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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
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
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).
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
v– 3( 010)
v– 4( 110) v
– 1( 100)
v– 5( 001) v
– 6( 101)
v– 2( 110)
Figure 1.4 Inverter voltage vectors.
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
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.
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
B
Br
–Br
–Hc Hc H
Figure 1.6 B–H hysteresis loop of atypical hard magnetic material.
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
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.
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
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).
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
B
Br
–Hc
T1 < T2
T1 T2
0–H
Figure 1.10 Temperature effecton demagnetization curve of PMmaterials.
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
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.
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
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
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
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).
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
$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).
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
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).
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
Figure 1.16 IPM motors for auto-motive cooling fans, using ferrite(left) and NdFeB magnets (right)(Ding 2013).
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
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).
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
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..
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
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.
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
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).
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
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).
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
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).
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
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).
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
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.
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
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.
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
b
120°
c
a
fb
fcfa
Figure 2.3 Presentation of machinephase variables in stator RF.
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
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.
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
Q
D
a
N
S
c
θ
iQ
vQ
vD
iD
b
Figure 2.5 A schematic view ofa two-winding fictitious PMSmachine.
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
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.
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
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.
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
ωr
ωr
q
Q
D
fQf
fd
d
fD
θdFigure 2.8 System transformationfrom two-axis stationary (D–Q) RFto rotor (d–q) RF.
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
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.
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
ωr
ωrθr
qvs
vq
λq
λd λm
λs
iq
a
vd idd
ls
Figure 2.10 A vector diagram ofPMS machines.
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
–+
–+
–+
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.
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
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.
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
Im
Re
fIf
fR
ζFigure 2.14 Presentation of a vec-tor variable in a complex coordinatesystem.
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
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.
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
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.
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
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.
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
ωr
ωr
q
x
d
yls
λs
αδ
Figure 2.19 A rotor RF to statorflux RF transformation by space vec-tor rotation.
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
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.
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
ωm
Te
TL
Motor
Load
Figure 2.21 A dynamic systemconsisting of a PMS machineconnected to a mechanical load.
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
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