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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
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2Challenge the future
Synchronous machines
• Introduction, construction
• Synchronous generators / motors
• Voltage equations, equivalent circuits and phasor diagrams
• Power and torque characteristics
• Capability curves
• Speed control
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3Challenge the future
Construction
Stator comparable to IM:
• laminated• distributed stator
windings
Rotor• high-speed:
cylindrical (p≤4) with distributed winding
• low-speed salient-pole (p≥4) with concentrated winding
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4Challenge the future
Synchronous machines
• Introduction, construction
• Synchronous generators / motors
• Voltage equations, equivalent circuits and phasor diagrams
• Power and torque characteristics
• Capability curves
• Speed control
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5Challenge the future
Synchronous generator
6021
npf =
pfn
2601=
frequency of the stator voltage or excitation voltage
synchronous speed of the rotor
p 2 4 6 8 10 60
ns (rpm) 3000 1500 1000 750 600 100for f1=50Hz
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6Challenge the future
P-pole machines
p is the number of poles (in some other books: number of pole-pairs)
)2
sin(2
)( θθ pNNa = )
2cos(ˆ),( t
pBtBs ωθθ −= mded
p θθ2
=
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7Challenge the future
Synchronous machines
• Introduction, construction
• Synchronous generators / motors
• Voltage equations, equivalent circuits and phasor diagrams
• Power and torque characteristics
• Capability curves
• Speed control
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8Challenge the future
Open circuit characteristic
pwf NkfE Φ= 1112
2π
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9Challenge the future
Position in the grid
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10Challenge the future
Connecting to the grid (infinite bus)
Before a synchronous machine can be connected to the infinite
bus,
1. voltage
2. frequency
3. phase sequence
4. phase
of the synchronous machine and the grid must be the same.
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11Challenge the future
Synchronous motor connected to
the grid
• Not self starting, therefore:
- damper cage for asynchronous starting and damping oscillations
- frequency converter
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12Challenge the future
Synchronous machines
• Introduction, construction
• Synchronous generators / motors
• Voltage equations, equivalent circuits and phasor diagrams
• Power and torque characteristics
• Capability curves
• Speed control
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13Challenge the future
Derivation of voltage equations
• The sketched stator
and rotor windings are
concentrated, but they
represent distributed
windings
• How can we derive
voltage equations and
equivalent circuits?
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14Challenge the future
Voltage equations
tRiu
d
dλ+=
−+++=
−+++=
+++=
fsrscsasbsabsasabsc
fsrscsabsbsasasabsb
fsrscsabsbsabsasasa
iMiLiMiM
iMiMiLiM
iMiMiMiL
)(
)(
)(
34
32
πθλπθλ
θλ
0=++ scsbsa iii
−+−=
−+−=
+−=
fsrscsabsasc
fsrsbsabsasb
fsrsasabsasa
iMiML
iMiML
iMiML
)()(
)()(
)()(
34
32
πθλπθλ
θλ
Maxwell, Faraday:
No star-point connection
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15Challenge the future
Voltage equations, equivalent circuit
++=−
++=
++=−
++=
++=++=
fcsc
sscsr
fsc
sscsc
fbsb
ssbsr
fsb
ssbsb
fasa
ssasr
fsa
ssasa
et
iLRi
t
Mi
t
iLRiu
et
iLRi
t
Mi
t
iLRiu
et
iLRi
t
Mi
t
iLRiu
d
d
d
)(d
d
dd
d
d
)(d
d
dd
d
d
)(d
d
d
34
32
πθ
πθ
θsabsas MLL −=Using
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16Challenge the future
Armature reaction
afr Φ+Φ=Φ
The rotating magnetic field consists of two parts1. the field created by the three-phase stator currents2. the field created by the rotor excitation
tE f d
dλ−=
Generator convention:
jfE ωλ= −
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17Challenge the future
Equivalent circuits
tE f d
dλ−=
Generator convention:
jfE ωλ= −
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18Challenge the future
Measuring the synchronous
inductance
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19Challenge the future
Phasor diagrams
Generator: jt f a s aV E RI L Iω= − −
Motor: jt f a s aV E RI L Iω= + +
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20Challenge the future
Synchronous condenser
• Synchronous machine that
• behaves like a capacitor or inductor
• may used for reactive power compensation in power systems
• has no mechanical load
• Can you sketch the phasor diagrams for capacitive and inductive
operation?
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21Challenge the future
Synchronous machines
• Introduction, construction
• Synchronous generators / motors
• Voltage equations, equivalent circuits and phasor diagrams
• Power and torque characteristics
• Capability curves
• Speed control
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22Challenge the future
Power characteristics
0=sR t tV V= (cos( ) jsin( ))f fE E δ δ= +*
*
2
(cos( ) jsin( ))3 3
j
sin( ) cos( )3 3 j
f tt a t
s
t f t f t
s s
E VS V I V
X
V E V E VS
X X
δ δ
δ δ
+ − = =
−= +
s
ft
X
EVP
)sin(3
δ=
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23Challenge the future
Torque characteristics
• Stability limits
• Also for negative load angle
)sin()sin(3 max δδωω
TX
EVPT
sm
ft
m
===
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24Challenge the future
Torque-speed characteristic
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25Challenge the future
Synchronous machines
• Introduction, construction
• Synchronous generators / motors
• Voltage equations, equivalent circuits and phasor diagrams
• Power and torque characteristics
• Capability curves
• Speed control
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26Challenge the future
Complex power locus2sin( ) cos( )
3 3 jt f t f t
s s
V E V E VS
X X
δ δ −= +
What happens if the power is increased?
What happens if the field current is increased?
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27Challenge the future
Capability curves
Capability is
limited by
• armature
heating
• field heating
• steady-state
stability limit
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28Challenge the future
Synchronous machines
• Introduction, construction
• Synchronous generators / motors
• Voltage equations, equivalent circuits and phasor diagrams
• Power and torque characteristics
• Capability curves
• Speed control
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29Challenge the future
Speed control of synchronous
machines
• How can the speed of synchronous machines be controlled?
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30Challenge the future
Frequency control
VSI is important.The cycloconverter is not discussed in this course.
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31Challenge the future
Flux weakening
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32Challenge 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