Lec # 03 equivalent circuit of a synchronous generator

Equivalent circuit of a synchronous generator

1. Equivalent Circuit of a
Synchronous Generator
NOOR NABI SHAIKH
DEPARTMENT OF ELECTRICAL ENGINEERING
MUET

2. N.N.SHAIKH 2
 The voltage E
A
is the internal generated voltage produced in one
phase of a synchronous generator. This E
A
not usually appears at the
terminals of the generator.[???]
 Only time the internal voltage E
A is the same as output voltage V
f of
a phase is when there is no I
A flowing in the machine. [!!!]
 Why V
f
is not equal to E
A
? And what is the relationship between V
f
&
E
A
?
 The answer to these questions yields the model of
synchronous generator (equivalent circuit of synchronous
generator).
Equivalent Circuit

3. N.N.SHAIKH 3
Following are the few factors that cause the difference
between E
A
& V
Ø
1. The distortion of the air – gap magnetic field 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.
By exploring first 3 – factors, a machine model can be formed. The effect of
salient – pole shape will be ignored.
[Making this assumption will cause the calculated answers to be slightly
inaccurate if machine does indeed have salient – pole rotors, but the errors are
relatively minor]

4. N.N.SHAIKH 4
1. ARMATURE REACTION (LARGEST EFFECT)
 When rotor rotates, E
A
is induced in the stator winding.
 If load is attached to the terminals of the generator, a current
flows I
A.
 This current will produce a magnetic field of its own in the
machine.
 This stator magnetic field distorts the original rotor magnetic field,
changing the resultant phase voltage V
f
.
 This effect is called armature reaction because the armature
(stator) current affects the magnetic field that produced it in the first
place.

5. N.N.SHAIKH 5
2 – pole rotor spinning
inside a 3 – phase
stator.
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.
[The voltage will be
+ve out of the
conductors at the top
and –ve into the
conductors at the
bottom of the figure]
Suppose generator is
connected to a lagging
load.
Due to the lagging load,
the peak current will
occur at angle behind
the peak voltage. This
effect is shown in figure
(b).
Current flowing in the
stator windings
produces a magnetic
field of its own BS
and its direction is
given by RHR shown
in figure (c).
The stator magnetic
field BS produces a
voltage of its own in
the stator, and this
voltage is called
Estat on the figure
(c).
The field BS adds to BR
distorting it into Bnet. The
voltage Estat adds to EA,
producing VØ at the
output of the phase.

6. N.N.SHAIKH 6
With two voltages present in the stator windings, the total voltage in a
phase
)1(+=
statA
EEV
f
The net magnetic field B
net
is
)2(+=
SRnet BBB
The angles of E
A
and B
R
are the same and the angles of E
stat
and B
S
are
the same, the resulting magnetic field B
net
will coincide with the net
voltage V
f
. The resulting voltages and currents are shown in figure (d).
To model the above armature reaction effects on the phase voltage Vf.
1.E
stat
lies at an angle of 90
o
behind the plane of maximum current I
A
.
2.E
stat
is directly proportional to I
A
.

7. N.N.SHAIKH 7
If X is a constant of proportionality, then the armature reaction voltage
can be expressed as;
)3(-
Astat
IjE C=
Then the voltage on a phase will be
)4(-=
AA
IjEV C
f
For equation (4) a simple circuit can be and if KVL applied to that circuit, the
equation will be same as eq.4
)5(-=
AA IjEV C
f
This is exactly the same equation as describing the armature reaction
voltage. Therefore the armature reaction voltage can be modeled as an
inductor in series with the internal generated voltage.

8. N.N.SHAIKH 8
 In addition to the effects of armature reaction, the stator coils have a
self – inductance and a resistance.
 If L
A
is stator self – inductance (and its corresponding reactance X
A
)
while the stator resistance is R
A
, then the total difference between E
A

and V
f
is
)6(---=
AAAAAA IRIjIjEV CC
f
 Combining reactances of armature reaction and self – inductance
)7(+=
AS
CCC
 Therefore the final equation describing V
f
is
)8(--=
AAASA IRIJEV C
f
It is now possible to sketch the equivalent circuit of 3-phase synchronous
generator

9. N.N.SHAIKH 9
The full equivalent circuit of a 3-phase synchronous generator
 A dc power source supplying the
rotor field circuit, which is modeled
by the coil’s inductance and
resistance in series.

 R
adj
controls the field current
connected in series with R
F
and L
F
.
 Stator or armature equivalent
circuit consists of 3 – phases, each
has an E
A
with a series X
S
and a
series R
A
.
 The voltages and currents of 3 –
phases are 120
o
apart in angle, but
otherwise the 3-phases are
identical.
 3 – phases can be either star or
delta connected.

10. N.N.SHAIKH 10
 If they are Y – connected then the terminal voltage VT is related to
the phase voltage by
fVV
T3=
 If they are delta connected, then
f
VV
T
=
As 3 – phases of synchronous generator are identical in all respects
except for phase angle normally leads to the use of a per-phase
equivalent circuit.
I
F I
A