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PowerPoint Slides
to accompany
Electric Machinery
Sixth Edition
A.E. Fitzgerald
Charles Kingsley, Jr.
Stephen D. Umans
Chapter 5
Synchronous Machines
5-0
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5.1 INTRODUCTION TO POLYPHASE SYNCHRONOUS MACHINES
Two types:
1-Cylindirical rotor: High speed, fuel or gas fired power plants
fe 
p n
p

n
2 60 120
To produce 50 Hz electricity
p=2, n=3000 rpm
p=4, n=1500 rpm
2-Salient-pole rotor: Low speed, hydroelectric power plants
To produce 50 Hz electricity
p=12, n=500 rpm
p=24, n=250 rpm
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5.1 INTRODUCTION TO POLYPHASE SYNCHRONOUS MACHINES
How does a synchronous generator work?
1- Apply DC current to rotor winding
(field winding)
2- Rotate the shaft (rotor) with constant
speed.
3- Rotor magnetic field will create flux
linkages in stator coils and as a result
voltage will be produced because of
Faraday’s Law.
Why is impossible to rotate a synchronous motor when it is
connected to 50 Hz electric power?
Because before connecting to supply, the shaft speed of rotor is
zero. If the motor is two-pole, when it is connected to 50 Hz
supply it suddenly needs to rotate 3000 rpm. This is impossible
for large synchronous motors.
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5.1 INTRODUCTION TO POLYPHASE SYNCHRONOUS MACHINES
How is DC current applied to the rotor?
1- Slip Rings
Note: Magnetic field of rotor
can also be produced by
permanent magnets for
small machine applications
2- Brushless Excitation System:
Excitation supplied from ac exciter and solid rectifiers. The
alternator of the ac exciter and the rectification system are on the
rotor. The current is supplied directly to the field-winding without
the need to slip rings.
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5.1 INTRODUCTION TO POLYPHASE SYNCHRONOUS MACHINES
T
  p
2
   R FF sin  RF
22
Steady-state torque equation
 R : Resultant air - gap flux per pole
FF : mmf of the dc field winding
 RF : electrical phase angle between  RF and FF
Torque-angle characteristic.
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5.1 INTRODUCTION TO POLYPHASE SYNCHRONOUS MACHINES
• Synchronous generators
work in parallel with the
interconnected system.
• Frequency and voltage are
constant.
•The behivor is examined
based on a generator
connected to an INFINITE BUS.
Generator
Infinite bus
f : constant
V : constant
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5.2 SYNCHRONOUS-MACHINE INDUCTANCES; EQUIVALENT CIRCUTS
a  L aaia  L abib  L acic  L af i f
b  Lbaia  Lbbib  Lbcic  Lbf i f
c  L caia  L cbib  L ccic  L cf i f
 f  L fa ia  L fbib  L fcic  L ff i f
Self inductances:
Fundamental component
L aa  Lbb  L cc  Laa0  Lal
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L ff  L ff 0  L fl
Leakage flux
component
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5.2 SYNCHRONOUS-MACHINE INDUCTANCES; EQUIVALENT CIRCUTS
Mutual inductances:
L ab  Lba  L ac  L ca  Lbc  L cb
L af  L fa  Laf cos  m e
2
1
 Laa0 cos
  Laa0
3
2
p
 m e   m  e t   e 0
2
L af  L fa  Laf cos(et   e0 )
2
Lbf  L fb  Laf cos(et   e0  )
3
2
L cf  L fc  Laf cos(et   e 0 
)
3
5-7
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5.2 SYNCHRONOUS-MACHINE INDUCTANCES; EQUIVALENT CIRCUTS


 a  
  
 b
 c  
  
 f  
 Laf



i
1
2   a 
 Laa0
Laa0  Lal
Laf cos(et   e 0  )  i
2
3  b 
1
1
2   ic 
 Laa0
 Laa0
Laa0  Lal
Laf cos(et   e 0 
)
2
2
3  i f 
 
2
2
cos(et   e 0 ) Laf cos(et   e 0  ) Laf cos(et   e 0 
)
L ff 0  L fl

3
3

Laa0  Lal
For balanced system
1
 Laa0
2
1
 Laa0
2
1
 Laa0
2
Laf cos(et   e 0 )
ia  ib  ic  0
1
a  ( Laa0  Lal )ia  Laa0ia  L af i f
2
3
a  ( Laa0  Lal ) ia  L af i f
2
a  Ls ia  L af i f
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Ls : Defined as synchronous inductance.
It is the effective inductance seen by phase a
under steady state balanced conditions.
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5.2.4 EQUIVALENT CIRCUTS
Terminal voltage for phase a
da
d ia d (L af i f )
d ia
va  Ra ia 
 Ra ia  Ls

 Ra ia  Ls
 eaf
dt
dt
dt
dt
L af  Laf cos(et   e 0 )
eaf  e Laf I f sin( et   e0 )
In complex form:
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Eˆ af  j
Eaf 
e L af I f
2
e
e Laf I f
2
j e 0
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5.2.4 EQUIVALENT CIRCUTS
Motor:
Generator:
Vˆa  Ra Iˆa  j X s Iˆa  Eˆ af
Vˆa  Eˆ af  Ra Iˆa  j X s Iˆa
Synchronous Reactance
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Synchronous-machine equivalent circuit showing airgap and leakage components of synchronous reactance
and air-gap voltage.
Figure 5.4
5-11
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Open-circuit characteristic of a synchronous machine.
Figure 5.5
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Typical form of an open-circuit core-loss curve.
Figure 5.6
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Open- and short-circuit characteristics of a synchronous
machine.
Figure 5.7
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Phasor
diagram for
short-circuit
conditions.
Figure 5.8
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Open- and
short-circuit
characteristics
showing
equivalent
magnetization
line for saturated
operating
conditions.
Figure 5.9
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Typical form of short-circuit load loss
and stray load-loss curves.
Figure 5.10
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(a) Impedance interconnecting two voltages;
(b) phasor diagram.
Figure 5.11
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Equivalent-circuit representation of a synchronous
machine connected to an external system.
Figure 5.12
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Example 5.6. (a) MATLAB plot of terminal voltage vs. 
for part (b). (b) MATLAB plot of Eaf vs. power for part (c).
Figure 5.13
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Equivalent circuits and phasor diagrams for Example 5.7.
Figure 5.14
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Characteristic form of synchronous-generator
compounding curves.
Figure 5.15
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Capability curves
of an 0.85 power
factor, 0.80
short-circuit ratio,
hydrogen-cooled
turbine generator.
Base MVA is rated
MVA at 0.5 psig
hydrogen.
Figure 5.16
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Construction
used for the
derivation of a
synchronous
generator
capability curve.
Figure 5.17
5-24
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Typical form of synchronous-generator V curves.
Figure 5.18
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Losses in a
three-phase,
45-kVA,
Y-connected,
220-V, 60-Hz,
six-pole
synchronous
machine
(Example 5.8).
Figure 5.19
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Direct-axis air-gap fluxes in a salient-pole
synchronous machine.
Figure 5.20
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Quadrature-axis air-gap fluxes in a salient-pole
synchronous machine.
Figure 5.21
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Phasor diagram of a salient-pole synchronous generator.
Figure 5.22
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Phasor diagram for a synchronous generator showing
the relationship between the voltages and the currents.
Figure 5.23
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Relationships between component
voltages in a phasor diagram.
Figure 5.24
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Generator phasor diagram for Example 5.9.
Figure 5.25
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Salient-pole synchronous machine and series impedance:
(a) single-line diagram and (b) phasor diagram.
Figure 5.26
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Power-angle characteristic of a salient-pole synchronous
machine showing the fundamental component due to
field excitation and the second-harmonic component due
to reluctance torque.
Figure 5.27
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(a) Single-line diagram and (b) phasor diagram for motor
of Example 5.11.
Figure 5.28
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Schematic
diagram of a
three-phase
permanentmagnet ac
machine. The
arrow indicates
the direction
of rotor
magnetization.
Figure 5.29
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