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# Synchronous Generator Operation - Electrical Machines, BE Electrical Engineering Electrical Engineering (EE) Notes | EduRev

## Electrical Engineering (EE) : Synchronous Generator Operation - Electrical Machines, BE Electrical Engineering Electrical Engineering (EE) Notes | EduRev

``` Page 1

Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

3 Synchronous Generator Operation
3.1 Cylindrical Rotor Machine
V
E
E t
x a
x l r a
I
Et
Ixa
Ixl
Ira
V
I
A
E
s
(a) (b)phasor diagram for R load
x
s
r
a
I
Z
s
E
t
V
Et
IZs IXs
V
?
f
(c) (d)phasor diagram for R-L load
Figure 30: Equivalent circuits
The synchronous generator, under the assumption of constant synchronous
reactance, may be considered as representable by an equivalent circuit comprising an ideal
winding in which an e.m.f. E
t
proportional to the ?eld excitation is developed, the winding
being connected to the terminals of the machine through a resistance r
a
and reactance
43
Page 2

Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

3 Synchronous Generator Operation
3.1 Cylindrical Rotor Machine
V
E
E t
x a
x l r a
I
Et
Ixa
Ixl
Ira
V
I
A
E
s
(a) (b)phasor diagram for R load
x
s
r
a
I
Z
s
E
t
V
Et
IZs IXs
V
?
f
(c) (d)phasor diagram for R-L load
Figure 30: Equivalent circuits
The synchronous generator, under the assumption of constant synchronous
reactance, may be considered as representable by an equivalent circuit comprising an ideal
winding in which an e.m.f. E
t
proportional to the ?eld excitation is developed, the winding
being connected to the terminals of the machine through a resistance r
a
and reactance
43
Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

(X
l
+X
a
) = X
s
all per phase. This is shown in Fig. 30. The principal characteristics of the
synchronous generator will be obtained qualitatively from this circuit.
Consider a synchronous generator driven at constant speed and with constant exci-
tation. On open circuit the terminal voltage V is the same as the open circuit e.m.f. E
t
.
Suppose a unity-power-factor load be connected to the machine. The ?ow of load current
produces a voltage drop IZ
s
in the synchronous impedance, and terminal voltage V is re-
duced. Fig. 31 shows the complexor diagram for three types of load. It will be seen that
the angle s between E
t
and V increases with load, indicating a shift of the ?ux across the
pole faces due to cross- magnetization. The terminal voltage is obtained from the complex
summation
V +Z
s
=E
t
or V = E
t
-IZ
s
(24)
Algebraically this can be written
V =
q
(E
2
t
-I
2
X
2
s
)-I
r
(25)
for non-reactive loads. Since normally r is small compared with X
s
V
2
+I
2
X
2
s
˜ E
2
t
= constant (26)
so that the V/I curve, Fig. 32, is nearly an ellipse with semi-axes E
t
and I
sc
. The
current I
sc
is that which ?ows when the load resistance is reduced to zero. The voltage V
falls to zero also and the machine is on short-circuit with V = 0 and
I =I
sc
= E
t
/Z
s
˜ E
t
/X
s
(27)
Fora laggingloadofzero power-factor, diagramisgiven in Fig.31The voltage
is given as before and since the resistance in normal machines is small compared with the
synchronous reactance, the voltage is given approximately by
V ˜ E
t
-IX
s
(28)
44
Page 3

Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

3 Synchronous Generator Operation
3.1 Cylindrical Rotor Machine
V
E
E t
x a
x l r a
I
Et
Ixa
Ixl
Ira
V
I
A
E
s
(a) (b)phasor diagram for R load
x
s
r
a
I
Z
s
E
t
V
Et
IZs IXs
V
?
f
(c) (d)phasor diagram for R-L load
Figure 30: Equivalent circuits
The synchronous generator, under the assumption of constant synchronous
reactance, may be considered as representable by an equivalent circuit comprising an ideal
winding in which an e.m.f. E
t
proportional to the ?eld excitation is developed, the winding
being connected to the terminals of the machine through a resistance r
a
and reactance
43
Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

(X
l
+X
a
) = X
s
all per phase. This is shown in Fig. 30. The principal characteristics of the
synchronous generator will be obtained qualitatively from this circuit.
Consider a synchronous generator driven at constant speed and with constant exci-
tation. On open circuit the terminal voltage V is the same as the open circuit e.m.f. E
t
.
Suppose a unity-power-factor load be connected to the machine. The ?ow of load current
produces a voltage drop IZ
s
in the synchronous impedance, and terminal voltage V is re-
duced. Fig. 31 shows the complexor diagram for three types of load. It will be seen that
the angle s between E
t
and V increases with load, indicating a shift of the ?ux across the
pole faces due to cross- magnetization. The terminal voltage is obtained from the complex
summation
V +Z
s
=E
t
or V = E
t
-IZ
s
(24)
Algebraically this can be written
V =
q
(E
2
t
-I
2
X
2
s
)-I
r
(25)
for non-reactive loads. Since normally r is small compared with X
s
V
2
+I
2
X
2
s
˜ E
2
t
= constant (26)
so that the V/I curve, Fig. 32, is nearly an ellipse with semi-axes E
t
and I
sc
. The
current I
sc
is that which ?ows when the load resistance is reduced to zero. The voltage V
falls to zero also and the machine is on short-circuit with V = 0 and
I =I
sc
= E
t
/Z
s
˜ E
t
/X
s
(27)
Fora laggingloadofzero power-factor, diagramisgiven in Fig.31The voltage
is given as before and since the resistance in normal machines is small compared with the
synchronous reactance, the voltage is given approximately by
V ˜ E
t
-IX
s
(28)
44
Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

s
Ixs
Et
I
V
Ir
s
I
Et
V
v
s
IXs
Et
I
Ir
V1
(a)phasor diagram for di?erent R loads (b)
Et
Ea
v
I
Et
Ea
v
Ir
Ixs
I
(c) (d)
Figure 31: Variation of voltage with load at constant Excitation
45
Page 4

Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

3 Synchronous Generator Operation
3.1 Cylindrical Rotor Machine
V
E
E t
x a
x l r a
I
Et
Ixa
Ixl
Ira
V
I
A
E
s
(a) (b)phasor diagram for R load
x
s
r
a
I
Z
s
E
t
V
Et
IZs IXs
V
?
f
(c) (d)phasor diagram for R-L load
Figure 30: Equivalent circuits
The synchronous generator, under the assumption of constant synchronous
reactance, may be considered as representable by an equivalent circuit comprising an ideal
winding in which an e.m.f. E
t
proportional to the ?eld excitation is developed, the winding
being connected to the terminals of the machine through a resistance r
a
and reactance
43
Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

(X
l
+X
a
) = X
s
all per phase. This is shown in Fig. 30. The principal characteristics of the
synchronous generator will be obtained qualitatively from this circuit.
Consider a synchronous generator driven at constant speed and with constant exci-
tation. On open circuit the terminal voltage V is the same as the open circuit e.m.f. E
t
.
Suppose a unity-power-factor load be connected to the machine. The ?ow of load current
produces a voltage drop IZ
s
in the synchronous impedance, and terminal voltage V is re-
duced. Fig. 31 shows the complexor diagram for three types of load. It will be seen that
the angle s between E
t
and V increases with load, indicating a shift of the ?ux across the
pole faces due to cross- magnetization. The terminal voltage is obtained from the complex
summation
V +Z
s
=E
t
or V = E
t
-IZ
s
(24)
Algebraically this can be written
V =
q
(E
2
t
-I
2
X
2
s
)-I
r
(25)
for non-reactive loads. Since normally r is small compared with X
s
V
2
+I
2
X
2
s
˜ E
2
t
= constant (26)
so that the V/I curve, Fig. 32, is nearly an ellipse with semi-axes E
t
and I
sc
. The
current I
sc
is that which ?ows when the load resistance is reduced to zero. The voltage V
falls to zero also and the machine is on short-circuit with V = 0 and
I =I
sc
= E
t
/Z
s
˜ E
t
/X
s
(27)
Fora laggingloadofzero power-factor, diagramisgiven in Fig.31The voltage
is given as before and since the resistance in normal machines is small compared with the
synchronous reactance, the voltage is given approximately by
V ˜ E
t
-IX
s
(28)
44
Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

s
Ixs
Et
I
V
Ir
s
I
Et
V
v
s
IXs
Et
I
Ir
V1
(a)phasor diagram for di?erent R loads (b)
Et
Ea
v
I
Et
Ea
v
Ir
Ixs
I
(c) (d)
Figure 31: Variation of voltage with load at constant Excitation
45
Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

1.0
0.9  Lagging
0.0 Lagging
100
100
0
Isc
which is the straight line marked for cosf = 0 lagging in Fig. 32. A leading load of
zero power factor Fig. 31. will have the voltage
V ˜ E
t
+IX
s
(29)
another straight line for which, by reason of the direct magnetizing e?ect of leading
currents, the voltage increases with load.
Intermediate load power factors produce voltage/current characteristics resembling
those in Fig. 32. The voltage-drop with load (i.e. the regulation) is clearly dependent upon
the power factor of the load. The short-circuit current I
sc
at which the load terminal voltage
falls to zero may be about 150 per cent (1.5 per unit) of normal current in large modern
machines.
3.1.2 Generator Voltage-Regulation
The voltage-regulation of a synchronous generator is the voltage rise at the terminals
when a given load is thrown o?, the excitation and speed remaining constant. The voltage-
rise is clearly the numerical di?erence between E
t
and V, where V is the terminal voltage
for a given load and E
t
is the open-circuit voltage for the same ?eld excitation. Expressed
46
Page 5

Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

3 Synchronous Generator Operation
3.1 Cylindrical Rotor Machine
V
E
E t
x a
x l r a
I
Et
Ixa
Ixl
Ira
V
I
A
E
s
(a) (b)phasor diagram for R load
x
s
r
a
I
Z
s
E
t
V
Et
IZs IXs
V
?
f
(c) (d)phasor diagram for R-L load
Figure 30: Equivalent circuits
The synchronous generator, under the assumption of constant synchronous
reactance, may be considered as representable by an equivalent circuit comprising an ideal
winding in which an e.m.f. E
t
proportional to the ?eld excitation is developed, the winding
being connected to the terminals of the machine through a resistance r
a
and reactance
43
Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

(X
l
+X
a
) = X
s
all per phase. This is shown in Fig. 30. The principal characteristics of the
synchronous generator will be obtained qualitatively from this circuit.
Consider a synchronous generator driven at constant speed and with constant exci-
tation. On open circuit the terminal voltage V is the same as the open circuit e.m.f. E
t
.
Suppose a unity-power-factor load be connected to the machine. The ?ow of load current
produces a voltage drop IZ
s
in the synchronous impedance, and terminal voltage V is re-
duced. Fig. 31 shows the complexor diagram for three types of load. It will be seen that
the angle s between E
t
and V increases with load, indicating a shift of the ?ux across the
pole faces due to cross- magnetization. The terminal voltage is obtained from the complex
summation
V +Z
s
=E
t
or V = E
t
-IZ
s
(24)
Algebraically this can be written
V =
q
(E
2
t
-I
2
X
2
s
)-I
r
(25)
for non-reactive loads. Since normally r is small compared with X
s
V
2
+I
2
X
2
s
˜ E
2
t
= constant (26)
so that the V/I curve, Fig. 32, is nearly an ellipse with semi-axes E
t
and I
sc
. The
current I
sc
is that which ?ows when the load resistance is reduced to zero. The voltage V
falls to zero also and the machine is on short-circuit with V = 0 and
I =I
sc
= E
t
/Z
s
˜ E
t
/X
s
(27)
Fora laggingloadofzero power-factor, diagramisgiven in Fig.31The voltage
is given as before and since the resistance in normal machines is small compared with the
synchronous reactance, the voltage is given approximately by
V ˜ E
t
-IX
s
(28)
44
Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

s
Ixs
Et
I
V
Ir
s
I
Et
V
v
s
IXs
Et
I
Ir
V1
(a)phasor diagram for di?erent R loads (b)
Et
Ea
v
I
Et
Ea
v
Ir
Ixs
I
(c) (d)
Figure 31: Variation of voltage with load at constant Excitation
45
Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

1.0
0.9  Lagging
0.0 Lagging
100
100
0
Isc
which is the straight line marked for cosf = 0 lagging in Fig. 32. A leading load of
zero power factor Fig. 31. will have the voltage
V ˜ E
t
+IX
s
(29)
another straight line for which, by reason of the direct magnetizing e?ect of leading
currents, the voltage increases with load.
Intermediate load power factors produce voltage/current characteristics resembling
those in Fig. 32. The voltage-drop with load (i.e. the regulation) is clearly dependent upon
the power factor of the load. The short-circuit current I
sc
at which the load terminal voltage
falls to zero may be about 150 per cent (1.5 per unit) of normal current in large modern
machines.
3.1.2 Generator Voltage-Regulation
The voltage-regulation of a synchronous generator is the voltage rise at the terminals
when a given load is thrown o?, the excitation and speed remaining constant. The voltage-
rise is clearly the numerical di?erence between E
t
and V, where V is the terminal voltage
for a given load and E
t
is the open-circuit voltage for the same ?eld excitation. Expressed
46
Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

as a fraction, the regulation is
e = (E
t
-V)/V perunit (30)
Comparing the voltages on full load (1.0 per unit normal current) in Fig. 32, it will
be seen that much depends on the power factor of the load. For unity and lagging power
factors there is always a voltage drop with increase of load, but for a certain leading power
factor the full-load regulation is zero, i.e. the terminal voltage is the same for both full and
and the regulation is negative. From Fig. 30, the regulation for a load current I at power
factor cosf is obtained from the equality
E
2
t
= (V cosf+Ir)
2
+(V sinf+IX
s
)
2
(31)
from which the regulation is calculated, when both E
t
and V are known or found.
3.1.3 Generator excitation for constant voltage
200
100
0
0 100
0.0 Lagging
0.8 Lagging
0.9  Lagging
Percent of full -load current per phase
Percent of no -load field excitation
upf
Figure 33: Generator Excitation for constant Voltage
Since the e.m.f. E
t
is proportional to the excitation when the synchronous
reactance is constant, the Eqn. 31 can be applied directly to obtain the excitation necessary
to maintain constant output voltage for all loads. All unity-and lagging power-factor loads
will require an increase of excitation with increase of load current, as a corollary of Fig. 32.
47
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