Synchronous machines operate at a constant synchronous speed. Unlike induction machines, the rotor rotates at the same speed as the rotating air gap field in the stator. Synchronous machines can operate as both generators and motors. They are commonly used as generators to produce electrical power. A synchronous generator contains a rotor with field windings excited by DC current and a stator with armature windings connected to an AC supply. The air gap flux is produced by both the rotor and stator fields. Synchronous machines can have cylindrical or salient pole rotors and are used in applications requiring reactive power compensation in power systems.

1. Synchronous Machines
(Introduction)
A synchronous machine rotates at a constant speed in
the steady state.
Unlike induction machine, the rotating air gap field and
the rotor in the synchronous machine at the same
speed, called the synchronous speed.
Synchronous machine can operate as both a generator
and a motor.
Synchronous machines are used primarily as
generators of electrical power.
Synchronous machine can be used to compensate the
reactive power in the power system.

2. Synchronous Machines
(Introduction)
Synchronous Generator
Synchronous Motor

3. Synchronous Machines
(Introduction)
A synchronous motor can draw either lagging or
leading reactive current from the ac supply.
A synchronous machine is a double excited machine.
Its rotor poles are excited by a dc current and its stator
windings (armature winding) are connected to the ac
supply.
The air gap flux is the resultant of the fluxes due to
both rotor current and stator current.
In induction machines, the only source of excitation is
the stator current, because rotor currents are induced
currents. Therefore induction motors always operate at
a lagging power factor.

4. Construction of Three Phase Synchronous Machines
The stator winding of the three phase synchronous
machines has a three phase distributed winding similar
to that of the three phase induction machine.
Unlike the dc machine, the stator winding, which is
connected to ac supply system is called the armature
winding.
The rotor winding has a winding called the field
winding, which is carries direct current. The field
winding on the rotating structure is fed from an external
dc source through slip rings and brushes.

5. Construction of Three Phase Synchronous Machines
Two common approaches to supplying the dc supply
to the rotor winding (filed winding):
• Supply the power from an external dc source to the
rotor by means of slip rings and brushes.
• Supply the dc power from a special power source
mounted directly on the shaft of the generator.
On the larger synchronous machine, brushless
exciter are used to supply the dc field current to the
machines. A brushless exciter is a small ac
generator with its field circuit mounted on the stator
and its armature circuit mounted on the rotor shaft.

6. Construction of Three Phase Synchronous Machines (A
Brushless Exciter Circuit)
A small three phase current is rectified and used to supply the
field circuit of the exciter, which is located on the stator. The
output of the armature of the exciter (on the rotor) is then
rectified and used to supply the field current of the main
winding.

7. Synchronous machines can be divided into two groups:
Construction of Three Phase Synchronous Machines
1. High speed machines with cylindrical (or non salient
pole) rotor.
2. Low speed machines with salient pole rotors.
The cylindrical or non salient pole rotor has one
distributed winding and essentially uniform air gap while
salient pole rotors have concentrated winding on the
poles and a uniform air gap.

8. Generator
Exciter
View of a two-pole round rotor generator and exciter
Round Rotor Generator

9. Cross-section of a large turbo generator. (Courtesy
Westinghouse)
Round Rotor Generator

10. Laminated iron
core with slots
Insulated copper
bars are placed in
the slots to form
the three-phase
winding
Metal frame
Details of a generator stator
Round Rotor Generator

11. Rotor block of a large generator. (Courtesy Westinghouse)
Round Rotor Generator

12. Generator rotor with conductors placed in the slots
Round Rotor Generator

13. DC current terminals
Shaft
Steel
retaining
ring
DC current
terminals
Wedges
Shaft
Large generator rotor completely assembled. (Courtesy
Westinghouse)
Round Rotor Generator

14. Salient pole generator
Stator of a large salient pole hydro generator; inset shows
the insulated conductors and spacers

15. Salient pole generator
Large hydro generator rotor with view of the vertical poles

16. Salient pole generator
Pole
DC excitation
winding
Fan
Slip
rings
Rotor of a four-pole salient pole generator

17. Synchronous generator
Mechanism of ac voltage generation
• Rotor flux is produced by a dc field current If.
• Rotor is driven by a prime mover, producing rotating
field in the air gap.
• A voltage is induced in the stator winding due to
the rotating field.
Induced voltage is sinusoidal due to the sinusoidal
distributed flux density in the air gap.

18. Synchronous generator
(The Speed of Rotation of a Synchronous Generator)
Synchronous generators are by definition synchronous,
meaning that the electrical frequency produced is
locked in or synchronized with the mechanical rate of
rotation of the generator.
The rate of rotation of the magnetic fields in the
machined is related to the stator electrical frequency is
120
P
n
f m
e 
Where fe = electrical frequency (Hz)
nm = mechanical speed of the magnetic field, rpm (=
speed of rotor)
P = number of poles

19. The Internal Generated Voltage of a Synchronous
Generator
The magnitude of the voltage induced in a stator phase
is
f
N
E C
A 

 2
or

 K
EA
Where
NC = no of conductors at an angle of 00
2
C
N
K 

20. The Equivalent Circuit of a Synchronous Generator
The voltage EA is the internal voltage generated produced in
one phase of a synchronous generator. However, this
voltage EA is not usually the voltage that appears at the
terminals of the generator.
There are many factors that cause the difference between
EA and VФ.
1. The distortion of the air gap magnetic filed by the
current flowing in the stator called armature reaction.
2. The self inductance of the armature coils.
3. The resistance of the armature coils.
4. The effect of salient pole rotor shapes.

21. The Development of a Model for Armature Reaction
Figure (a) shows a two pole rotor spinning inside a three
phase stator. A rotating magnetic field produces the internal
generated voltage EA.
There is no load connected to the stator. The rotor
magnetic field BR produces an internal generated voltage
EA whose peak value coincides with the direction of BR.
With no load on the generator, there is no armature current
flow, and EA will be equal to the phase voltage VФ.

22. The Development of a Model for Armature Reaction
Figure (b): The resulting voltage produces a lagging
current flow when connected to a lagging load

23. The Development of a Model for Armature Reaction
Figure (c): The stator current produces its own magnetic
filed BS, which produces its own voltage Estat in the stator
windings of the machine
The current flowing in the stator in the stator windings
produces a magnetic filed of its own. This stator magnetic
filed is called BS and its direction is given by the right hand
rule. The stator magnetic filed Bs produces a voltage of its
own in the stator, and this voltage is called Estat.

24. The Development of a Model for Armature Reaction
Figure (d): The field BS adds to BR, distorting it into Bnet. The voltage
Estat adds to EA, producing VФ at the output of the phase.
With two voltages present in the stator windings, the total
voltage in a phase is just the sum of the internal generated
EA and the armature reaction voltage Estat:
stat
A E
E
V 



25. The Development of a Model for Armature Reaction
The net magnetic field Bnet is just the sum of the rotor
and the stator magnetic fields:
S
R
net B
B
B 

Since the angles of EA and BR are the same and the
angles of Estat and Bs, are the same, the resulting
magnetic field Bnet will coincide with the net voltage VФ.
We know, the voltage Estat is directly proportional to the
current IA. If X is a constant of proportionality, then the
armature reaction voltage can be expressed as:
A
stat jXI
E 


26. The Development of a Model for Armature Reaction
The voltage on a phase is
A
A jXI
E
V 



27. The Development of a Model for Armature Reaction
In addition to the effects of armature reaction, the stator
coils have a self inductance and a resistance. If the
stator self inductance is called LA (and its corresponding
reactance is called XA) while the stator resistance is
called RA, then the total difference between EA and VФ is
given by
A
A
A
A
A
A I
R
I
jX
jXI
E
V 




Combine the armature reaction effects and the self
inductance in the machine
A
S X
X
X 


28. The Development of a Model for Armature Reaction
So
A
A
A
S
A I
R
I
jX
E
V 




29. The Development of a Model for Armature Reaction
If the machine is Wye (Y ) connection

 V
VT 3
If the machine is Delta (Δ) connection

V
VT
The Per Phase Equivalent Circuit of a Synchronous
Generator

30. The Phasor Diagram of A Synchronous Generator
The Phasor Diagram of A Synchronous Generator at
Unity Power Factor

31. The Phasor Diagram of A Synchronous Generator
(a) Lagging (b) Leading

32. Per Unit System
Definition:
value
Base
value
Actual
pu
,
Unit
Per 
Base value (in normal):
– Choose rated power for base value of power
– Choose rated voltage for base value of voltage
Other variables:
rated
base S
S  rated
base V
V 
base
base
base
V
S
I 
base
base
base
S
V
Z
2


33. 3
rated
,
LL
base
rated
base
V
V
,
S
S 

base
base
base
rated
,
L
base
base
base
I
V
Z
,
I
V
S
I 


3
base
L
pu
base
LL
pu
I
I
I
and
V
/
V
V 

3
base
A
pu
A,
base
S
pu
,
S
Z
R
R
and
Z
X
X 

Select
then
Per Unit System

34. XS, pu RA, pu
+
-
EA, pu VT, pu
If, pu
IA,pu
Per Unit System
Equivalent circuit in per unit system
T
pu
,
S
pu
,
A
pu
,
A
pu
,
A V
)
jX
R
(
I
E 


Usually
VT,pu = 1.0, which is the rated voltage of the generator

35. Power and Torque in Synchronous Generator




 cos
I
E
P A
A
m
ind
conv 3
Power converted from mechanical to electrical is
m
app
in
P 


Input mechanical power
Where γ is the angle between EA and IA

36. Power and Torque in Synchronous Generator
The difference between the input power to the
generator and the power converted in generator is
mechanical (friction & windage), core and stray losses.
Real output power is

 cos
I
V
P L
T
out 3 (Line quantities)

  cos
I
V
P A
out 3 (Phase quantities)
Reactive output power is

 sin
I
V
Q L
T
out 3

  sin
I
V
Q A
out 3
(Line quantities)
(Phase quantities)

37. Power and Torque in Synchronous Generator
If the armature resistance RA is ignored (since Xs >> RA)

38. Power and Torque in Synchronous Generator
Since the resistances are assumed to be zero
s
A
out
conv
X
sin
E
V
P
P
P



 
3
Where torque angle, δ is the angle between VФ and EA
The power of the generator is maximum when δ = 900
s
A
max
X
E
V
P 

3
The maximum power indicated by this equation
called static stability limit of the generator.
The induced torque is
s
m
A
ind
X
sin
E
V



 
3

39. EXAMPLE 1
At a location in Europe, it is necessary to supply 300kw of 60Hz power.
The only power sources available operate at 50Hz. It is decided to
generated the power by means of a motor-generator set consisting of a
synchronous motor driving a synchronous generator. How many poles
should each of the two machines have in order to convert 50Hz power
to 60Hz power?

40. EXAMPLE 2
• A 2300V 1000kVA 0.8-PF-lagging 60-Hz two-pole Y-connected synchronous
generator has a synchronous reactance of 1.1 Ω and an armature resistance of 0.15
Ω. At 60 Hz, its friction and windage loses are 24 kW, and its core loses are 18kW.
The field circuit has a dc voltage of 200 V, and the maximum IF is 10 A. The
resistance of the field circuit is adjustable over the range from 20 to 200Ω. The OCC
of this generator is shown below.
a) How much field current is required to make VT equal to 2300 V when the
generator is running at no load?
b) What is the internal generated voltage of this machine at rated conditions?
c) How much field current is required to make VT equal to 2300 V when the
generator is running at rated conditions?
d) How much power and torque must the generator’s prime mover be capable of
supplying?

41. Example 3
Assume that the field current of the generator in Example 2 has been adjusted to a value
4.5 A.
a) What will the terminal voltage of this generator be if it is connected to a ∆-connected
load with an impedance of 20<30° Ω ?
b) Sketch the phasor diagram of this generator?
c) What is the efficiency of the generator at these conditions?
d) Now assume that another identical ∆-connected load is to be paralleled with the first
one. What happens to the phasor diagram for the generator?
e) What is the new terminal voltage after the load has been added?
f) What must be done to restore the terminal voltage to its original value?

42. Example 4
Assume that the field current of the generator in Problem 5-2 is adjust to achieve rated
voltage (2300 V) at full load conditions in each of the questions below.
a) What is the efficiency of the generator at rated load?
b) What is the voltage regulation of the generator if it is loaded to rated
kilovolt amperes with 0.8-PF- lagging loads?
c) What is the voltage regulation of the generator if it is loaded to rated
kilovolt amperes with 0.8-PF- leading loads?
d) What is the voltage regulation of the generator if it is loaded to rated
kilovolt amperes with unity-power-factor loads?
e) Use MATLAB to plot the terminal voltage of the generator as a function of load for
all three power factors.

43. Measuring synchronous generator model parameter
The behavior of a real synchronous generator is determine by
• The relationship between field current and flux (and therefore between
field current and EA)
• The synchronous reactance, Xs
• The armature resistance, RA
The quantities above are determined by open circuit test and short
circuit test

44. Open Circuit Test
• To perform this test, the generator is turned at the rated speed.
• The terminals are disconnected from all loads.
• The field current is set to zero.
First step:
Second step:
The field current is gradually increased in steps, and the terminal
voltage is measured at each step along the way with the terminals
open. (IA = 0, so EA is equal to VФ)
Plot EA or VA versus IF from this information

45. Air gap line
This plot called open circuit characteristics
Open Circuit Test
The curve almost perfectly linear, until
some saturation is observed at high field
currents.
The unsaturated iron in the frame of the
synchronous machine has a relunctance
several thousand times lower than the air
gap reluctance, so at the first almost all the
magnetomotive force is across the air gap,
and the resulting flux increase is linear.
When the iron finally saturates, the
reluctance of the iron increases
dramatically, and the flux increases much
more slowly with an increase in
magnetomotive forces. The linear portion
of an OCC is called the air gap line of
characteristic.

46. Short Circuit Test
Adjust the field current to zero again and short circuit terminals of the
generator through a set of ammeters. Then the armature current IA or the
line current IL is measured as the field increased.

47. Short Circuit Test
When the terminals are short circuited, the armature currents IA is
S
A
A
A
jX
R
E
I


Its magnitude is
2
2
S
A
A
A
jX
R
E
I


Refer to Figure (b), BS almost cancels BR, the net magnetic field Bnet is
very small, so the machine is unsaturated and the SCC is linear.

48. Short Circuit Test
The internal machine impedance is
A
A
)
unsat
(
S
A
)
unsat
(
S
I
E
X
R
Z 

 2
2
If XS >> RA, this equation reduces to
A
OC
,
A
A
S
I
V
I
E
X 


1) Get the internal generated voltage EA from the OCC at the field
changing.
2) Get the short circuit current flow IA,SC at that field current from SCC.
3) Find XS by equation above.
Therefore, an approximate method for determining the synchronous
reactances at a given field current is

49. The saturated synchronous reactance may also found by taking the
rated terminal voltage (line to line) measured on the OCC and dividing
by the current read from SCC corresponding to the field current that
produces at rated terminal voltage.
ba
A
SC
,
A
rated
,
A
)
sat
(
S
A
)
sat
(
S
I
E
I
E
jX
R
Z 


