Control of Permanent Magnet Synchronous Motors...$18,000 $16,000 $14,000 $12,000 $10,000 US Dollars (in millions) $8,000 $6,000 $4,000 $2,000 $0 1985 1990 1995 2000 2005 Year 2010

Control of Permanent MagnetSynchronous Motors

Sadegh Vaez-Zadeh

School of Electrical and Computer EngineeringUniversity of Tehran

© Sadegh Vaez-Zadeh 2018

OXFORD University Press

Website

Please see the link to the book’s companion website at “http://www.oup.co.uk/companion/PMSControl2018” for additional materials, including:

• Preface• Sample material from book• Chapter summaries

Supply Inverter

Control

System

Motor

Figure 1.1 A controlled PMS mo-tor system including power supply,power converter, motor, and controlsystem.

Control of Permanent Magnet Synchronous Motors. Sadegh Vaez-Zadeh. © Sadegh Vaez-Zadeh 2018.Published in 2018 by Oxford University Press. DOI 10.1093/oso/9780198742968.001.0001

g1 g3

a b c

T3T1

g5T5

g6

T6

g2

T2

g4

T4

VDC

Figure 1.2 Schematic view of athree-phase two-level voltage sourceinverter.Table 1.1 Inverter switching states.

Sa = 1 T1 ON T4 OFFSa = 0 T1 OFF T4 ONSb = 1 T3 ON T6 OFFSb = 0 T3 OFF T6 ONSc = 1 T5 ON T2 OFFSc = 0 T5 OFF T2 ON


Carrier wave

Modulating

signals

Per phase

output

voltages

Tc

T2 on

T5 on

vDC

Figure 1.3 Principle of sinusoidalpulse wave modulation (only a smallfraction of a cycle for sine modulatingsignals is shown).


v– 3( 010)

v– 4( 110) v

– 1( 100)

v– 5( 001) v

– 6( 101)

v– 2( 110)

Figure 1.4 Inverter voltage vectors.


v–k+1

v–k+1 t k+1

v–k t k v–

k

v–s

Figure 1.5 Space vector modula-tion in terms of two inverter voltagevectors.


B

Br

–Br

–Hc Hc H

Figure 1.6 B–H hysteresis loop of atypical hard magnetic material.


B

Load Line

Demagnetization

Curve

Br

–Hc 0–H

Figure 1.7 Demagnetization curveof a typical PM material in amachine.

B

Br/2

Br

–Hc –Hc/2

BHmax

0–H

Figure 1.8 Graphical representa-tion of maximum energy product ofa typical PM material in connectionwith its demagnetization curve.


80

(a)

72_New Design

4-poles

surface

mounted

PM motor

72

36

23 MGOe

72_New Design

72

36

23 MGOe

70

60

50

40

30

Torq

ue (

Nm

)

Ou

tpu

t P

ow

er

(W)

20

10

0

2800

2400

2000

1600

1200

800

400

00 300 600 900

Speed (rpm)

1200 1500 0 300 600 900

Speed (rpm)

1200 1500

(b)

Figure 1.9 The effect of the energy products of magnets with linear B–H demagnetization curves on a PM motorperformance with three different energy product values and two different motor designs: torque vs speed (a) and outputpower vs speed (b) (Gutfleisch et al. 2011).


B

Br

–Hc

T1 < T2

T1 T2

0–H

Figure 1.10 Temperature effecton demagnetization curve of PMmaterials.


14

–14 –12 –10 –8

H (k Oe)

B (

kG)

–6 –4 –2 0

12

10

8

6

4

2

0

Ceramic

SmCo

NdFeB

Alnico

Figure 1.11 Demagnetization cha-racteristics of common PMmaterials.


Table 1.2 Comparative properties of PM materials.

PM material Remanence Coercivity Energy product Curie temperature Price Applications

NdFeB High High High Low High Very high

SmCo High High High High Very high Low

Ferrite Low Low Low High Low High

Alnico High Very low Low High Low Low


62%

NdFeB

Ferrite

SmCo

Alnico

1%

3%34%

2010

Figure 1.12 Estimated breakdownof global permanent magnet valueby type in 2010, total value: $9 bn(Gutfleisch et al. 2011).


$18,000

$16,000

$14,000

$12,000

$10,000

$8,000

US

Dollars

(in

million

s)

$6,000

$4,000

$2,000

$01985 1990 1995 2000 2005

Year

2010 2015 2020

Alnico Rare Earth Ferrite Total

Figure 1.13 Breakdown of global permanent magnet sales by type during 1985–2020 (Dent 2012).


140

120

100

80

k T

on

60

40

20

02005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020

China Japan Europe Other regions (including USA)

Figure 1.14 Estimated and forecasted worldwide production of NdFeB material by region during 2005–2020(Benecki et al. 2010).

2008

2003

0% 20% 40% 60% 80% 100%

HDD

Motor

Automobile

Optical device

Acoustic

MRI

Figure 1.15 The application ofNdFeB magnets in terms of sectors in2003 and 2008 (Kara et al. 2010).


Figure 1.16 IPM motors for auto-motive cooling fans, using ferrite(left) and NdFeB magnets (right)(Ding 2013).


98

96

94

92

90

% E

ffic

ien

cy

88

86

1 10 100

HP

PM

Premium efficiency®

IEEE 841

Energy efficient

1,000

Figure 1.17 Full load PMS motorefficiency in comparison with induc-tion motor efficiency, illustrated fromBaldor Electric (US Department ofEnergy 2014).


Induction motor (5.0 HP) 15,953 cm3

Comparison in motor weight

(5.0 HP)PM motor (5.0 HP) 4,698 cm3

Induction

motor

(a)

PM motor 18 kg

45 kg70%

Smaller

in volume

(b)

Figure 1.18 Advantages of PMSmotors over induction motors: (a) sizecomparison and (b) weight compari-son (Kang 2009), with permissionfrom Yaskawa America, Inc..


q

q q

q

d

d d

d

(a)

(c) (d)

(b)

Figure 1.19 PMS motor types based on the location of PM rotor poles: (a) surface-mounted, (b) inset,(c) interior, and (d) radial interior.


Figure 1.21 Rotor laminations ofIPM motor with V-shaped polesused in 2010 Prius hybrid vehicle(Burress et al. 2011).

(b)

(c)

(d)

(a)

Figure 1.22 Magnetization orien-tations of motor poles: (a) radial,(b) parallel, (c) radial sinusoidal, and(d) sinusoidal angle.

Figure 1.20 Permanent magnetpoles mounted on the surface of therotor core (Kikuchi and Kenjo 1997).


0.4

0.3

0.2

0.1

0

Magn

eti

c fl

ux d

en

sity

(T

)

Angle (deg)

Radial

Parallel

–0.1

–0.2

0 30 60 90 120 150 180Figure 1.23 Magnetic flux densitydistribution along the circumferentialof the air gap for radial and parallelPM pole magnetizations (Shin-Etsurare earth magnets).


Stator

Rotor

Win

din

gs

Low

Qu

ality

Magn

et

(a)

High Q

uality Magnet

(b)Stator

High Quality Magnet

Rotor

Low

Qu

ality

Magn

et

Win

din

gs

Figure 1.24 Modulated PM poles: (a) surface-mounted poles and (b) interior type poles (Isfahaniet al. 2008).


0.6

(a) (b) (c)

0.5

0.4

0.3F

lux d

en

sity

0.2

0.1

0.6

0.5

0.4

0.3

0.2

0.1

0.6

0.5

0.4

0.3

0.2

0.1

00

0 020 40 0 20

Displacement (mm)

40 0 20 40

Figure 1.25 Flux density distribu-tion of the PM poles (circled line)together with their fundamental com-ponents (solid line): (a) modular polewith both weak and strong field in-tensity PM materials, (b) conven-tional pole with weak magnetic fieldintensity PM material, and (c) con-ventional pole with strong magneticfield intensity PM material (Isfahaniet al. 2008).


b

q

120°

θm

d

a

c

(a)

120°

b

q

d

θm

a

c

(b)

Figure 2.1 Schematic view of PMS machines with (a) surface-mounted poles and (b) interior poles.


Assumed

N

S

S

N

Actual

d q

B(θ)

θ Figure 2.2 Actual and assumedpatterns of air gap flux densitydistribution produced by a pair ofPM poles.


b

120°

c

a

fb

fcfa

Figure 2.3 Presentation of machinephase variables in stator RF.


a

+

+

–

––

+

Rs

Rs

Rs

ia

ec

ea

eb

va

vb

vc

ib

ic

b

c

nFigure 2.4 A three-phase equiva-lent circuit model of PMS machines.


Q

D

a

N

S

c

θ

iQ

vQ

vD

iD

b

Figure 2.5 A schematic view ofa two-winding fictitious PMSmachine.


Q

D

a

fQ

fD

fafc

θ

fb

c

b

Figure 2.6 System transformationfrom three-axis stationary (a–b–c) totwo-axis stationary (D–Q) RF.


Rs

vD pλD

iD

+

+

–

–

(a)

vQ pλQ

RsiQ

+

–

+

–

(b)

Figure 2.7 Equivalent circuit mo-del of PMS machines in two-axisstationary RF. (a) D-axis circuit, (b)Q-axis circuit.


ωr

ωr

q

Q

D

fQf

fd

d

fD

θdFigure 2.8 System transformationfrom two-axis stationary (D–Q) RFto rotor (d–q) RF.


q

d

a

b

fb

fq

fcfa

fd

θr

c

ωr

ωr

Figure 2.9 System transformationfrom three-axis stationary (a–b–c)RF to rotor (d–q) RF.


ωr

ωrθr

qvs

vq

λq

λd λm

λs

iq

a

vd idd

ls

Figure 2.10 A vector diagram ofPMS machines.


–+

–+

–+

ωr Lq iq

ωr Ld id

vd vq

id Rs(a) (b)

iq Rs

ωr λm

Figure 2.12 Steady-state equiva-lent circuit model of PMS machinesin rotor RF. (a) d-axis circuit and (b)q-axis circuit.

id Rs

(a) (b)

–

+

+

–

Ld

ωr Lq iq

ωr Ld id

ωr λm

iq Rs

Lq

vd vq

+

–

Figure 2.11 Equivalent circuit mo-del of PMS machines in rotor RF (a)d-axis circuit and (b) q-axis circuit.


y

q

d

ωr

ωr

ffq

x

fx

fd

δ

λs

λm

Figure 2.13 System transform-ation from rotor (d–q) RF to statorflux linkage (x–y) RF.


Im

Re

fIf

fR

ζFigure 2.14 Presentation of a vec-tor variable in a complex coordinatesystem.


b

c

2/3fb

2/3fc

2/3faa

120˚

f

Figure 2.15 The vector variable interms of space vectors of phase vari-able components.


ωr

ωr

αs

θr

γs

δ

vspλs

λs

λm

ls

lsRs

a

q

d

Figure 2.16 A space vector dia-gram of PMS machines.


ωr

ωr

q

f

a

d

ζsζ = ζs – θr

θr

Figure 2.18 A stationary RF to ro-tor RF transformation by space vec-tor rotation.

isRs

+

–vs es

Figure 2.17 A space vector equiva-lent circuit model of PMS machinesin stationary RF.


ωr

ωr

q

x

d

yls

λs

αδ

Figure 2.19 A rotor RF to statorflux RF transformation by space vec-tor rotation.


id

vd

idT

idc

Rc Rc

Rs

–

+

+

–

+

–

id

vq

iqT

iqc

Rs

ωr LqiqT

ωr Ld idT

ωr λm

Figure 2.20 Steady-state equiva-lent circuit model of PMS machinesin rotor RF including iron losses: (a)d-axis circuit and (b) q-axis circuit.


ωm

Te

TL

Motor

Load

Figure 2.21 A dynamic systemconsisting of a PMS machineconnected to a mechanical load.


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Documents

Control of Permanent Magnet Synchronous Motors...$18,000 $16,000 $14,000 $12,000 $10,000 US Dollars (in millions) $8,000 $6,000 $4,000 $2,000 $0 1985 1990 1995 2000 2005 Year 2010