CHAPTER-FIVE Synchronous Machines
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Transcript of CHAPTER-FIVE Synchronous Machines
CHAPTER-FIVESynchronous
Machines
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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
Facts Used principally in large power applications because of their
High operating efficiency Reliability Controllable power factor
Rotates at constant speed in the steady statei.e. The rotating air gap field and the rotor rotate at the same
speed. It is a doubly excited machinei.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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Stator
Rotor+
Vf
-
If
If
If
N
R
S
DC Machines
The DC excitation current in the stator generates a Resultant flux. and induced voltage in the rotor.
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Synchronous machines
Stator
Rotor+Vf-
If
If
N
R
S
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 StructuresStator and Rotor
1. 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.
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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
Salient Pole rotor
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Cont’d
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Non-Salient(Cylindrical) Rotor
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Mechanical and Electrical Angle1. Mechanical angle
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.
2. Electrical Angle The Generated Voltage depends on the number of
poles is called Electrical Angle.
MechElec
P2
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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 the angular speed of the rotor in mechanical radians per second.
m
rotorofSpeedn
nandf m
:60
22
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Synchronous Speed
The Synchronous speed defined as
It can be seen that the frequency of the induced emf is proportional to the rotor speed and this speed is called Synchronous speed
PfNNPf S
S 120602
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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 a
Phase b
Phase c
120o
120o
120o
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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
as'
as
bs
bs'
as
bs
cs
cs' vas
vbs
vcscs
32
32
cos2
mmf
cos2
mmf
cos2
mmf
scss
cs
sbss
bs
sass
as
iN
iN
iN
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Rotating Magnetic FieldsMagnetic 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
DC
VtEsta Ista
Xsyn Rsta
Flux
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Equivalent Circuit of Synchronous Machine
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Contd. Consider the terminal
Voltage leads the current by Φ. Determine the Generated Voltage
Consider Triangle ONM
)(
0
Satg
t
jXRIVE
IIandVV
O
Vt
IaRa
IaXsEg
IaN
M
Φ
VtCos Φ IaRa
VtSinΦ
22
222
222
sincos
sincos
)()()(
Saaag
Saaag
XIVRIVE
XIVRIVE
NMONOM
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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 open-circuit Armature Voltage to the field current Of ’’=If2 needed to produce rated armature current
CSCR
Open- and short-circuit characteristics of a synchronous machine.
Ia1
Ia2=In
The SCR exactly equals the per unit synchronous reactance so that
2
1
f
f
II
SCR
fISh
gS
ups
IE
phasepercurrentcctShortphasepervoltagecctOpenZ
SCRX
0
..
1
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