Basic Topology
• In stator, a three-phase winding similar to the one
described in chapter 4. Since the main voltage is
induced in this winding, it is also called armature
winding.
Chapter 4
Synchronous
Generators
• In rotor, the magnetic field is generated either by a
permanent magnet or by applying dc current to rotor
winding. Since rotor is producing the main field, it is also
called field winding. Two rotor designs are common:
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The Speed of Rotation of a Synchronous Generator
o Salient-pole rotor with “protruding” poles
fe =
N
Slip
rings
nm P
120
S
S
Where
N
N
S
(a)
fe = electrical frequency, in Hz
o Round or Cylindrical rotor with a uniform air gap
nm = mechanical speed of magnetic field, in rpm
= rotor speed, in rpm
BR
N
N
P = number of poles
S
End View
Side View
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The Internal Generated Voltage of a Synchronous Generator
• It was shown previously, the magnitude of the voltage
induced in a given stator phase was found to be
= 2∅ = ∅
• The induced voltage is proportional to the rotor flux for a
given rotor angular frequency in electrical Radians per
second.
(a) Plot of flux versus field current for a
synchronous generator.
(b) The magnetization curve for the synchronous
generator.
• Since the rotor flux depends on the field current IF, the
induced voltage EA is related to the field current as
shown below. This is generator magnetization curve or
the open-circuit characteristics of the machine.
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The Equivalent Circuit of a Synchronous Generator
The Equivalent Circuit of a Synchronous Generator
1. Armature Reaction distortion of the air gap flux
produced by the stator created magnetic field.
2. Self Inductance of the armature coils (X).
3. Resistance of the armature coils (R).
EA
+ EAR - +
Enet
-
jX The net magnetic field in the air gaps is
= + RA
IA
+
Vϕ
We can represent the armature reaction by a
reactance X of the form
= −
-
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Armature Reaction: If a load is connected to the
stator windings a current will flow resulting in a
magnetic field Bs. This varying field produces a
voltage in the stator windings Es so that
∅ = + 3 Reasons why ≠ ∅
jX AR
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The Equivalent Circuit of a 3Φ Synchronous Generator
The Equivalent Circuit of a Synchronous Generator
• The two reactances (self + armature) may be combined
into a single reactance called the synchronous reactance
of the machine:
X S = X AR + X The per phase equivalent circuit of a synchronous generator.
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The Phasor Diagram of a Synchronous Generator
• The Kirchhoff’s voltage law equation for the armature
circuit is
Power and Torque in Synchronous Generators
E A = Vϕ + I A (RA + jX S )
• The phasor diagrams for unity, lagging, and leading
power factors load are shown here:
Unity
Lagging
Leading
The angle between ∅ is known as the
torque angle δ
< =< −< ∅
Figure 4-15:
11
The power-flow diagram of a
synchronous generator.
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• If the armature resistance is ignored (Since RA << XS),
• The input mechanical power is given by
Pin = τ appωm
I ACos(θ ) =
• The power converted from mechanical to electrical
power is given by
E ASin(δ )
XS
PCONV POUT =
3V φ E ASin(δ )
XS
Pconv = τ ind ωm = E AI ACos(γ )
! " = #$ % & • The real and reactive electrical output power is given by
POUT = 3Vφ I ACos(θ )
QOUT = 3Vφ I ASin(θ )
Note: 1.Pout = Pconv for Ra = 0.
2. Pout (max) occurs for δ = 90°.
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The Effect of Load Changes on a Synchronous
Generator Operating Alone
• Induced torque of the generator is given by
τ
ind
=
The behavior of a synch. Gen under load depends on
the power factor of the load and whether the generator
is acting alone or in parallel with other synchronous
generators.
3V φ E ASin(δ )
ωm X S
• Note that this equation offers an alternative form for the
induced torque presented before by
τ
ind
An increase in load is an increase in the real and/or
reactive power supplied by the generator. Such a load
increase results in an increase in . With constant
field resistance the field current and field flux will
remain constant. If also the prime mover maintains
constant speed ω, then the internal voltage =
∅is also constant.
= KBnet BR Sin(δ )
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4
The Effect of Load Changes on a Synchronous
Generator Operating Alone
The Effect of Load Changes on a Synchronous
Generator Operating Alone
• At constant field current and rotor speed
a. Lagging p.f. with load at same p.f.
()! * *&*+ #$ ,. !. &. ∅
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• At constant field current and rotor speed
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The Effect of Load Changes on a Synchronous
Generator Operating Alone
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The Effect of Load Changes on a Synchronous
Generator Operating Alone
• At constant field current and rotor speed
• At constant field current and rotor speed
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Synchronous Generator Example 1
The Effect of Load Changes on a Synchronous
Generator Operating Alone
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Synchronous Generator Example 1
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Synchronous Generator Example 1
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Synchronous Generator Example 1
Synchronous Generator Example 1
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Synchronous Generator Example 2
Synchronous Generator Example 2
Ex 2
Ex 2
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Synchronous Generator Example 2
Synchronous Generator Example 2
Ex 2
Ex 2
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