1) The document discusses the effect of varying field excitation on two alternators sharing a load and an alternator connected to an infinite bus. It provides a numerical example of how the armature current, power factor, active power, and reactive power shared by two alternators changes when the field excitation of one alternator is adjusted. 2) An infinite bus is defined as a voltage source with zero impedance and infinite inertia that maintains a constant voltage and frequency regardless of load variations. When an alternator is connected to an infinite bus, any change in its field excitation will cause an armature current that helps regain synchronism. 3) For an alternator operating on an infinite bus, a change in field excitation will change the induced

1. Electrical Machines-II
6th Semester, EE and EEE
By
Dr. Binod Kumar Sahu
Associate Professor, Electrical Engg.
Siksha ‘O’ Anusandhan, Deemed to be University,
Bhubaneswar, Odisha, India
Lecture-19

2. 2
Learning Outcomes: - (Previous Lecture_18)
 Effect of varying field excitation on two alternators running in parallel:
a. At no load.
b. Under loaded condition.

3. 3
Learning Outcomes: - (Today’s Lecture_19)
 To solve some numerical on effect of varying field excitations on two
alternators sharing a load.
 Synchronous generator (Alternator) on an infinite bus.
 Effect of change in varying excitation on an alternator connected to infinite
bus.

4. 4
Numerical on load sharing due to varying field excitation: -
1. Two similar three phase star-connected alternators supply in parallel a load of 1000 kW at
10 kV at a pf 0.8 lagging, sharing equally. The synchronous impedance of each machine is
(4 + j 50) Ω/phase. The field excitation of the first alternator is so adjusted that its armature
current becomes 50 A lagging. Determine the armature current, power factor, active power
shared, reactive power shared and excitation emf of both the alternators.
Solution: -
Terminal voltage of the alternator, Vt = 10 x 103/√3 = 5773.5 V.
Power shared by alternator-1, P1 = power shared by alternator-2, P2 = 1000/2 = 500 kW.
Load power factor is 0.8 lagging. So, load current,
IL = 1000 x 103/(√3 x 10 x 103 x 0.8) = 76.168 A
Before changing the field excitation:
Power factor of alternator-1 = power factor of alternator-2 = 0.8 lagging.
So, power factor angle for both the alternators = 36.870.
Armature current of both the alternators,
Ia1 = Ia2 = P1/(√3 x VL x cosφ) = 500 x 103/(√3 x 10 x 103 x 0.8) = 36.084 A.
Induced emf of both the alternators:
0 0 0
1 2 1 1 5773.5 0 36.084 36.87 (4 50) 7102.3 11.01at sE E V I Z j Volt
   
            

5. 5
Armature current of alternator-1 after varying its field excitation: Ia1
/ = 50 A.
It is knows to us that change in field excitation changes both armature current and power factor
but their product remains same.
i.e. Ia1cosφ1 = Ia1
/cosφ1
/
So, new power factor of alternator-1, cosφ1
/ = (36.084 x 0.8)/50 = 0.577 lagging.
Since the power factor of alternator-1 has decreased from 0.8 lagging to 0.577 lagging, its field
excitation of has been increased.
So, new power factor angle of alternator-1 = cos-1(0.577) = 54.760.
New value of armature current of alternator-1,
Now, new armature current of alternator-2,
So, new power factor of alternator-2 = cosφ2
/ = cos(4.90) = 0.996 lagging.
New complex power shared by alternator-1,
0 0 0
12' ' 76.168 36.87 50 54.76 28.79 4.9 .L aaI I I A
  
          
0
1' 50 54.76 .aI A

  
*
/ 0 0
1 13 ' 3 5773.5 0 50 54.76 500 707.32t aS V I kW j kVAR
  
          
 

6. 6
New complex power shared by alternator-2,
Total complex power before changing the field excitation
After changing the field excitation, complex power shared by both the alternators:
*
/ 0 0
1 23 ' 3 5773.5 0 28.79 4.9 500 42.59t aS V I kW j kVAR
  
          
 
*
0 0
1 2
3 3 5773.5 0 76.168 36.87 1000 750
, 500 375
2
phtS V I kW j kVAR
S
So S S kW j kVAR
  
          
 
   
/ /
1 2 500 707.32 500 42.59 1000 750S S S kW j kVAR kW j kVAR kW j kVAR       

7. 7
P1 = 500
kW
P2 = 500
kW
Q1 = 375
kVAR
Q2 = 375
kVAR
S1
S2
S
P
Q
1 
2
P1 = 500
kW
P2 = 500
kW
Q1 = 707.32
kVAR
Q2 = 42.51
kVAR
S1
S2
S
P
Q
1
2

Power sharing
before changing
the field excitation
Power sharing
after changing the
field excitation

8. 8
Alternator on an Infinite Bus: -
Infinite Bus: -
 A bus-bar that maintains constant voltage and frequency irrespective of the load
variation on it is called an infinite bus.
 A large number of alternators interconnected together to form a supply system may be
regarded as an infinite bus.
 So, an infinite bus is a voltage source having zero internal impedance and infinite
rotational inertia.
 Therefore, a synchronous machine switched on to or disconnected from the infinite
bus, can not change the voltage and frequency of the supply system.

9. 9
Effect of varying excitation:-
a. No load operation: -
 Initially, assume that |E| = |V| and are in phase opposition in the local circuit
formed by interconnection of incoming alternator and infinite bus.
 So, at no load no current flows either to or from the bus. Therefore the alternator is
said to be floating on the bus.
 Now, if the excitation of alternator is increased, induced emf of alternator ‘E’
becomes more than bus-bar voltage ‘V’.
 The resultant emf ‘Er = E – V’ gives rise to armature current ‘Ia’, which lags by
900 and leads bus voltage ‘V’ by 900.
G1 G2 G3 Gn
…. Incoming
Alternator
Infinite Bus
XSXS XS XSXS
Infinite BusAlternator
XS
V = Constant
f = Constant
Ia
E
Field Excitation
of Alternator
Prime Mover-1
Te
Tm

10. 10
 This armature current produces demagnetizing effect
causing the increased induce emf to decrease. After
some time automatically E reduces and becomes
same as the bus-bar voltage.
 Similarly, decrease in excitation of alternator,
reduces its induced emf causing armature current
‘Ia’.
 Now, in this case armature current ‘Ia’ leads induced
emf (E) by 900 which increases the air-gap flux, due
to magnetizing effect of armature reaction.
 Increase in flux, increases the emf of alternator, and
finally makes the resultant emf zero.
 So any change in field excitation, automatically sets
in an armature current ‘Ia’ which helps in regaining
the synchronism.
E
V
rE
aI
E
V
aI
E
rE
V

11. 11
b. On load operation:-
 It is known to us that, change in excitation changes the induced emf ‘E’ but cannot
change the active power output of the alternator. Active power can only be altered by
changing the mechanical power input to the alternator.
 Expression for active power output/phase is :
 In the above power expression, V, and Xs are constant. So, chage in excitation changes
the value of ‘E’, but maintains the products Esinδ and Iacosφ constant.
 This can be easily understood from the phasor diagram.
 Initially, assume that the alternator is operating at unity power factor with induced
emf ‘E’, load angle ‘δ’, armature current ‘Ia’, and power factor angle ‘φ = 00’.
 If the excitation is increased, induced emf increases from ‘E’ to ‘E1’, load angle
decreases from ‘δ’ to ‘δ1’, armature current increases from ‘Ia’ to ‘Ia1’ and power
factor angle increases from ‘φ’ to ‘φ1’ in lagging direction.
 But, Esinδ = E1sinδ1, and Iacosφ = Ia1cosφ1.
a
s
EV
P sin VI cos
X
  

12. 12
VIa
jIa1X
s
E1EE2
Ia1
Ia2
jIaXs
jIa2
Xs
 1
1
2
2
1 1
2 2
a
a
a
I cos
I cos
I cos





0aI sin 
1 1aI sin
2 2aI sin
1 1
2 2
Esin
E sin
E sin






13. 13
 Similarly if the alternator is operating at unity power factor and its field excitation is
decreased, induced emf decreases from ‘E’ to ‘E2’, load angle increases from ‘δ’ to ‘δ2’,
armature current increases from ‘Ia’ to ‘Ia2’ and power factor angle increases from ‘φ’ to
‘φ2’ in leading direction.
 But, Esinδ = E2sinδ2, and Iacosφ = Ia2cosφ2.
The following important points may be noted for the phasor diagram:
 The alternator current is minimum at unity power factor and starts increasing, if the field
excitation is changed. This mode of operation is called normal excitation.
 If the alternator is operating at lagging power factor, increase in field excitation increases
the induced emf ‘E’, decreases the load angle ‘δ’, increases the armature current ‘Ia’ and
decreases the power factor ‘cosφ’ and vice-versa.
 When the alternator is operating at lagging power it is said to be over excited.

14. 14
 If the alternator is operating at leading power factor, increase in field excitation
reduces the induced emf ‘E’, increases the load angle ‘δ’, increases the armature
current ‘Ia’ and decreases the power factor ‘cosφ’ and vice-versa.
 Change in excitation changes the reactive component of current Iasinφ keeping its
active component Iacosφ constant.
 So, change in field excitation changes the reactive power of the alternator keeping its
active power constant.
 When the alternator is operating at leading power it is said to be under excited.
,
,
If Ecos V Alternator is normallyexcited
If Ecos V Alternator isoverexcited
If Ecos V Alternator isunderexcited







15. 15
Thank you