speed of rotation & internal generated voltage

1. Speed of Rotation & Internal
Generated Voltage of a
Synchronous Generator
NOORNABI SHAIKH
DEPARTMENT OF ELECTRICAL ENGINEERING
MUET

2. N.N.SHAIKH 2
SPEED OF ROTATION (SYNCHRONOUS GENERATOR)
By definition synchronous generators are synchronous, meaning
that the electrical frequency produced is locked in or
synchronized with the mechanical rate of rotation of the
generator.
When dc is supplied to the rotor field windings, the rotor
magnetic field points in whatever direction the rotor is turned.
Now the rate of rotation of magnetic field is related to the stator
electrical frequency by:
120
=
Pn
f m
e

3. N.N.SHAIKH 3
Since the rotor turns at the same speed as the magnetic field,
above equation relates the speed of rotor rotation to the resulting
electrical frequency.
Electrical power is generated at 50 or 60 Hz, so the generator
must turn at a fixed speed depending on the number of poles on
the machine.
 To generate 50 Hz power in a 4 – pole machine, the rotor must
turn at 1500 rpm, as
rpm
P
f
n e
m 1500=
4
50×120
=
120
=

4. N.N.SHAIKH 4
Internal Generated Voltage
 The equation for the induced voltage in a wire is
fieldmagneticin theconductoroflength=l
ctordensity vefluxmagnetic=B
fieldmagneticot therelativewiretheofvelocity=
.)×(=
v
lBve
 For 2 – pole stator, the voltage induced voltage in a single
turn can be expressed as
teind ωωφ cos=
 If the coil in the stator has Nc turns of wire, then the total
induced voltage of coil will be:
tNe Cind ωωφ cos=

5. N.N.SHAIKH 5
 Induced Voltage in a 3 – Phase Set of Coils
If 3 coils, each of Nc turns, are placed around the rotor magnetic field
as shown in the figure, the induced voltages in each of then will be the
same in magnitude but will differ in phase by 120o
.
VtNte
VtNte
VtNte
o
Ccc
o
Cbb
Caa
)240-(sin=)(
)120-(sin=)(
sin=)(
,
,
,
ωωφ
ωωφ
ωωφ
Therefore, a 3 – phase set of currents can generate a uniform rotating
magnetic field in a machine stator, and a uniform rotating magnetic
field can generate a 3 – phase set of voltages in such a stator

6. N.N.SHAIKH 6
 The RMS voltage in a 3 – phase stator
The peak voltage in any phase of a 3 – phase stator of this sort
fNE
fNE
isstatorphasethisofphaseanyofvoltagermsthetherefore
fNE
becanequationabovefSince
NE
CA
CA
C
C
φπ
φ
π
φπ
πω
ωφ
2=
2
2
=
3,
2=
,2=
=
max
max
NOTE
The rms voltage at the terminals of the machine will depend on
whether the stator is Y – Δ connected. If the machine is Y –
connected, then the terminal voltage will be √3 times EA; If the
machine is Δ – connected, then the terminal voltage will just be equal
to EA

7. N.N.SHAIKH 7
Internal Generated Voltage of a Synchronous Generator
The magnitude of the voltage induced in a given stator phase was found
)1(2= fNE CA φπ
Voltage EA depends on the flux φ in the machine, the frequency or speed
of rotation, and the machine’s construction. For synchronous machine,
eq. (1) sometimes rewritten in a simpler form that emphasizes the
quantities that are variable during machine operation.
)2(= ωφKEA
Where K is a constant representing the construction of the machine. If ω
is expressed in electrical radians per second, then
2
= CN
K
If ω is expressed in mechanical radians per second, then
2
=
PN
K C

8. N.N.SHAIKH 8
 The internal generated voltage EA is directly proportional to the φ
and to speed, but φ itself depends on the current flowing in the rotor
field circuit.
ωφKEA =
 Since The field current IF is related to the flux φ in the manner shown
in figure (a)
 Since EA is directly proportional to the flux Ø, the EA is related to the
field current as shown in figure (b)
Magnetization curve for the
synchronous generator