CHAPTER-FIVE
Synchronous Machines
Introduction



A synchronous machine is an ac rotating machine
whose speed under steady state condition is
proportional to the frequency of the current in its
armature.
The magnetic field created by the armature
currents rotates at the same speed as that created
by the field current on the rotor, which is rotating
at the synchronous speed, and a steady torque
results.
Synchronous machines are commonly used as
Generators especially for large power systems,
such as turbine generators and hydroelectric
generators in the grid power supply.
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Synchronous Generator
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Facts

Used principally in large power applications because of their



High operating efficiency
Reliability
Controllable power factor
Rotates at constant speed in the steady state
i.e. The rotating air gap field and the rotor rotate at the same
speed.
 It is a doubly excited machine
i.e. Rotor poles are excited by a DC current
Stator are connected to the ac supply
 It can draw leading or lagging reactive current from the ac
supply system.

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DC Machines
N
+
If
Vf
Rotor
If
Stator
If
S
R
The
DC excitation current in the stator generates a Resultant flux.
and induced voltage in the rotor.
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Synchronous machines
+
Vf
-
N
If
Rotor
Stator
If
S




R
The DC excitation current in the rotor generates a flux.
The turbine drives the rotor and produces a rotating flux
The rotating flux induce AC three phase voltage in the
stator winding.
The generated power of a synchronous machine can be
adjusted by controlling the magnitude of the rotor field current.
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Synchronous Machine Structures
Stator and Rotor
The stator is termed as stationary armature where
the generated power can be easily taken out. The
armature winding of a conventional synchronous
machine is almost invariably on the stator and is
usually a three phase winding.
2. The rotor is the rotating member of the machine
 The field winding is usually on the rotor and excited
by dc current, or permanent magnets.
 The dc power supply required for excitation usually
is supplied through a dc generator
 This dc generator known as exciter, which is
often mounted on the same shaft as the
synchronous machine.
1.
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Rotor structures:
There are two types of rotor structures
1.
Salient pole rotor
For low speed applications, such as hydroelectric
generators, Diesel Generator etc.
2. Non-Salient pole (cylindrical) rotor
For high speed synchronous machines, such as steam
turbine generators, Gas turbine, etc
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Salient Pole rotor
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Cont’d
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Non-Salient(Cylindrical) Rotor
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Mechanical and Electrical Angle
Mechanical angle
1.


Any angle Measured on the surface of a
synchronous Machine is a Mechanical Angle.
Always the total Mechanical angle over the complete
surface being 3600 or 2pi radian.
Electrical Angle
2.

The Generated Voltage depends on the number of
poles is called Electrical Angle.

Elec
P

 Mech
2
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Contd.

Example, we consider a four pole machine. As the
rotor rotates for one revolution
the induced
emf varies for two cycles
and hence

For a general case, if a machine has P poles, the
relationship between the electrical and mechanical
units of an angle can be readily deduced as
,similarly,
Where  is the angular frequency of electrical radians per
second and  m the angular speed of the rotor in
2 n
mechanical radians per second.
  2f and  m 
60
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n :  Speed of rotor
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Synchronous Speed

The Synchronous speed defined as
P NS
120 f
f 
 NS 
2 60
P

It can be seen that the frequency of the
induced emf is proportional to the rotor speed
and this speed is called Synchronous speed
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Distributed Three Phase Windings



The stator of a synchronous
machine consists of a laminated
electrical steel core and a three
phase winding.
The stator lamination of a
synchronous machine that has a
number of uniformly distributed
slots.
Coils are to be laid in these slots
and connected in such a way that
the current in each phase winding
would produce a magnetic field in
the air gap around the stator.
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Contd.


Stator coils are connected to form a three phase
winding. Each phase is able to produce a specified
number of magnetic poles.
The windings of the three phase are arranged uniformly
around the stator periphery and are labeled in the
sequence that phase ‘a’ is 120o(electrical) ahead of
phase ‘b’ and 240o(electrical) ahead of phase ‘c’.
Phase c
120o
120o
Phase a
120o
Phase b
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bs
Contd.
Stator windings are
sinusoidally distributed with
Ns equivalent turns and
their magnetic axes are
displaced by 120o.
Where
 Ns: the number of turns of
the equivalent sinusoidally
distributed stator windings.
 s: the angular
displacement about stator

vbs
as'
cs
bs
as
cs'
bs'
vas
as
vcs
cs
Ns
mmf as 
ias cos  s
2
N
mmf bs  s ibs cos s  23 
2
N
mmf cs  s ics cos s  23 
2
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Rotating Magnetic Fields
Magnetic Field of a Distributed Phase Winding
 The magnetic field distribution of a distributed phase winding can be
obtained by adding the fields generated by all the coils of the winding.

The mmf distribution along the air gap is a square wave. Because of the
uniform air gap, the spatial distribution of magnetic field strength is the
same as that of mmf.
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Magnetic Field of Three Phase Windings

The resultant mmf generated by a three phase winding
becomes
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Graphical Analysis
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Contd.


The Resultant mmf wave has a constant
amplitude of 3/2 FM and rotates at constant
Synchronous speed
Using Per-Phase Analysis the equivalent
circuit of Synchronous Generator
Xsyn
Rsta
Flux
Esta
Ista
Vt
DC
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Equivalent Circuit of Synchronous Machine
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Contd.


V  Vt  and I  I 0
Eg  Vt   I ( R a  jX S )
Consider the terminal
Voltage leads the
current by Φ.
Determine the
Generated Voltage
Consider Triangle ONM
M
IaXs
Eg
IaRa
Vt
(OM )2  (ON )2  ( NM )2
VtSinΦ
E  V cos  I a Ra   V sin   I a X S 
2
g
2
2
Φ
Eg  V cos  I a Ra   V sin   I a X S 
2
2
O
VtCos Φ
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Ia
N
IaRa
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Open- and Short-Circuit Characteristics

The Short-Circuit -Ratio (SCR) is the
ratio of the field current Of ’=If1
needed to generate rated opencircuit Armature Voltage to the field
current Of ’’=If2 needed to produce
rated armature current
Ia2=In
Ia1
I f1
SCR 
If2
The SCR exactly equals the per unit
synchronous reactance so that
1
X s p .u . 
SCR
Open  cct  voltage per phase Eg 0
ZS 

Short  cct  current per phase I Sh
Open- and short-circuit
characteristics of a synchronous
machine.
I
f
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