Post on 26-Jun-2015
1Challenge the future
Overview Electrical Machines and
Drives
• 7-9 1: Introduction, Maxwell’s equations, magnetic circuits• 11-9 1.2-3: Magnetic circuits, Principles• 14-9 3-4.2: Principles, DC machines• 18-9 4.3-4.7: DC machines and drives• 21-9 5.2-5.6: IM introduction, IM principles• 25-9 Guest lecture Emile Brink• 28-9 5.8-5.10: IM equivalent circuits and characteristics• 2-10 5.13-6.3: IM drives, SM• 5-10 6.4-6.13: SM, PMACM• 12-10 6.14-8.3: PMACM, other machines• 19-10: rest, questions• 9-11: exam
2Challenge the future
Permanent magnet AC machines
(6.13)
• Introduction• Calculation example• Brushless DC motor (rectangular / trapezoidal waveforms)• PMSM (sinusoidal waveforms)• For these machine types
• Construction• Electromotive force• Voltage equations and equivalent circuit• Power balance• Force or torque
3Challenge the future
PM AC machine
4Challenge the future
Rotor layouts
1 surface mounted magnets• Ld≈Lq• L small because of
large air gap2 inset magnets
• Ld<Lq• reluctance torque
3 embedded magnets, radial magnetization
• Ld<Lq• reluctance torque
4 embedded magnets,circumferential magnetization
• flux concentration
5Challenge the future
Permanent magnet AC machines
(6.13)
• Introduction• Calculation example• Brushless DC motor (rectangular / trapezoidal waveforms)• PMSM (sinusoidal waveforms)• For these machine types
• Construction• Electromotive force• Voltage equations and equivalent circuit• Power balance• Force or torque
6Challenge the future
PM AC machine: calculation
example
• air gap radius rs
• axial length ls• magnet length lm• air gap length lg• number of turns Ns
• remanent flux density Brm
• recoil permeability µrm
• rotor speed ωm
Determine and sketch• air gap flux density in gap• flux linkage as a function of rotor
position• induced voltage
7Challenge the future
PM AC machine
8Challenge the future
PM AC machine
d dm mC S
H s J n Aτ⋅ = ⋅∫ ∫∫� �� �
� 022 =+ ggmm lHlH
d 0S
B n A⋅ =∫∫� �
�
rgrmm
mg B
ll
lB
µ+=
gm BB =
rmrmm BHB += µµ0
gg HB 0µ=
Using Ampère’s law:
Magnetic flux continuity
BH curve of magnet
BH curve of air
Result
9Challenge the future
PM AC machine
ssgs lrBNNBA πλ ==max
mssgspmpm lrBNft
E ωλλ24
d
dmaxmax ===
BlvEpm =max
For one phase without load:
10Challenge the future
Permanent magnet AC machines
(6.13)
• Introduction• Calculation example• Brushless DC motor (rectangular / trapezoidal waveforms)• PMSM (sinusoidal waveforms)• For these machine types
• Construction• Electromotive force• Voltage equations and equivalent circuit• Power balance• Force or torque
11Challenge the future
Construction: PMAC or BDCM
PMSM:• sinusoidal B• distributed windings• sinusoidal voltage• sinusoidal currents• continuous position sensor• smooth force
BDCM:• rectangular B• concentrated windings• trapezoidal voltage• rectangular currents• 6 step position sensor• force ripple
12Challenge the future
Brushless DC
machine
Name may be confusing
Idea:• PM excitation on rotor:
no brushes• mechanic commutator
replaced by converter
13Challenge the future
ec
eb
ia
ea
icπ ωt2π0
ib
Why trapezoidal voltage?
Brushless DC machine
14Challenge the future
Brushless DC machine operation
• Six step operation• Six times per revolution position information necessary
15Challenge the future
PM AC machine
ssgs lrBNNBA πλ ==max
mssgspmpm lrBNft
E ωλλ24
d
dmaxmax ===
BlvEpm =max
For one phase without load:
16Challenge the future
BDCM voltage equations
tRiu
d
dλ+=
+++=
+++=
+++=
)(
)(
)(
θλλθλλθλλ
pmcscsasbsabsasabsc
pmbscsabsbsasasabsb
pmascsabsbsabsasasa
iLiMiM
iMiLiM
iMiMiL
0=++ scsbsa iii
+=+−=
+=+−=
+=+−=
)()()(
)()()(
)()()(
θλθλλθλθλλθλθλλ
pmcscspmcscsabsasc
pmbsbspmbsbsabsasb
pmasaspmasasabsasa
iLiML
iLiML
iLiML
Maxwell, Faraday:
No star-point connection:
sabsas MLL −=
17Challenge the future
BDCM voltage equations
Single-phase equivalent circuit
Three-phase equivalent circuit
tRiu a
aa d
dλ+=
++=
++=
++=
pmcc
scc
pmbb
sbb
pmaa
saa
et
iLRiu
et
iLRiu
et
iLRiu
d
dd
dd
d
18Challenge the future
BDCM torque
Always two phases conducting:
IrlNBIEP
T sssgm
pm
m
42 max ===
ωωBlIrFrT ss ==
IEt
ILRIiuiuP pm
syyxx max
221
2 2d
d22 ++=+=
Electrical input power
Mechanical output power
Increase stored energy
Losses= + +
Torque:
Power balance gives same result as Lorentz
19Challenge the future
BDCM pros and cons
• Main problem:• Six times per period irregularities in the torque because
• Hall sensors different and positioned with limited accuracy• Motor coils are slightly different• The EMF (voltage induced by magnets) are different• Controller branches are different• Current can not be a square wave. Why not?
• Consequences• Not nice for position servo• Can be improved by hysteresis in Hall sensors
• Strengths BDCM• Simple controller with six step position sensor• Sensorless operation possible at higher speeds.
20Challenge the future
Permanent magnet AC machines
(6.13)
• Introduction• Calculation example• Brushless DC motor (rectangular / trapezoidal waveforms)• PMSM (sinusoidal waveforms)• For these machine types
• Construction• Electromotive force• Voltage equations and equivalent circuit• Power balance• Force or torque
21Challenge the future
Construction: PMAC or BDCM
PMSM:• sinusoidal B• distributed windings• sinusoidal voltage• sinusoidal currents• continuous position sensor• smooth force
BDCM:• rectangular B• concentrated windings• trapezoidal voltage• rectangular currents• 6 step position sensor• force ripple
22Challenge the future
PM AC machine
23Challenge the future
PM synchronous machine
24Challenge the future
PM synchronous machine
Cosinusoidal because of• skewing• end teeth
How can the voltage be calculated?
−Φ−=Φ
−Φ−=Φ
Φ−=Φ
)cos(ˆ
)cos(ˆ
)cos(ˆ
34
32
π
π
τπ
τπ
τπ
x
x
x
p
p
p
pmpmc
pmpmb
pmpma
25Challenge the future
PMSM voltage equations
Single-phase equivalent circuit
Three-phase equivalent circuit
tRiu a
aa d
dλ+=
++=
++=
++=
pmcc
scc
pmbb
sbb
pmaa
saa
et
iLRiu
et
iLRiu
et
iLRiu
d
dd
dd
ds sa sabL L M= −
pmacsabbsabasaa NiMiMiL Φ+++=λ
26Challenge the future
PMSM voltage equations
What should be the current phase to make maximum force?
)cos(ˆ xppmpma τ
πΦ−=Φ
−=
−=
=
)sin(ˆ
)sin(ˆ
)sin(ˆ
34
32
π
π
τπ
τπ
τπ
xee
xee
xee
p
p
p
pmpmc
pmpmb
pmpma
++=
++=
++=
pmcc
scc
pmbb
sbb
pmaa
saa
et
iLRiu
et
iLRiu
et
iLRiu
d
dd
dd
d
pmaas
pmacsabbsabasaa
NiL
NiMiMiL
Φ+=
Φ+++=λ
27Challenge the future
PMSM currentsI1i
I2i
I3i
E1i
E2i
E3i
−=
−=
=
)sin(ˆ
)sin(ˆ
)sin(ˆ
34
32
π
π
τπ
τπ
τπ
xii
xii
xii
p
p
p
c
b
a
28Challenge the future
PMSM power and force
iNv
ie
v
pF pm
p
pmmech ˆˆ2
3
2
ˆˆ3Φ===
τπ
ccbbaa iuiuiup ++=
Maximum three-phase force:
Voltage t
x
p dd
τπω =22 )ˆ()ˆˆ(ˆ iLNiRu pm ωω +Φ+=
cpmcbpmbapmacba
cba ieieiet
iiiLRiRiRip ++++++++=
d
)(d 22221
222
mechfCupmf pppie
t
WiRp ++=++= ˆˆ
2
3
d
dˆ2
3 2
29Challenge the future
Example: Archimedes Wave Swing
30Challenge the future
Linear AWS
generator
31Challenge the future
Linear generator AWS
32Challenge the future
Measure
ment
33Challenge the future
Permanent magnet AC machines
(6.13)
• Introduction• Calculation example• Brushless DC motor (rectangular / trapezoidal waveforms)• PMSM (sinusoidal waveforms)• For these machine types
• Construction• Electromotive force• Voltage equations and equivalent circuit• Power balance• Force or torque
34Challenge the future
Overview Electrical Machines and
Drives
• 7-9 1: Introduction, Maxwell’s equations, magnetic circuits• 11-9 1.2-3: Magnetic circuits, Principles• 14-9 3-4.2: Principles, DC machines• 18-9 4.3-4.7: DC machines and drives• 21-9 5.2-5.6: IM introduction, IM principles• 25-9 Guest lecture Emile Brink• 28-9 5.8-5.10: IM equivalent circuits and characteristics• 2-10 5.13-6.3: IM drives, SM• 5-10 6.4-6.13: SM, PMACM• 12-10 6.14-8.3: PMACM, other machines• 19-10: rest, questions• 9-11: exam