trans Ind

Appl,

ol 23,pp 327-333, Mar iApr

1987

121T.M Jahns,

G

B Kliman, and T W Neumann, interior

Permanent-Magnet Synchronous Motors for Adjustable-

Speed Drives,

IEEE

Trans Ind Appl, vol 22, pp

738-747,JulyiAug 1986

an IPM Suitable for Field-Weakened Operation, Proc

ICEM90, pp 1059-1065, 1990

E41 W

L

Soong, D

A

Staton, and T J

E

Mille r, Design of

a New Axially-Laminated Interior Permanent Magnet

Motor,

Proc

IEEE IAS Ann Meet pp 27-36, 1993

157A Fratta, G P Troglia, A Vagati and F Villata, Evalu-

ation of Torque Ripple in High-Performance Synchro-

nous Reluctance Machines, Proc IEEE

I A S

Ann Meet ,

167 T Matsuo and T A Lipo, Current Sensorless Field

Oriented Control of Synchronous Reluctance Motor,

Proc IEEE IAS Ann

Meet

pp 672-678, 1993

131A Fratta, A Vagati and F Villata, Design Criteria

of

RatedTorque

T Nmy

Rated

Power P W)+

*

a i

base

speed pp

163-170,

1993

jlj

Expe r imen ta l Resu l t s

177 T M

Jahns, Flux-Weakening Regime Operation

of

an

The parameters of prototype PM are Interi or Permanent-Magnet Synchronous Motor Drive,

an

SPM

motor with the rotor shown in Fig. 2(a),

Fig. 2(c). They are indicated by open circles in Fig

3

The experimental and simulated output power

listed in Table 3 . The prototype

PM

motor a 1s

ZEEE TrdnJ

Ind APPl, vel 23, PP 681-689 , JulyiAug

1987

181B K

Bose, A High-Performance Inverter-Fed Drive Sys-

tem

of

an interior Permanent Magnet Synchronous Ma-

chine,

IEEE

Truns

Ind Appl,

ol 2 4 , pp 987-997,

Nov iDec 1988

and

b

an IPM

motor

with the rotor shown

In

versus speed characteristics are shown in Fig.

7 .

The

solid curves show the maximum power capability,

and are strictly calculated considering the armature

resistance. The broken curves show the calculated

results based on the equations in this article, in

which the armature resistance is neglected and the

ceiling voltage given by subtracting the maximum

resistance drop RI,, SV) from the actual ceiling-

voltage (50V) is used instead of the actual

Vam.

he

differences between both simulated results with

and without consideration of the resistance appear

at high speeds, in which the power factor decreases

19) S.

Morimoto,

T.

Ueno, M. Sanada,

Y .

Takeda, T. Hirasa,

and

A.

Yamagiwa, Effects and Compensation of Magnetic

Saturation in Permanent Magnet Synchronous Motor

Drives,

Proc. IEEE IAS A n n . M e a . ,

pp. 59-64,

1993.

110) R.F. Schiferl and T.A. Lipo, Power Capability of Salient

Pole Permanent Magnet Synchronous Motors in Variable

Speed Drive Applications,

IEEE Tram.

Ind.

Appl ,

vol.

26,

pp. 115-123,Jan./Feb. 1990.

111) S.

Morimoto,

Y.

Takeda, T. Hirasa, and

K.

Taniguchi,

Expansion of Operating Limits for Permanent Magnet

Motor

by

Current Vector Control Considering inverter

Capacity, IE E E Trans. Ind Appl.,ol. 26,

pp.

866-871,

Sept./Oct. 1990.

I

Industry Appl icntionsMngnzine November December

1996

Inverter Driven Synchronous

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