EE8401 Electrical Machines II Department of EEE 2020-2021

UNIT I - SYNCHRONOUS GENERATOR

PART A
1. Write the EMF equation of a three-phase alternator.
The emf equation of alternator is E = 4.44 Kc KdФ f T volts. Where E =
Induced emf per phase, Kc = Pitch factor, Kd = Distribution factor, T = No of turns
connected in series in each phase.
2. Two reaction theory is applied only to salient pole machines.State the
reason(Nov/Dec 2014) (April/May 2019)
According to two reaction theory,the armature mmf Fa is resolved in to two
components,one along the d-axis and another along q-axis.d-axis reactance can be
obtained from occ and scc.
E f  Vt  I a Ra  jX d I d  jX q I q
The current Ia lags terminal voltage Vt by Φ. Then add Ia Ra in phase with Ia to Vt. The
drop Id Xdleads Id by 90o as in case purely reactive circuit current lags voltage by
90o i.e. voltage leads current by 90o . Similarly the drop Iq Xq leads Xq by 90o . The
total e.m.f. is Ef.
3. What are the advantages of salient pole type construction used for
Synchronous machines?
i. They allow better ventilation
ii. The pole faces are so shaped that the radial air gap length increases from the
pole center to the pole tips so that the flux distribution in the air-gap is sinusoidal
in shape which will help the machine to generate sinusoidal emf.
iii.Due to the variable reluctance the machine develops additional reluctance
power which is independent of excitation.
4. How does electrical degree differ from mechanical degree?
Mechanical degree is the unit for accounting the angle between two points
based on their mechanical or physical placement. Electrical degree is used to account
the angle between two points in rotating electrical machines. Since all electrical
machines operate with the help of magnetic fields, the electrical degree is accounted
with reference to the magnetic field. 180 electrical degree is accounted as the angle
between adjacent North and South poles.
 electrical =  mech. (P/2) where P = No.of poles
5. Why are Alternators rated in kVA and not in kW?
The continuous power rating of any machine is generally defined as the power
of the machine or apparatus can deliver for a continuous period so that the losses
incurred in the machine gives rise to a steady temperature rise not exceeding the limit
prescribed by the insulation class. Apart from the constant loss incurred in Alternators
is the copper loss, occurring in the 3 –phase winding which depends on I2 R, the
square of the current delivered by the generator. As the current is directly related to
apparent – power delivered by the generator, the Alternators have only their apparent
power ratings in VA/kVA/MVA.
6. What do you mean by "single layer" and “double layer"
winding?(Nov/Dec 2011) (May 2017)
In single layer winding, there- is only one coil side per slot- But in double layer
winding, in each slot there are two coil sides namely upper coil side and lower coil
side. Hence, in single layer winding, the number of coils is half the number of slots,
but in double layer winding, the number of coils is equal to the number of slots.
7. Where the damper windings are located? What are their functions?(Nov/Dec
2011)
Damper windings are provided in the pole shoes of the salient pole rotor.
Slots or holes are provided in the pole shoes. Copper bars are inserted in the slots and
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the ends of all the bars in both the sides are short circuited by copper end rings to have
a closed circuit. These windings are useful in preventing the hunting in alternators;
they are also needed, in synchronous motor to provide the starting torque.
8. What are the causes of changes in terminal voltage of Alternators when
loaded?(Nov/Dec 2012)
Variations in terminal voltage in Alternators on load condition are due to the
following three causes: 1. Voltage drop due to the resistance of the winding, IR. 2.
Voltage drop due to the leakage reactance of the winding, IXl. 3. Voltage variation
due to the armature reaction effect, IXa.
9. What is meant by armature reaction in Alternators?(Nov/Dec 2013 & Nov/Dec
2015)
The effect of armature flux on the flux produced by the field ampere turns is
called as armature reaction.
10. Distinguish between the synchronous reactance and the potier reactance of a
synchronous generator. (April/May 2019)
 The Synchronous Reactance (XS) is the imaginary reactance employed to account for
the voltage effects in the armature circuit produced by the actual armature
leakage reactance and by the change in the air gap flux caused by the armature reaction.
 Potier reactance is the air gap reactance (leakage reactance) of the synchronous
machine at full load (rated voltage and current of armature).
10. What do you mean by synchronous reactance?
Synchronous reactance Xs= (Xl + Xa). The value of leakage reactance Xl is
constant for a machine based on its construction. Xl depends on saturating condition of
the machine. Xa , which represent the armature reaction effect between two
synchronously acting magnetic fields. The sum of leakage flux and armature reaction
reactance makes the total reactance XS to be called synchronous reactance.
11. What is meant by synchronous impedance of an Alternator?
The complex addition of resistance, R and synchronous reactance , jXs can be
represented together by a single complex impedance Zs called synchronous
impedance. In complex form Zs = (R + jXs ) ; In polar form Zs = | Zs |   ; Where,
Z s  R 2  X s2 and  = tan-1 (Xs /R).
12. Define the term voltage regulation of Alternator. (Nov/Dec 2013,Nov/Dec
2015,May/June 2016) (May 2017)(Nov 2019)
The voltage regulation of an Alternator is defined as the change in terminal
voltage from no-load to load condition expressed as a fraction or percentage of
terminal voltage at load condition; the speed and excitation conditions remaining
same.
13. Why is the synchronous impedance method of estimating voltage regulation
considered as pessimistic method?
Compared to other methods, the value of voltage regulation obtained by the
synchronous impedance method is always higher than the actual value and therefore
this method is called the pessimistic method.
14. Why is the MMF method of estimating the voltage regulation considered as
the optimistic method?
Compared to the EMF method, MMF method, involves more number of
complex calculation steps. Further the OCC is referred twice and SCC is referred once
while predetermining the voltage regulation for each load condition. Reference of
OCC takes care of saturation effect. As this method require more effort, the final
result is very close to the actual value. Hence this method is called optimistic method.
15. State the condition to be satisfied before connecting two alternators in
parallel.(Nov/Dec 2016)
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The following are the three conditions to be satisfied by synchronizing the
additional alternator with the existing one or the common bus-bars.
 The terminal voltage magnitude of the incoming Alternator must be made equal
to the existing Alternator or the bus-bar voltage magnitude.
 The phase sequence of the incoming Alternator voltage must be similar to the
bus-bar voltage.
 The frequency of the incoming Alternator voltage must be the same as the bus-
bar voltage.
16. List the factors that affect the load sharing in parallel operating generators?
The total active and reactive power delivered to the load, connected across the
common bus-bars, are shared among Synchronous generators, operating in parallel,
based on the following three factors
1.Prime-mover characteristic/input, 2. Excitation level and 3. Percentage synchronous
impedance and its R/X ratio.
17. What is meant by infinite bus-bars?(May/June 2014)
The source or supply lines with non-variable voltage and frequency are called
infinite bus-bars. The source lines are said to have zero source impedance and infinite
rotational inertia.
18. What is meant by floating when the synchronous motor is connected to an
infinite bus?
For starting a synchronous motor, a D.C motor is mechanically coupled with it.
The D.C motor is started and its speed is adjusted to a value near about the syn speed
of the synchronous motor. The excitation is gradually increased. The synchronous
machine is now working as an alternator. The excitation is increased till the EMF
induced is equal to the A.C bus bar voltage. If it is now synchronized with A.C
supply, we will say the machine is 'floating' on the bus bar. The alternator will neither
supply power nor take power from the bus bars.
19. Why is the field system of an alternator made as a rotor?(Apirl/May 2012)
Number of brush, voltage drop across the brush, number of phases of windings
in rotor and weight of motor are reduced.
20. What is synchronizing power of an alternator?(Apirl/May 2012)
When two alternators are operated parallel after synchronism, suppose due to
change in input parameter of second alternator it act as motor, first alternator
supplies power to second alternator. That power is called as synchronous power.
21. How will you distinguish between the two types of large synchronous
generator from their appearance?(May/June 2014,May/June 2016)
1. Salient pole type,the pole are projected out from the surface of the rotor and
are characterized by large diameters and short axial length.
2.Non-salient type,the poles are non-salient(i.e.)they do not project out from
the surface of the rotor.
22. What are the methods to predetermine the voltage regulation of an
alternator?
i. EMF method
ii. MMF method
iii.ZPF method
23. Distinguish between full-pitch coil and short-pitch coil.( Nov/Dec 2016)
Full-pitch coil Short-pitch coil
A full pitched coil is defined as the coil Short Pitch Coil/ Chorded Coil is defined
whose two coil sides are 180 electrical as the coil having the coil span less than 180
degree apart. degree.
If Chording Angle ξ is zero then it is a full Chording Angle ξ = 180° – Coil Span
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pitch coil.
The rms value of EMF Generated in a Full The rms value of EMF Generated in a Short
Pitched Winding of N turns, E = Pitched Winding of N turns E =
1.141 πfNØ 1.141 πfNØCos(ξ/2) .Short Pitched Coil
reduces the output voltage by a factor Kp ,
Kp= Pitch Factor = Cos(ξ/2)
24. Distinguish the use of salient pole and round rotor synchronous
machines.(May/June 2015)(Nov/Dec 2019)
salient pole Round rotor
Rotor poles are projected Smooth cylindrical type rotor
Mechanical strength is low Mechanical strength is high
It has large diameter and small axial It has small diameter and large axial
length length
This type of rotor used for low speed This type of rotor used for high speed
applications applications
Opearting noise is high Opearting noise is low
Non uniform airgap between stator and Uniform airgap between stator and rotor
rotor
25. Draw typical open circuit and short circuit characteristics of synchronous
machine. (May/June 2015)
O.C
Short Ciruict Current, Isc
Generated Voltage, Eg

S.C

Field Current, If

26. What is the necessity of chording in the armature winding of a synchronous

machine? (May 2017)
Fractional-pitch winding, when used in ac synchronous and asynchronous generator
armatures, in addition to saving copper, (1) reduce the MMF harmonics produced by
the armature winding and (2) reduce the EMF harmonics induced in the
winding,without reducing the magnitude of the fundamental EMF wave to a great
extent.
27. Distinguish between transient and sub-transient reactances. (May 2017)
An important factor in determining the magnitude of a fault current is a
variable reactance that changes rapidly after the initiation of the fault until it reaches a
steady state. Subtransient Reactance, usually denoted as X''d, is the reactance used to
determine the current during the first cycle after the occurance of the fault. In about
0.1 second this reactance increases to the level known as Transient Reactance usually
denoted as X'd, and after 0.5 to 2 seconds it increases to the leven known as
Synchronous Reactance and denoted as Xd, and this determines the fault current after
a steady condition is reached.
28. Write the equation for frequency of emf induced in an alternator.(Nov 2018)
voltage per phase = 4.44 Kc Kd f ΦT = 4.44 Kf Kc Kd f ΦT Volts

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P = No. of poles, Z = No. of Conductors or Coil sides in series/phase i.e. Z =
2T…Where T is the number of coils or turns per phase (Note that one turn or coil has
two ends or sides)
f = frequency of induced EMF in Hz, Φ = Flux per pole (Weber), N = rotor speed
(RPM) Kd= Distribution factor, Kp= Pitch factor
29.Identify the synchronous generator used in hydro electric power plant.(Nov 2018)
Salient pole machines are employed because the hydraulic turbine in the hydroelectric
plants operates at low speeds compared to steam plants, therefore generators in hydro
plant requires large number of field poles to produce the rated frequency.

PART –B
1. (i)Describe with neat sketches, the constructional details and operating
principle of salient pole type alternator. (Nov/Dec 2016)(Nov/Dec2018)
Construction of Alternators:
An alternator has 3,-phase winding on the stator and a d.c. field winding on the rotor.
a. Stator
It is the stationary part of the machine and is built up of silicon steel laminations
having slots on its inner periphery. A 3-phase winding is placed in these slots
and serves as the armature winding of the alternator. The armature winding is
always connected in star and the neutral is connected to ground.
b. Rotor
The rotor carries a field winding which is supplied with direct current through
two slip rings by a separate d.c. source. This
d.c. source (called exciter) is generally a small d.c. shunt or compound generator
mounted on the shaft of the alternator. Rotor construction is of two types,
namely;
1. Salient (or projecting) pole type
2. Non-salient (or cylindrical) pole type
Salient pole type:
In this type, salient or projecting poles are mounted on a large circular steel frame
which is fixed to the shaft of the alternator as shown in Fig. (1). The individual field
pole windings are connected in series in such a way that when the field winding is
energized by the d.c. exciter, adjacent poles have opposite polarities.

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Fig. 1. Salient Pole Rotor

Low and medium-speed alternators (120-400 r.p.m.) such as those driven by

diesel engines or water turbines have salient pole type rotors due to the following
reasons: (a) The salient field poles would cause an excessive windage loss if driven
at high speed and would tend to produce noise. (b) Salient-pole construction cannot
be made strong enough to withstand the mechanical stresses to which they may be
subjected at higher speeds.Since a frequency of 50 Hz is required, we must use a
large number of poles on the rotor of slow-speed alternators (Used in hydro turbines
and Diesel Engines). Low- speed rotors always possess a large diameter to provide
the necessary spate for the poles. Consequently, salient-pole type rotors have large
diameters and short axial lengths.
(ii)Derive the emf equation of alternator. (Nov/Dec 2011, Nov/Dec 2012,
Nov/Dec 2013, Nov/Dec2014, Nov/Dec 2015, Nov/Dec 2016, May 2017)(Nov
2018)
Lets,
P = No. of poles
Z = No. of conductors or Coil sides in series/phase i.e. Z = 2T…Where T is the
number of coils or turns per phase (Note that one turn or coil has two ends or sides)
f = frequency of induced EMF in Hz
Φ = Flux per pole (Weber)
N = rotor speed (RPM)

Kd= Distribution factor =

Where Distribution factor = Kd =

Kc or KP = Cos α/2
If induced EMF is assumed sinusoidal then,
Kf = Form factor = 1.11
In one revolution of the rotor i.e. in 60/N seconds, each conductor is cut by a flux
of ΦP Webers.
dΦ = ΦP and also dΦ = 60/N seconds

then induced E.M.F per conductor ( average) = ….. (i)

But we know that:
f = PN / 120 or N= 120f / P
Putting the value of N in Equation (i), we get,

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Average value of EMF per conductor ∴ (N= 120f/P)

If there are Z conductors in series per phase,
then synchronous generator average E.M.F per phase = 2 f Φ Z Volts = 4 f ΦT Volts ….. (Z =
2T)
Also we know that;
Form Factor = RMS Value / Average Value
= RMS value = Form Factor x Average Value,
VAV = 1.11 x 4fΦT = 4.44fΦT Volts.
 (Note that is exactly the same equation as the EMF equation of the transformer)
And the actual available voltage of generator per phase
VPH = 4.44 KC KD f ΦTPH
V = 4.44 Kf KC KD f ΦT Volts.
Where:
 V = Actual generated Voltage per phase
 KC = Coil Span Factor or Pitch Factor
 KD = Distribution Factor
 Kf = Form Factor
 f = frequency
 T = Number of coils or number of turns per phase
Note: If alternator or AC generator is star connected as usually the case, then the Line
Voltage is √3 times the phase voltage as derived from the above equation.
2. (i)Explain the condition for parallel operation of 3 phase alternator with neat
diagram. (Nov 2012) (May 2017)
Condition for Parallel Operation of Alternator
There are some conditions to be satisfied for parallel operation of the alternator.
Before entering into that, we should understand some terms which are as follows.
 The process of connecting two alternators or an alternator and an infinite bus
bar system in parallel is known as synchronizing.
 Running machine is the machine which carries the load.
 Incoming machine is the alternator or machine which has to be connected in
parallel with the system.
The conditions to be satisfied are
1. The phase sequence of the incoming machine voltage and the bus bar voltage
should be identical.
2. The RMS line voltage (terminal voltage) of the bus bar or already running
machine and the incoming machine should be the same.
3. The phase angle of the two systems should be equal.
4. The frequency of the two terminal voltages (incoming machine and the bus bar)
should be nearly the same. Large power transients will occur when frequencies
are not nearly equal.
Departure from the above conditions will result in the formation of power surges and
current. It also results in unwanted electro-mechanical oscillation of rotor which leads
to the damage of equipment.
General Procedure for Paralleling Alternators
The figure below shows an alternator (generator 2) being paralleled with a running
power system (generator 1). These two machines are about to synchronize for
supplying power to a load. Generator 2 is about to parallel with the help of a switch,
S1. This switch should never be closed without satisfying the above conditions.

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1.
To make the terminal voltages equal. This can be done by adjusting the
terminal voltage of incoming machine by changing the field current and make
it equal to the line voltage of running system using voltmeters.
2. There are two methods to check the phase sequence of the machines. They are
as follows
 First one is using a Synchroscope. It is not actually check the phase
sequence but it is used to measure the difference in phase angles.
 Second method is three lamp method (Figure 2). Here we can see three light
bulbs are connected to the terminals of the switch, S1. Bulbs become bright
if the phase difference is large. Bulbs become dim if the phase difference is
small. The bulbs will show dim and bright all together if phase sequence is
the same. The bulbs will get bright in progression if the phase sequence is
opposite. This phase sequence can be made equal by swapping the
connections on any two phases on one of the generators.

1. Next, we have to check and verify the incoming and running system frequency.
It should be nearly the same. This can be done by inspecting the frequency of
dimming and brightening of lamps.

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2. When the frequencies are nearly equal, the two voltages (incoming alternator
and running system) will alter the phase gradually. These changes can be
observed and the switch, S1 can be made closed when the phase angles are
equal.
(ii)Explain about the various methods of Synchronization. (May 2012) (May
2017)
Techniques for Synchronization
There are different techniques being available for the synchronization of alternators.
The primary purpose of these techniques is to check all four conditions discussed
above. The common methods used for synchronizing the alternators are given below.
1. Three Dark Lamps Method
2. Two Bright, One Dark Method
3. Synchroscope Method
Three Dark Lamps Method
The figure below shows the circuit for bright lamp method used to synchronize the
alternators. Assume that alternator is connected to the load supplying rated voltage
and frequency to it. Now the alternator-2 is to be connected in parallel with alternator-
1.
Three lamps (each of which is rated for alternator terminal voltage) are connected
across the switches of the alternator-2. From the figure it is clear that the moment
when all the conditions of parallel operation are satisfied, the lamps should be more or
less dark.
To synchronize the alternator-2 with bus bar, the prime mover of the alternator-2 is
driven at speed close to the synchronous speed decided by the bus bar frequency and
number of poles of the alternator.
Now the field current of the generator-2 is increased till voltage across the machine
terminals is equal to the bus bar voltage (by observing the readings on voltmeters).
If lamps go ON and OFF concurrently , indicating that the phase sequence of
alternator-2 matches with bus bar. On the other hand, if they ON and OFF one after
another, it resembles the incorrect phase sequence.
By changing the connections of any two leads of alternator-2 after shutting down the
machine, the phase sequence can be changed.

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Depending on the frequency difference between alternator-2 voltage and bus bar
voltage, ON and OFF rate of these lamps is decided. Hence, the rate of flickering has
to be reduced to match the frequency. This is possible by adjusting the speed of
alternator by its prime mover control.
When all these parameters are set, the lamps become dark and then the synchronizing
switch can be closed to synchronize alternator-2 with alternator-1.
The main disadvantage of this method is that rate of flickering only indicates the
difference between the alternator-2 and the bus bar. But the information of alternator
frequency in relation to bus bar frequency is not available in this method.
Suppose, if the bus bar frequency is 50Hz, the rate of flickering of lamps is same
when the frequency of the alternator is either 51 or 49 Hz, as the difference in these
two cases is 1Hz.
Two Bright and One Dark Lamp Method
The connections for this method are shown in figure below and it is useful in finding
whether the alternator frequency is lower or higher than the bus bar frequency.
Here, the lamp L2 is connected across the pole in the middle line of synchronizing
switch as similar to the dark lamp method, whereas the lamps L1 and L3 are
connected in a transposed manner.
The voltage condition checking is similar to the previous method and after it, the
lamps glow bright and dark one after another. The lower or higher value of alternator
frequency in comparison with bus bar frequency is determined by the sequence in
which the lamps become dark and bright.

The sequence of becoming bright and dark L1- L2 – L3 indicates that the incoming
generator frequency is higher than the bus bar frequency. Hence, the alternator speed
has to be reduced by prime mover control till the flickering rate is brought down to a
small.
On the other hand, the sequence flickering L1- L3 – L2 indicates that incoming
alternator frequency is less than that of bus bar.
Hence, the speed of the alternator is increased by the prime mover till the rate of
flickering is brought down to as small as possible. The synchronizing switch is then
closed at the instant when lamps L1 and L3 are equally bright and lamp L2 is dark.

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The disadvantage of this method is that the correctness of phase sequence cannot be
checked. However, this requirement is unnecessary for permanently connected
alternators where checking of phase sequence is enough to be carried out for the first
time of operation alone.
Synchroscope Method
It is similar to the two bright and one dark lamp method and indicates whether the
alternator frequency is higher or lower than the bus bar frequency. A synchroscope is
used for better accuracy of synchronization and it consists of two pairs of terminals.
One pair of terminals marked as ‘existing’ has to be connected across the bus bar
terminals or to the existing alternator and other pair of terminals marked as ‘incoming’
has to be connected across the terminals of incoming alternator.
The synchroscope has circular dial over which a pointer is hinged that is capable of
rotating in clockwise and anticlockwise directions.

After the voltage condition is checked, the operator has to check the synchroscope.
The rate at which the pointer rotates indicates the difference of frequency between the
incoming alternator and the bus bar.
Also, the direction to which the pointer rotates (to either fast or slow) gives the
information, whether the incoming alternator frequency is higher or lower than the bus
bar frequency and hence the pointer moves either fast or slow.
The appropriate correction has to be made to control the speed of the alternator so as
to bring the rate of rotation of pointer as small as possible.Therefore, synchroscope
along with voltmeters are enough for synchronization process. However, in most of
the cases a set of lights along with synchroscope is used as a double-check system.
These are the methods of synchronizing the generators. This process must be done
carefully to prevent the disturbances in the power system as well as to avoid a serious
damage to the machine. Only three lamps methods are not preferred today due to less
accuracy and manual operation.
These processes need a skilled and experienced person to handle the equipment while
synchronizing. In most cases synchroscope method with set of lamps is used as
mentioned above.

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Modern synchronization equipments automate the whole synchronization process with
the use of microprocessor based systems that avoids manual lamps and synchroscope
observations. These methods are easier to manage and more reliable.
3. (i)Explain how will you determine the d and q axis reactance of a synchronous
machine in your laboratory. (Nov/Dec 2011, May/June 2014, May/June
2015, May 2017)
The method used to determine Xq and Xd, the direct and quadrature axis reactance is
called slip test.
In an alternatore we apply excitation to the field winding and voltage gets induced
in the armature. But in the slip test, a three phase supply is applied to the armature,
having voltage must less than the rated voltage while the field winding circuit is kept
open. The circuit diagram is shown in the Fig. 1.

Fig.1 Circuit diagram for slip test

The alternator is run at a speed close to synchronous but little less than synchronous
value.The three phase currents drawn by the armature from a three phase supply
produce a rotating flux. Thus the armature m.m.f. wave is rotating at synchronous speed
as shown in the Fig. 2.

Fig. 2 Rotating armature m.m.f.

Note that the armature is stationary, but the flux and hence m.m.f. wave produced by
three phase armature currents is rotating. This is similar to the rotating magnetic field
existing in an induction motor.The rotor is made to rotate at a speed little less than the
synchronous speed. Thus armature m.m.f. having synchronous speed, moves slowly
past the filed poles at a slip speed (ns -n) where n is actual speed of rotor. This causes
an e.m.f. to be induced in the field circuit.
When the stator m.m.f. is aligned with the d-axis of field poles then flux Φd per
poles is set up and the effective reactance offered by the alternator is Xd.When the
stator m.m.f. is aligned with the q-axis of field poles then flux Φq per pole is set up
and the effective reactance offered by the alternator is Xq. As the air gap is
nonuniform, the reatance offered also varies and hence current drawn the armature
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also varies cyclically at twice the slip frequency. The r.m.s. current is minimum when
machine reactance is Xd and it is maximum when machine reactance is Xq. As the
reactance offered varies due to nonuniform air gap, the voltage drops also varies
cyclically. Hence the impedance of the alternator also varies cyclically. The terminal
voltage also varies cyclically. The voltage at terminals is maximum when current and
various drops are minimum while voltage at terminals is minimum when current and
various drops are maximum.The waveforms of voltage induced in rotor, terminal
voltage and current drawn by armature are shown in the Fig. 3. It can observed that
rotor field is aligned with the armature m.m.f., its flux linkage are maximum, but the
rate of change of flux is zero. Hence voltage induced in field goes through zero at this
instant. This is the position where alternator offers reactance Xd. While when rate of
change of flux associated with rotor is maximum, voltage induced in field goes
through its maximum. This is the position where alternator offers reactance Xq.The
reactances can be calculated as

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(ii)For the salient synchronous machine, derive the expression for power developed
as a function of load angle. (Nov/Dec 2011) (May 2017)

Thus the total power consists of a fundamental component and a second harmonic
component which is present because the armature reaction flux has a tendency to pass
through the field structure along its minimum reluctance path i.e. along field pole axis
and direct axis.
Since 2𝛿 exists because of difference in reluctance along p and q axes and is
called reluctance power and the term is called reluctance torque. The first term is
identical with that obtained for the cylindrical machine and component of power is
known as electromagnetic power.
Now dP/d𝛿 gives the Synchronizing power.

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4. (i)Explain the EMF and MMF method of evaluating the synchronous

reactance.(Nov/Dec 2012,Nov/Dec 2014, May/June 2015,Nov/Dec 2016, May
2017)
The Synchronous Impedance Method or Emf Method is based on the concept of
replacing the effect of armature reaction by an imaginary reactance. For calculating
the regulation, the synchronous method requires the following data; they are the
armature resistance per phase and the open circuit characteristic.The open circuit
characteristic is the graph of the circuit voltage and the field current. This method also
requires short circuit characteristic which is the graph of the short circuit and the field
current.
For a synchronous generator following are the equation given below

Where,
For calculating the synchronous impedance, Zs is measured, and then the value of
Ea is calculated. From the values of Ea and V, the voltage regulation is calculated.
Calculation of Synchronous Impedance
The following steps are given below for the calculation of the synchronous
impedance.
 The open circuit characteristics and the short circuit characteristic are drawn on the
same curve.
 Determine the value of short circuit current Isc and gives the rated alternator voltage
per phase.
 The synchronous impedance ZS will then be equal to the open circuit voltage divided
by the short circuit current at that field current which gives the rated EMF per phase.

The synchronous reactance is determined as

The graph is shown below.

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From the above figure consider the field current If = OA that produces rated alternator
voltage per phase. Corresponding to this field current, the open circuit voltage is AB

Therefore,
Assumptions in the Synchronous Impedance Method
The following assumptions made in the synchronous Impedance Method are given
below.
 The synchronous Impedance is constant
The synchronous impedance is determined from the O.C.C and S.C.C. It is the ratio
of the open circuit voltage to the short circuit current. When the O.C.C and S.C.C are
linear, the synchronous impedance ZS is constant.
 The flux under test conditions is the same as that under load conditions.
It is assumed that a given value of the field current always produces the same flux.
This assumption introduces considerable error. When the armature is short circuited,
the current in the armature lag the generated voltage by almost 90 degrees, and hence
the armature reaction is almost completely demagnetizing.
 The effect of the armature reaction flux can be replaced by a voltage drop proportional
to the armature current and that the armature reaction voltage drop is added to the
armature reactance voltage drop.
 The magnetic reluctance to the armature flux is constant regardless of the power
factor.
For a cylindrical rotor machine, this assumption is substantially true because of the
uniform air gap. Regulation obtained by using a synchronous impedance method is
higher than that obtained by actual loading. Hence, this method is also called
the Pessimistic method.
At lower excitations, ZS is constant, since the open circuit characteristics coincide
with the air gap line. This value of ZS is called the linear or Unsaturated
Synchronous Impedance. However, with increasing excitation, the effect of
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saturation is to decrease ZS and the values beyond the linear part of the open circuit
called as Saturated Value of the Synchronous Impedance.
MMF Method of Voltage Regulation
MMF Method is also known as Ampere Turn Method. The synchronous impedance
method is based on the concept of replacing the effect of armature reaction with an imaginary
reactance, the Magnetomotive force (MMF). The MMF method replaces the effect of
armature leakage reactance with an equivalent additional armature reaction MMF so that this
MMF may be combined with the armature reaction MMF.
To calculate the voltage regulation by MMF Method, the following information is required.
They are as follows:
 The resistance of the stator winding per phase.
 Open circuit characteristics at synchronous speed.
 Short circuit characteristic
Step to Draw Phasor Diagram of MMF Method
The phasor diagram at a lagging power factor is shown below:

 The armature terminal voltage per phase (V) is taken as the reference phasor along
OA.
 The armature current phasor Ia is drawn lagging the phasor voltage for lagging power
factor angle ϕ for which the regulation is to be calculated.
 The armature resistance drop phasor IaRa is drawn in phase with Ia along the line AC.
Join O and C. OC represents the emf E’.

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 Considering the open current characteristics shown above the field current
I’f corresponding to the voltage E’ is calculated.
 Draw the field current I’f leading the voltage E’ by 90 degrees. It is assumed that on a
short circuit all the excitation is opposed by the MMF of armature reaction. Thus,

From the short circuit current characteristics (SSC) shown above, determine the field
current If2 required to circulate the rated current on short circuit. This is the field current
required to overcome the synchronous reactance drop IaXa.
 Draw the field current If2 in phase in opposition to the current armature current Ia. Thus,

Determine the phasor sum of the field currents I’f and If2. This gives the resultant field
current If which would generate a voltage E0 under no-load conditions of the alternator. The
open-circuit emf E0 corresponding to the field current if is found from the open circuit
characteristics.
The regulation of the alternator is found from the relation shown below:

This is all about MMF method of voltage regulation.

(ii)Explain the procedure for POTIER method to calculate voltage regulation
of alternator.(May 2012) (May 2017)

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Potier Triangle or Zero Power Factor Method:
The Potier triangle determines the voltage regulation of the machines. This method depends
on the separation of the leakage reactance of armature and their effects. The graph of the
Potier triangle is shown in the figure below. The triangle formed by the vertices a, b, c has
shown below in the figure is called Potier Triangle.

Consider a point B on the Zero Power Factor Curve corresponding to rated terminal voltage
V and a field current of OM = If = Ff/Tf. If for this condition of operation the armature
reaction MMF has a value expressed in equivalent field current will be given as:

Then the equivalent field current of the resultant MMF would

be represented as shown below:

This field current OL would result in a generated voltage Eg =

Lc from the no-load saturation curve. Since for lagging zero power factor operation, the
generated voltage will be:

The vertical distance ac must be equal to the leakage reactance voltage DROP IaXaL where
Ia is the rated armature current.
Therefore,

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For Zero Power Factor operation with the rated current at any other terminal voltage, such
as V2. As the armature current is of the same value, both the Ia and XaL voltage and the
armature MMF must be of the same value.
Therefore, for all the conditions of operation with rated armature current at zero lagging
power factor, the Potier Triangle must be located between the terminal voltage V, a point on
the ZPFC, and the corresponding Eg point on the O.C.C.
If the Potier triangle cab is moved downward so that the side ab is kept horizontal and b is
kept on the ZPFC, the point c will move on the O.C.C. When the point b, reaches the point
e, the Potier triangle cab will move on the position fde shown in the figure. The location of
point f on the O.C.C will determine the voltage Eg2. When the point b, reaches the point b’,
the Potier Triangle will be in the position c’a’b’. This is the limiting position that
corresponds to short the circuit condition because the terminal voltage is zero at the point
b’.
The initial part of the O.C.C is almost linear, another triangle Oc’b’is formed by the O.C.C.
The hypotenuse of the Potier triangle and the baseline. A similar triangle such as ckb, can
construct from the Potier triangle in any other location by drawing a line kc parallel to Oc’.
Steps for Construction of Potier Triangle on ZPFC
Take a point b on the ZPFC preferably well upon the knee of the curve.
Draw bk equal to b’O. (b’ is the point for zero voltage, full load current). Ob’ is the short
circuit excitation Fsc.
Through k draw, kc parallel to Oc’ to meet O.C.C in c.
Drop the perpendicular ca on to bk.
Then, to scale ca is the leakage reactance drop IaXaL and ab is the armature reaction MMF
FaR or the field current IfaR equivalent to armature reaction MMF at rated current.
The effect of field leakage flux in combination with the armature leakage flux gives rise to
an equivalent leakage reactance Xp, known as the Potier Reactance. It is greater than the
armature leakage reactance.

For cylindrical rotor machines, the Potier reactance Xp is approximately equal to the
leakage reactance XaL. in salient pole machine, Xp may be as large as 3 times XaL.
Assumptions for Potier Triangle
The following assumptions are made in the Potier Triangle Method. They are as follows:-
The armature resistance Ra is neglected.
The O.C.C taken on no-load accurately represents the relation between MMF and Voltage
on load.
The leakage reactance voltage Ia XaL is independent of excitation.
The armature reaction MMF is constant.
It is not necessary to plot the entire ZPFC for determining XaL and Fa, only two points b
and b’ are sufficient. Point b corresponds to a field current which gives the rated terminal
voltage while the ZPF load is adjusted to draw rated current. Point b’ corresponds to the
short circuit condition (V = 0) on the machine. Thus, Ob’ is the field current required to
circulate the short circuit current equal to the rated current.
5. What is synchronizing power of an alternator? Derive an expression for the
synchronizing power between the two alternators connected in parallel.
(April/May 2012)

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6. (i)A four pole alternator has an armature with 25 slots and 8 conductors per slot and
rotates at 1500 rpm and the flux per pole is 0.05Wb. Calculate the emf generated, if
winding factor is 0.96 and all the conductors are in series. (Nov/Dec 2012)
Solution:
Z=25*8=200 conductors
¢=0.05 wb
N=1500 rpm
𝐾𝑓 = 0.96
E=4.44f¢T𝐾𝑓 𝐾𝐶 𝐾𝑑 𝐾𝑑 = 1, 𝐾𝐶 = 1
E=4.44*50*0.05*100*0.96
E=1065.4 Volts

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(ii)A 3-Phase, star-connected, 1000KVA, 11,000V alternator has rated current of
52.5A. The ac resistance of the winding per phase is 0.45Ω.The test results are
given below:
OC Test: field current = 12.5A,voltage between lines = 422V.
SC Test: field current = 12.5A, line current = 52.5A
Determine the full load voltage regulation of the alternator (i) 0.8 pf lagging and
(ii) 0.8 pf leading. (May/June 2014)(April/May 2019)

7. (a)Define armature reaction and explain the effect of armature reaction on different
power factor loads of synchronous generators. Mention the methods to reduce it.
(Nov/Dec2015, April/May 2012, May/June 2016, Nov 2019)

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Armature Reaction in a Synchronous Machine
The effect of Armature (stator) flux on the flux produced by the rotor field poles is
called Armature Reaction. When the current flows through the armature winding of the an
alternator, a flux is produced by the resulting MMF. This armature flux reacts with the main
pole flux, causing the resultant flux to become either less than or more than the original main
field flux.
For simplicity, we consider a 3 phase, 2 pole alternator shown in the figure below.

The winding of each pole is assumed to be concentrated, but the effects of armature reaction
will be the same as if a distributed winding were also used. The armature reaction in
synchronous machine affects the main field flux and vary differently for different power
factors.
Here armature reaction is discussed for following three conditions, namely unity power
factor, zero power factor lagging and zero power factor leading. The power factor can be
defined as the cosine of the angle between the armature phase current and the induced EMF
in the armature conductor in that phase.
Armature Reaction at Unity Power Factor
The direction of rotation of the rotor is considered clockwise. By applying right hand rule, the
direction of the induced emf in various conductors can be found. The direction of rotation of
the conductors is taken anticlockwise with respect to the rotor poles.
Suppose that the alternator is supplying current at unity power factor. The phase current IA,
IB, and IC will be in phase with their respective generated voltages, i.e., EA, EB, and EC as
shown in the figure below.

The positive direction of fluxes ϕA, ϕB, ϕC are shown in the figure below.

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The projection of a phasor on the vertical axis gives its instantaneous value.
At t=0, the instantaneous values of currents and fluxes are given by the equation shown

below.
Where the subscript m denotes the maximum values of current and flux. Thus, the flux ϕA is
along OA and the fluxes ϕB and ϕC are negative and acts opposite to each other represented
by OB and OC respectively as shown in the figure below. The resultant of the fluxes can be
found by resolving the fluxes horizontally and vertically.

Resolving along the horizontal direction we get

Similarly, resolving along the vertical direction we get

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The resultant armature reaction flux is given by

If the rotor is rotated, 30 degrees in a clockwise direction, the corresponding phasor diagram
is shown below.

At the instant when ωt = 30⁰, the instantaneous values of currents and fluxes are given as

The space diagram for fluxes at ωt = 30⁰ is shown below.

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Here, ϕB = 0. The resultant armature reaction flux is given by the equation shown below.

The direction of the resultant flux ϕAR is along OD, which makes an angle with the horizontal
in the clockwise direction.
Hence, it is observed that the resultant flux ϕAR sets up by the current in the armature remains
constant in magnitude equal to 1.5 ϕm and it rotates at synchronous speed. When the current is
in phase with the induced voltage the armature reaction flux ϕAR lags behind the main field by
90⁰. This is called Cross Magnetizing Flux.
Armature Reaction at Lagging Power Factor
If the alternator is loaded with an inductive load of zero power factor lagging. The phase
current IA, IB and IC will be lagging with their respective phase voltages EA, EB and EC by
90⁰. The figure below shows the phasor diagram of armature reaction at lagging load.

At time t = 0, the instantaneous values of currents and fluxes are given by

The space diagram of the magnetic fluxes is shown below.

The resultant flux ϕAR is given by the equation shown below.

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The direction of the armature reaction flux is opposite to the main field flux. Therefore, it will
oppose and weaken the main field flux. It is said to be demagnetized.
Armature Reaction at Leading Power Factor
If the alternator is loaded with a load of zero power factor leading. The phase currents IA,
IB and IC will be leading their respective phase voltages EA, EB and EC by 90⁰. The phasor
diagram is shown below.

At time t = 0, the instantaneous values of currents and fluxes are given by the equations
shown below.

The direction of the flux is shown below in the phasor diagram.

The resultant flux is given by the equation shown below

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The direction of the armature reaction flux is in the direction of main field flux. It is known
as magnetizing flux.
The following methods are used in order to reduce the effect of armature reaction.
The armature reaction causes the distortion in main field flux.
This can be reduced if the reluctance of the path of the cross-magnetising field is
increased.The armature teeth and air gap at pole tips offer reluctance to armature flux.
Thus by increasing length of air gap, the armature reaction effect is reduced.
If reluctance at pole tips is increased it will reduce distorting effect of armature reaction.By
using special construction in which leading and trailing pole tip portions of laminations are
alternately omitted.
The effect of armature reaction can be neutralized by use of compensating winding.
It is always placed in series with armature winding.
The armature ampere conductors under pole shoe must be equal to compensating winding
ampere conductors which will compensate armature mmf perfectly.
The armature reaction causes shifting the magnetic neutral axis.
Therefore there will be some flux density at brush axis which produces emf in the coil
undergoing commutation.
This will lead to delayed commutation.
Thus the armature reaction at brush axis must be neutralized.
This requires another equal and opposite mmf to that of armature mmf.
This can be applied by interpoles which are placed at geometric neutral axis at midway
between the main poles.
(b)Derive an expression for real and reactive power outputs of
asynchronous generator. (May/June 2015)
Using the simplified generator power flow diagram it can be seen that the difference between
mechanical input power and electrical ouput power is the combined rotational loss plus I2RI2R losses.
If the field currend is provided by a pilot exciter and synchronous exciter, the power for the
rotor I2RI2R losses is supplied from the mechanical system and may be grouped with rotational
losses.

Power converted, Pconv is the product of electromagnetic torque and speed

Pconv=τωs
and will equal the power delivered to the armature circuit. Power and torque equations for balanced
synchronous generators can then be obtained from analysis of the per-phase equivalent circuit and
phasor diagram.

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From the above circuit, the electrical output power output from one phase may be written as
P1ϕ=VIAcosθ
For three phases Power and Reactive Power are given by
Pout=3VIAcosθ
Q=3VIAsinθ
The electrical input power can be found from either the real part of the product of induced voltage
phasor and armature current phasor or the output power plus armature Ohmic losses:
Pconv=Pout+3I2ARA
In large machines, the resistive losses in the machine are small as a percentage of the total power
flow. (Note this does not mean they are small, 1.0 percent resistive loss in a 100MW machine is still
1MW losses and cooling must be designed accordingly). If this is the case, for approximate analysis
purposes resistive losses can be neglected and input power will equal output power. The phasor
diagram is also simplified accordingly:

From the above diagram it can be seen that

Esinδ=IAXScosθ
Ecosδ−V=IAXSsinθ
and therefore
<
P=3VE/XS*sinδ
Q=3VE/XS*cosδ−3V2/XS
Using the equation for power conversion, the torque may be written as
τ=3VE/XSωssinδ
8. (i)In a 50-KVA, Y-connected, 440-V, 3-phase, 50Hz alternator, the effective
armature resistance is 0.25Ω/phase. The synchronous reactance is 3.2 Ω/phase and
leakage reactance is 0.5Ω/phase. Determine at rated load at unity power factor: (a)
Internal e.m.f. Ea, (b)no-load e.m.f, EO,(c) percentage regulation on full load, (d)
value of synchronous reactance which replaces armature reaction.(May/June2016)

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(ii)A three phase, star connected,1000 kVA, 2000V, 50Hz alternator gave the
following open circuit and short circuit test readings:
Field 10 20 25 30 40 50
current(A):
O.C. 800 1500 1760 2000 2350 2600
voltage(V):
S.C.armature - 200 250 300 - -
current(A):
The armature effective resistance per phase is 0.2Ω. Draw the characteristic curves
and determine the full load percentage regulation at i.0.8 p.f lagging, ii. 0.8 p.f
leading by MMF method.
The armature effective resistance per phase is 0.2Ω. Draw the characteristic curves and determine
the full load percentage regulation at i.0.8 p.f lagging, ii. 0.8 p.f leading by MMF method.
( Nov/Dec2015) (May 2017)

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9. A 220V, 50Hz, 6-pole star connected alternator with ohmic resistance of

0.06Ω/phase, gave the following data for open-circuit, short-circuit and full load
zero power factor characteristics. Find the percentage voltage regulation at full-load
current of 40A at power factor of 0.8 lag by i.emf method, ii.mmf method and
iii.zpf method. Compare the results so obtained. (May/June 2015)
Field 0. 0.4 0.6 0.8 1.0 1.2 1.4 1.8 2.20 2.6 3.0 3.4
current(A) 20 0 0 0 0 0 0 0 0 0 0
Open 29 58 87 116 146 172 19 23 261. 28 30 31
circuit 4 2 5 4 0 0
voltage(V)
Short 6. 13. 20 26. 32. 40 46. 59 - - - -
circuit 6 2 5 4 3
current(A)
Zpf - - - - - 0 29 88 140 17 20 23
terminal 7 8 0
voltage
(V)

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10. The following data were obtained for the OCC of a 10MVA, 13 KV ,3-phase,
50Hz, Y-connected synchronous generator.
Field
50 75 100 125 150 162.5 200 250 300
current(A):
O.C.
6.2 8.7 10.5 11.8 12.8 13.2 14.2 15.2 15.9
Voltage(KV):
An excitation of 100A causes the full-load current to flow during the Short-circuit
test. The excitation required to give the rated current at zero pf and rated voltage is
290A.
(i) Calculate the adjusted synchronous reactance of the machine.
(ii) Calculate the leakage reactance of the machine assuming the resistance to be
negligible.
(iii) Determine the excitation required when the machine supplies full-load at 0.8pf
lagging by using the leakage reactance and drawing the mmfphasor diagram. What
is the voltage regulation of the machine? Also calculate the voltage regulation for
this loading using the adjusted synchronous reactance. Compare and comment upon
the two results.(May/June2016)

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12. A three phase star connected alternator is rated at 1500 KVA,12000 V. The
armature effective resistance and synchronous reactance are 2Ω and 35Ω
respectively. Calculate the percentage regulation for the load of 1200 KW at 0.8
lagging and leading powerfactors. Draw the phasor diagram for the same. (Nov 2019)
Given Data:
P = 1500 KVA
V = 12000 V
Ra = 2Ω
Xs = 35Ω
Pload = 1200 KW
cosΦ = 0.8 (lag,lead)
Formula:
E0 = ((VcosΦ+ IRa)2+ (VsinΦ +/-IXS)2)1/2
Voltage regulation = E0 –V/V*100
Solution:
1200000 = √3*12000*I* 0.8
Therefore, I = 72.17 A
IRa = 144.34 V
IXS = 2165.1V
V/Phase = 12000/√3= 6928.2V

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E0 = 6324.57V( for 0.8 lagging pf)

E0 =1999.9 V( for 0.8 leading pf)
Voltage regulation =8.71( for for 0.8 lagging pf)
Voltage regulation =-71.1.( for for 0.8 leading pf)

VI IXs
IRa
13. A 1500 KVA 6600V three phase star connected alternator with a resistance of
0.4 Ω and reactance of 6Ω per phase delivers full load current at a power factor
0.8 lagging and normal rated voltage . Estimate the terminal voltage for the
same excitation and load current at 0.8 pf leading. (Nov 2019)
Given:
P= 1500 KVA
Ra = 0.4 Ω
Xs = 6Ω
Solution:
At 0.8 pf lagging
I full load = 1500000/√3*6600 = 131.22 A
Termainal voltage = 6600/√3 = 3810.5V
I Ra = 131.22*0.4 = 52.49 V
I Xs = 787.32 V
E0 = ((VcosΦ+ IRa)2+ (VsinΦ +/-IXS)2)1/2
= (3810.5*0.8+52.49) 2+(3810.5*0.6+787.32) 2)1/2
= 4366V
At 0.8 pf leading with E0 =4366V find V
4366 = ( 0.8V+ 52.49) 2+(0.6 V – 787.32) 2)1/2
V= 3749.34 V
UNIT II - SYNCHRONOUS MOTOR
PART A
1. Name the methods of starting a synchronous motors (May/June 2014)
i. By an extra 3 phase induction motor. ii. By providing damper winding in
pole shoes. iii. By operating the pilot exciter as a dc motor
2. Why a synchronous motor is called as constant speed motor? (April/May
2012,Nov/Dec 2018)
Synchronous motor work on the principle of force developed due to the
magnetic attraction established between the rotating magnetic field and the main pole
feed. Since the speed of rotating magnetic field is directly proportional to frequency
the motor operates at constant speed.
3. What are V and inverted V curves of synchronous motor ? (Nov/Dec 2011)
(May 2017)
The variation of magnitude of line current with respect to the field current is
called V curve. The variation of power factor with respect to the field current is called
inverted V curve.
4. What happens when the field current of a synchronous motor is increased
beyond the normal value at constant input?

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Increase in emf causes the motor to have reactive current in the leading
direction. The additional leading reactive current causes the magnitude of line current,
accompanied by the decrease in power factor.
5. Distinguish between synchronous phase modifier and synchronous condenser
A synchronous motor used to change the power factor or power factor in the
supply lines is called synchronous phase modifier. A synchronous motor operated at
no load with over excitation condition to draw large leading reactive current and
power is called a synchronous condenser.
6. How the synchronous motor can be used as synchronous condenser? (Nov/Dec
2011& 2012 & 2014) (May 2017)(Nov 2018)
Synchronous motor is operated on over excitation so as to draw leading
reactive current and power from the supply lines. This compensates the lagging
current and power requirement of the load making the system power factor to become
unity. The motor does the job of capacitors and hence called as synchronous
condenser.
7. Mention the methods of starting of 3-phase synchronous motor.(May/June
2014)
i. A D.C motor coupled to the synchronous motor shaft.
ii. A small induction motor coupled to its shaft
iii. Using damper windings as a squirrel cage induction motor.
8. What is meant by hunting of synchronous motor? (April/May 2012, Nov/Dec
2013, Nov/Dec 2015, Nov/Dec 2016)
When the load applied to the synchronous motor is suddenly increased or
decreased, the rotor oscillates about its synchronous position with respect to the stator
field. This action is called hunting.
9. Write important differences between a 3-phase synchronous motor and a 3-
phase induction motor.(May/June 2014)
i. Synchronous motor is a constant speed motor where as induction motor
speed will decrease on load. ii. Synchronous motor requires A.C and D.C supplies
where as induction motor requires only A.C supply. iii. Synchronous motor can be
worked under various power factors such as lagging, leading and unity. But induction
motor can be run with lagging power factor only.
10. What could be the reasons if a 3-phase synchronous motor fails to
start?(Nov/Dec 2014& May/June2015)
It is usually due to the following reasons
i. Voltage may be too low. ii. Too much starting toad.
iii. Open circuit in one phase or short circuit. iv. Field excitation may be excessive.
11. How does a change of excitation affect its power factor?
When the excitation is reduced, the motor draws a lagging current and when
the excitation is increased, the armature current is leading the applied voltage. It may
also happen for some value of excitation, that current may be in phase with the voltage
i.e. power factor is unity.
12. What is phase swinging?
Phase swinging is otherwise called as hunting. When the load on the
synchronous motor is varying or the supply frequency is pulsating the speed of the
machine will fluctuate causing vibration on the rotor, which is called hunting or phase
swinging.
13. Under which condition a synchronous motor will fail to pull in to step?
( i) No field excitation.(ii) Excessive load. (iii) Excessive load inertia.
14. Write the applications of synchronous motor.
(i) power factor improvement in sub-stations and in Industries. (ii) Industries
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for power applications (iii) constant speed drives such as motor -generator set, pumps
and compressors.
15. Why a synchronous motor is a constant speed motor?
It runs always with a constant speed called synchronous speed N =120 f/P.
where f is the supply frequency and P is the no- of poles.
16. How the synchronous motor is made self-starting?
By providing damper windings in the pole face's, it will start and run like a
squirrel cage induction motor.
17. State the characteristic features of synchronous motor.
a. The motor is not inherently self starting. b. The speed of operation is always
in synchronous with the supply frequency irrespective of load conditions. c. The
motor is capable of operating at any power factor.
18. In what way synchronous motor is different from other motors?
All dc and ac motors work on the same principle. Synchronous motor operates
due to magnetic locking taking place between stator and rotor magnetic fields.
19. What are the uses of damper winding in synchronous motor? (Nov/Dec 2013,
Nov/Dec 2016) (May 2017) (April/May 2019)
1.Starting of synchronous motor; 2.Reduce the Oscillations
20. What is the phasor relation between induced emf and terminal voltage of a 3
phase synchronous motor?
The rotating magnetic field is initially established by the prime source of
supply V. The main field then causes an emf (e) to get induced in the 3 phase winding.
Hence when the machine operates as a synchronous motor the emf phasor always lags
the terminal voltage phasor by the load/torque angle  .
21. What is meant by pull out torque?
When the load on the motor is increased, the load angle is also increased, i.e. the
rotor goes on progressively falling back in phase and draws more current. If we
increase the load further, then the motor pulls out of synchronism and stops. The
torque developed at pull out point is called pull out torque.
22. Give some merits and demerits of synchronous motor(May/June 2016)
Merits
i. This motor runs at constant speed (synchronous spaed) even at full load.
ii. Can be operated with leading power factor, for power factor improvement.
Demerits
i. Two sources of supply are necessary
ii. Since damper-winding resistance is low, it take large currents, from supply mains.
23. When is synchronous motor is said to receive 100% excitation? (Nov/Dec
2015)
The valueof excitation for which back emf Eb is equal (in magnitude) to
applied voltage V is known as 100% excitation.
24. How can we change the operating speed of synchronous motor?(May/June
2016)
It runs either at synchronous speed or not at all. That is, while running it
maintains a constant speed. The speed is independent of load. Once the motor is in
operation, the speed of the motor is dependent only on the supply frequency. Speed of
the synchronous motor can be controlled by inverter units
25. Draw the typical torque angle characteristics of synchronous machine.
(May/June2015)

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26. A 3-phase synchronous motor driving a constant load torque draws power
from infinite bus at leading power factor. How power angle and power factor will
change if the excitation is increased ? (May 2017)
The increase in voltage in the DC field circuit [approximated by a series R-L
combination] causes a proportional increase in the current in the same circuit. This has
a directly proportional impact on the induced voltage of the stator, in that the power
factor changes. With an increase in field current [or voltage] beyond rated value, the
power factor becomes leading, while a decrease causes a relatively lagging pf and the
power angle will decrease.
27. Name the various torques associated with a synchronous motor?(April/May
2019)
 Starting torque
 Running torque
 Pull-in torque
 Pull-out torque
28. How hunting can be prevented? (Nov/ Dec 2019)
Hunting can be reduced by providing damper winding. These windings consists of
short circuited copper bars embedded in the faces of the field poles of the synchronous
notors.When rotating at constant load is unitform, there is no relative motion between
the rotor and stator forward rotating fields and hence no current is induced in these
windings. But when hunting takes place, the relative motion of rotor sets up eddy
currents in these windings which flow such as to suppress the oscillations. The
dampers should have low resistance to be more effective.
29. List the merits of three phase synchronous motor over three phase induction
motors? (Nov 2019)
Merits
i. This motor runs at constant speed (synchronous spaed) even at full load.
ii. Can be operated with leading power factor, for power factor improvement.
PART-B
1. (a)Illustrate through neat phasor diagram, the functioning of synchronous
machine with varying excitation under constant real power load.(May/June
2015)
Let,
Ef to represent the excitation voltage
Vt to represent the terminal voltage
Ia to represent the armature current
Θ to represent the angle between terminal voltage and armature current
ᴪ to represent the angle between the excitation voltage and armature current
δ to represent the angle between the excitation voltage and terminal voltage
ra to represent the armature per phase resistance.
We will take Vt as the reference phasor in order to phasor diagram for synchronous motor.
In order to draw the phasor diagram one should know these two important points which are
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written below:
(1) We know that if a machine is made to work as a asynchronous motor then direction of
armature current will in phase opposition to that of the excitation emf.
(2) Phasor excitation emf is always behind the phasor terminal voltage.
Above two points are sufficient for drawing the phasor diagram for synchronous motor. The
phasor diagram for the synchronous motor is given below,

In the phasor one the direction of the armature current is opposite in phase to that of the
excitationemf.. It is usually customary to omit the negative sign of the armature current in the
phasor of the synchronous motor so in the phasor two we have omitted the negative sign of
the armature current. Now we will draw complete phasor diagram for the synchronous motor
and also derive expression for the excitation emf in each case. We have three cases that are
written below:

(a) Motoring operation at lagging power factor.

(b) Motoring operation at unity power factor.
(c) Motoring operation at leading power factor.

Given below are the phasor diagrams for all the operations.
(a) Motoring operation at lagging power factor: In order to derive the expression for the
excitation emf for the lagging operation we first take the component of the terminal voltage
in the direction of armature current Ia. Component in the direction of armature current is
VtcosΘ.
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As the direction of armature is opposite to that of the terminal voltage therefore voltage drop
will be –Iara hence the total voltage drop is (VtcosΘ – Iara) along the armature current.
Similarly we can calculate the voltage drop along the direction perpendicular to armature
current. The total voltage drop comes out to be (Vtsinθ – IaXs). From the triangle BOD in the
first phasor diagram we can write the expression for excitation emf as

(b) Motoring operation at unity power factor: In order to derive the expression for the
excitation emf for the unity power factor operation we again first take the component of the
terminal voltage in the direction of armature current Ia. But here the value of theta is zero and
hence we have ᴪ = δ. From the triangle BOD in the second phasor diagram we can directly
write the expression for excitation emf as

(c) Motoring operation at leading power factor: In order to derive the expression for the
excitation emf for the leading power factor operation we again first take the component of the
terminal voltage in the direction of armature current Ia. Component in the direction of
armature current is VtcosΘ. As the direction of armature is opposite to that of the terminal
voltage therefore voltage drop will be (–Iara) hence the total voltage drop is (VtcosΘ – Iara)
along the armature current. Similarly we can calculate the voltage drop along the direction
perpendicular to armature current. The total voltage drop comes out to be (Vtsinθ + IaXs).
From the triangle BOD in the first phasor diagram we can write the expression for excitation
emf as

(b)List out the main characteristic features of synchronous motor.

Synchronous motors have the following characteristics: ·
 A three-phase stator similar to that of an induction motor. Medium voltage stators
are often used. ·
 A wound rotor (rotating field) which has the same number of poles as the stator,
and is supplied by an external source of direct current (DC). Both brush-type and
brushless exciters are used to supply the DC field current to the rotor. The rotor
current establishes a north/south magnetic pole relationship in the rotor poles
enabling the rotor to “lock-in-step” with the rotating stator flux. ·
 Starts as an induction motor. The synchronous motor rotor also has a squirrel-cage
winding, known as an Amortisseur winding, which produces torque for motor
starting. · Synchronous motors will run at synchronous speed in accordance with
the formula: 120 x Frequency Synchronous RPM = Number of Poles Example: the
speed of a 24 -Pole Synchronous Motor operating at 60 Hz would be: 120 x 60 / 24
= 7200 / 24 = 300 RPM Synchronous Motor Operation ·
 The squirrel-cage Amortisseur winding in the rotor produces Starting Torque and
Accelerating Torque to bring the synchronous motor up to speed. ·
 When the motor speed reaches approximately 97% of nameplate RPM, the DC
field current is applied to the rotor producing Pull-in Torque and the rotor will
pull-in-step and “synchronize” with the rotating flux field in the stator. The motor
will run at synchronous speed and produce Synchronous Torque. ·
 After synchronization, the Pull-out Torque cannot be exceeded or the motor will
pull out-of-step. Occasionally, if the overload is momentary, the motor will “slip-a-
pole” and resynchronize. Pull-out protection must be provided otherwise the motor
will run as an induction motor drawing high current with the possibility of severe
motor damage

2. Discuss the following (i) Constant excitation circle (ii) Constant power circle (Nov
2014) (May 2017)

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3. Draw the V and inverted V curves and explain the effect of excitation on armature
current and power factor of synchronous motor. (Nov/Dec 2011,Nov/Dec
2012,Nov/Dec 2013, Nov/Dec 2014, Nov/Dec2015, May/June 2016, Nov/Dec
2016, May 2017) (April/May 2019)(Nov/Dec 2019)

V Curve of a Synchronous Motor

V curve is a plot of the stator current versus field current for different constant loads. The
Graph plotted between the armature current Ia and field current If at no load the curve is

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obtained known as V Curve. Since the shape of these curves is similar to the letter “V”, thus
they are called V curve of synchronous motor.
The power factor of the synchronous motor can be controlled by varying the field current If.
As we know that the armature current Ia changes with the change in the field current If. Let us
assume that the motor is running at NO load. If the field current is increased from this small
value, the armature current Ia decreases until the armature current becomes minimum. At this
minimum point, the motor is operating at unity power factor. The motor operates at lagging
power factor until it reaches up to this point of operation.
If now, the field current is increased further, the armature current increases and the motor
start operating as a leading power factor. The graph drawn between armature current and
field current is known as V curve. If this procedure is repeated for various increased loads, a
family of curves is obtained.
The V curves of a synchronous motor are shown below.

The point at which the unity power factor occurs is at the point where the armature current is
minimum. The curve connecting the lowest points of all the V curves for various power
levels is called the Unity Power Factor Compounding Curve. The compounding curves for
0.8 power factor lagging and 0.8 power factor leading are shown in the figure above by a red
dotted line.
The loci of constant power factor points on the V curves are called Compounding Curves. It
shows the manner in which the field current should be varied in order to maintain constant
power factor under changing load. Points on the right and left of the unity power factor
corresponds to the over excitation and leading current and under excitation and lagging
current respectively.
The V curves are useful in adjusting the field current. Increasing the field current If beyond
the level for minimum armature current results in leading power factor. Similarly decreasing
the field current below the minimum armature current result results in lagging power factor.
It is seen that the field current for unity power factor at full load is more than the field current
for unity power factor at no load.
The figure below shows the graph between power factor and field current at the different
loads.

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It is clear from the above figure that, if the synchronous motor at full load is operating at
unity power factor, then removal of the shaft load causes the motor to operate at a leading
power factor.
4. Explain the various starting methods of a synchronous motor.(Nov 2012&
2014,Nov/Dec 2016,May/June 2016, May 2017)(April/May 2019)
Methods of starting Synchronous Motor:
We have to think about an alternative to rotate the rotor at a speed almost equal that of
synchronous speed.So this can be possible by employing various methods to start
the synchronous motor.The following are the different methods to start a synchronous motor.
1.Using pony Motors:
In this method, some external devices like small induction motor used to bring rotor near
to synchronous motor.This external device is called Pony motor.
When the rotor attains synchronous speed, dc excitation to the rotor is switched on.After
some time synchronism is developed and then pony motor is decoupled.Due to synchronism
promoter continues to rotate as a synchronous motor.
2.Using damper winding:
In a synchronous motor, we have normal field winding and in addition to this
additional winding consisting of copper bars is placed in the slots in the pole faces.These bars
short-circuited with the help of end rings.This additional winding on the rotor is
called damper winding.This winding as it is short-circuited, it acts like squirrel cage rotor
winding of an induction motor.The schematic diagram of this damper winding is shown in
the below figure.

Once the stator is excited by a three phase supply, the motor starts rotating as an
induction motor at sub-synchronous speed. Then d.c. supply is given to the field winding.At a
particular instant, motor gets pulled into synchronism and starts rotating at a synchronous
speed. As the rotor rotates at synchronous speed, the relative motion between damper
winding and the rotating magnetic field is zero.Hence when the motor is running as
a synchronous motor, there cannot be any induced emf in the damper winding.
So damper winding is active only at the start, to run the motor as an induction motor at

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start.Afterwards, it is out of the circuit.As damper winding is short circuited and motor gets
started as an induction motor, it draws high current at the start so induction motor starters like
star-delta, autotransformer etc. used to start the synchronous motor as an induction motor.
3.As a Slip Ring Induction Motor:
The above method of starting synchronous motor as a squirrel cage induction motor
does not provide high starting torque.So to achieve this, instead of shorting the damper
Winding, it is designed to form a three phase star or delta connected winding.
The three ends of this winding are brought out through slip rings. An external rheostat
then can be introduced in series with the rotor circuit. So when the stator is excited, the motor
starts as a slip ring induction motor and due to resistance added in the rotor provides high
starting torque.
The resistance is then gradually cut off, as motor gathers speed.When motor attains
speed near synchronous, d.c. excitation is provided to the rotor, then motor gets pulled into
synchronism and starts rotating at synchronous speed.The damper winding is shorted by
shorting the slip rings.
The initial resistance added in the rotor not only provides high starting torque but also
limits high inrush of starting current.Hence it acts as a rotor resistance
starter.The synchronous motor started by this method is called a slip ring induction motor is
shown in the below figure.

It can be observed from the above figure that the same three phase rotor winding acts
as a normal rotor winding by shorting two of the phases. From the positive terminal, current
'I' flows in one of the phases, which divides into two other phases at start point as 1/2 through
each, when the switch is thrown on d.c. supply side.
4.Using Small D.C. Machine:
Many times, large synchronous motors are provided with a coupled dc machine. This
machine is used as a dc motor to rotate the synchronous motor at asynchronous speed.Then
the excitation to the rotor is provided.Once the motor starts running as a synchronous motor,
the same dc machine acts as a dc generator called exciter.The field of the synchronous
motor is then excited by this exciter itself.

5. A 75kW, 400V, 4 pole, 3 phase, star connected synchronous motor has a resistance
and synchronous reactance per phase of 0.04Ω and 0.4 Ω respectively. Compute
for full load 0.8pf lead the open circuit emf per phase and gross mechanical power
developed. Assume an efficiency of 92.5%. (May 2014)

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6. (i)A 2000V, 3 phase, 4 pole, star connected synchronous motor runs at 1500rpm.
The excitation is constant and corresponding to an open circuit voltage of
2000V. The resistance is negligible in comparison with synchronous reactance
of 3.5Ω /ph. For an armature current of 200A.Determine (i) power factor (ii)
power input (iii) torque developed.

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(ii)A 5kW,3 phase Y-connected 50 Hz,440 V, cylindrical rotor synchronous motor
operates at rated condition with 0.8 pf leading. The motor efficiency excluding
field and stator losses is 95% and Xs=2.5 Ω. Calculate 1.Mechanical power
developed 2.armature current 3.back emf 4.power angle 5.maximum or pull out
torque of the motor.

7. (i)Derive an expression for the maximum torque developed per phase of a

synchronous motor.(May 2012)
We know that torque equation in synchronous motor or generator is directly proportional to
the stator filed strength, rotor field strength and the sine of angle between them. This is true
for all rotating electrical machine.
If Fs, Fr and λ be the stator field strength, rotor field strength and angle between Fs & Fr,
then the torque is given as
Te = FsFrSinλ
The above torque equation is a general equation applicable for all rotating electrical
machine. In this post we will derive a general torque equation for synchronous machine. For
this purpose, let us consider a uniform air gap two pole machine as shown below.

Current in the stator winding produces stator mmf which is assumed to be sinusiodally
distributed in the air gap periphery. The peak value of this stator mmf Fs is directed along
the stator winding axis as shown in figure. In the above figure, Fs is taken horizontal with
Fs directed from left to right. Similarly, rotor current produces rotor mmf which is also
assumed sinusiodally distributed in the air gap. The peak value of rotor mmf Fr is along the
rotor winding axis as shown in figure. It should be noted that Fs and Fr is the peak value of
resultant mmf due to all stator and rotor winding.
These stator and rotor mmf in turn causes appearance of stator and rotor poles. Stator mmf
Fs causes appearance of North pole in the left side whereas South pole at the right side of
stator. Similarly, North and South pole are produced due to rotor mmf as shown in figure.

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These stator and rotor magnetic poles interact with each other and tend to align their
magnetic axis. This results in development of electromagnetic torque.
In the above figure, the length of air gap is ‘g’ and average radius i.e. average of stator and
rotor radii is ‘r’. The effective axial length of synchronous machine is ‘l’.
For deriving general torque equation for synchronous motor / generator, following
assumptions are made:
1. The stator and rotor iron have infinite permeability. This effectively means
that saturation is neglected.
2. All the magnetic flux crosses the air gap perpendicularly. This means that flux
leakage is assume to be absent.
3. The air gap length is very small when compared to the axial length of synchronous
machine. This means that the value of flux density at stator surface, rotor surface and at any
point in the air gap is same.
4. Only fundamental sine component of stator and rotor mmf wave is considered.
Based on the above assumptions, the torque equation for any rotating electrical machine is
given as
Te = -(π/8)P2ØFsSinδs Nm
= -(π/8)P2ØFrSinδr Nm
P = Number of poles
Ø = Resultant air gap flux per pole
Fr = Rotor mmf
Fs = Stator mmf

In the above phasor, FR is the resultant of stator mmf Fs and rotor mmf Fr. The angle
between Fr & FR i.e. δr is called the load angle. Similarly, the angle between the resultant
air gap flux FR and Stator mmf Fs i.e. δs is called load angle. The angle λ between the stator
and rotor mmf is called the torque angle.
The negative sign in the torque equation of synchronous machine implies that
electromagnetic torque acts in such a direction to minimize the torque angle λ. It must be
noted here that, the above torque equation is valid not only for synchronous motor or
generator rather it is valid for all rotating electrical machine.
(ii) Explain how synchronous motor can be used as a synchronous condenser. Draw
the phasor diagram. (May 2012) (May 2017) (April/May 2019).
Like capacitor bank, we can use an overexcited synchronous motor to improve the
poor power factor of a power system. The main advantage of using synchronous motor is that
the improvement of power factor is smooth.
When a synchronous motor runs with over-excitation, it draws leading current from
the source. We use this property of a synchronous motor for the purpose.
Here, in a three-phase system, we connect one three-phase synchronous motor and run it at
no load.

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Suppose due to a reactive load of the power system the system draws a current IL from the
source at a lagging angle θL in respect of voltage. Now the motor draws a IM from the same
source at a leading angle θM. Now the total current drawn from the source is the vector sum
of the load current IL and motor current IM. The resultant current I drawn from the source has
an angle θ in respect of voltage. The angle θ is less than angle θ L. Hence power factor of the
system cosθ is now more than the power factor cosθL of the system before we connect the
synchronous condenser to the system.
The synchronous condenser is the more advanced technique of improving power
factor than a static capacitor bank, but power factor improvement by synchronous condenser
below 500 kVAR is not economical than that by a static capacitor bank. For major power
network we use synchronous condensers for the purpose, but for comparatively lower rated
systems we usually employ capacitor bank.
The advantages of a synchronous condenser are that we can control the power
factor of system smoothly without stepping as per requirement. In case of a static capacitor
bank, this fine adjustments of power factor cannot be possible rather a capacitor bank
improves the power factor stepwise.
The short circuit withstand-limit of the armature winding of a synchronous motor is
high. Although, synchronous condenser system has some disadvantages. The system is not
silent since the synchronous motor has to rotate continuously.
An ideal load less synchronous motor draws leading current at 90o(electrical).
8. (i)A 1000kVA, 1100V, three phase starconnected synchronous motor has an
armature resistance and reactance per phase of 3.5Ω and 40Ω respectively.
Determine the induced emf and angular retardation of the rotor when fully loaded at
0.8 p.f lagging and 0.8 p.f leading. (Nov/Dec2015)

(ii)Derive the expression for power delivered by a synchronous motor in terms of

load angle. (Nov/Dec2015) (May 2017)
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The phasor diagram of a synchronous motor is shown below. From the phasor diagram,
Let
V = Supply voltage / phase
Ia = Armature current / phase
Ra = Armature resistance / phase
α = Load angle
φ = Power factor angle

Input Power to Motor :

Motor input power / phase = V Ia Cos φ
Total input power for 3-φ star-connected motor,
P = √ 3 VL IL Cos φ
= 3 Vph Iph Cos φ
Where
VL and IL are line values
Vph and Iph are phase values
Power Developed by Motor :
The mechanical power developed / phase,
Pm = Back emf * Armature current * Cosine of the angle between Eb and Ia
= Eb Ia Cos ( α - φ ) for lagging p.f
= Eb Ia Cos ( α + φ ) for leading p.f
The copper loss in a synchronous motor takes place in the armature windings.
Therefore,
Armature copper loss / phase = Ia2 Ra
Total copper loss = 3 Ia2 Ra
By subtracting the copper loss from the power input, we obtain the mechanical power
developed by a synchronous motor as
Pm = P - Pcu
For three-phase,
Pm = √ 3 IL IL Cos φ – 3 Ia2 Ra
Power Output of the Motor :
To obtain the power output we subtract the iron, friction, and excitation losses from the
power developed.
Therefore,
Net output power, Pout = Pm - iron, friction, and excitation losses.
The above two stages can be shown diagrammatically called as Power Flow Diagram of a
Synchronous Motor

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The power developed in a synchronous motor as follows.
Motor Input Power, P
1. Stator ( Armature ) copper loss Pcu
2. Mechanical power developed, Pm
a. Iron, friction, and excitation losses
b. Output power, Pout
Net Power Developed by a Synchronous Motor :
The expression for power developed by the synchronous motor in terms of α, θ, V,
Eb, and Zs are as follows :
Let
V = Supply voltage
Eb = Back emf / phase
α = Load angle
θ = Internal or Impedance angle = Tan-1 ( Xr / Zs )
Ia = Armature current / phase = Er / Zs
Zs = Ra + J Xs = Synchronous impedance
Mechanical power developed / phase,

The armature resistance is neglected

If Ra is neglected, then Zs ≈ Xs and θ = 90°. substituting these values in the above
equation

9. (i)Draw and explain the phasor diagram of a synchronous motor operating at

lagging and leading powerfactor. (Nov/Dec2015)
Let,
Ef to represent the excitation voltage
Vt to represent the terminal voltage
Ia to represent the armature current
Θ to represent the angle between terminal voltage and armature current
ᴪ to represent the angle between the excitation voltage and armature current
δ to represent the angle between the excitation voltage and terminal voltage
ra to represent the armature per phase resistance.
We will take Vt as the reference phasor in order to phasor diagram for synchronous
motor. In order to draw the phasor diagram one should know these two important points
which are written below:
(1) We know that if a machine is made to work as a asynchronous motor then direction of
armature current will in phase opposition to that of the excitation emf.
(2) Phasor excitation emf is always behind the phasor terminal voltage.
Above two points are sufficient for drawing the phasor diagram for synchronous motor.
The phasor diagram for the synchronous motor is given below,

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In the phasor one the direction of the armature current is opposite in phase to that of the
excitationemf.. It is usually customary to omit the negative sign of the armature current in the
phasor of the synchronous motor so in the phasor two we have omitted the negative sign of
the armature current. Now we will draw complete phasor diagram for the synchronous motor
and also derive expression for the excitation emf in each case. We have three cases that are
written below:

(a) Motoring operation at lagging power factor.

(b) Motoring operation at unity power factor.
(c) Motoring operation at leading power factor.

Given below are the phasor diagrams for all the operations.
(a) Motoring operation at lagging power factor: In order to derive the expression for the
excitation emf for the lagging operation we first take the component of the terminal voltage
in the direction of armature current Ia. Component in the direction of armature current is
VtcosΘ.
As the direction of armature is opposite to that of the terminal voltage therefore voltage drop
will be –Iara hence the total voltage drop is (VtcosΘ – Iara) along the armature current.
Similarly we can calculate the voltage drop along the direction perpendicular to armature
current. The total voltage drop comes out to be (Vtsinθ – IaXs). From the triangle BOD in the
first phasor diagram we can write the expression for excitation emf as

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(b) Motoring operation at unity power factor: In order to derive the expression for the
excitation emf for the unity power factor operation we again first take the component of the
terminal voltage in the direction of armature current Ia. But here the value of theta is zero and
hence we have ᴪ = δ. From the triangle BOD in the second phasor diagram we can directly
write the expression for excitation emf as

(c) Motoring operation at leading power factor: In order to derive the expression for the
excitation emf for the leading power factor operation we again first take the component of the
terminal voltage in the direction of armature current Ia. Component in the direction of
armature current is VtcosΘ. As the direction of armature is opposite to that of the terminal
voltage therefore voltage drop will be (–Iara) hence the total voltage drop is (VtcosΘ – Iara)
along the armature current. Similarly we can calculate the voltage drop along the direction
perpendicular to armature current. The total voltage drop comes out to be (Vtsinθ + IaXs).
From the triangle BOD in the first phasor diagram we can write the expression for excitation
emf as

(ii)Illustrate the phenomenon of hunting and the use of damper winding with
the help of dynamic equations. (May/June 2015)

Hunting in Synchronous Motor

The phenomenon is oscillation of the rotor about its equilibrium or steady state
position in synchronous machines is called hunting in synchronous motor.
Hunting effect can be occur in synchronous motor. Because of hunting effect synchronous
motor is not self starting.hunting means momentary fluctuations in rotor speed.
In synchronous machine magnetic locking is take place between rotor and stator its known as
cogging.
A suddenly change in load causes sudden change in torque or load angle(A). Rotor is
oscillation by angle(A) at steady States position because of moment of inertia. the stator
magnetic field rotates fast and in very short duration. position of stator magnetic field.
Due to moment of inertia rotor is in previous position but its try to moves in clockwise
direction due to attraction. After some time rotor try to rotate anticlockwise direction.This
effect is continues ans stator will oscillates in clockwise and anticlockwise direction. This
phenomena of rotor known as hunting. Its because of inertia of rotor. Because of hunting
synchronous motor is not self starting.
The word hunting is used because rotor is hunt to its new position. And its also known
as the phase swinging.
Effect of hunting:-
 Produced large variation in currents.
 Its produced mechanical stresses on rotor shaft.
 Its lead to loss of synchronism.
Causes of hunting :-
 When fault occur in system.
 Suddenly Change in load.
 Suddenly change in excitation.
Method to remedies for hunting:-
There are two methods are following below,

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By using flywheel :-
The prime mover is fitted with a flywheel. It is increase the inertia and maintains the
rotor speed at constant.
By using damper winding :-
Damper winding’s are placed in rotor pole faces. It is made from low resistance
copper bars. Which are short circuited at both end but copper rings. Damper winding cuts the
stator rotating flux. hence, emf is induced in it according to the lenz’s Law. This emf oppose
the oscillation. So By damping winding we can damped the oscillation. The magnitude of
damping torque is proportional to the slip speed.
10. (i)A 3300V, delta connected motor has a synchronous reactance per phase
of 18Ω. It operates at a leading power factor of 0.707 when drawing 800KW
from the mains. Calculate its excitation emf.(May/June2016)

(ii)Enumerate in detail the effect of varying excitation on armature current

and power factor of synchronous motor. (May/June2016)

Prior to understanding this synchronous motor excitation, it should be remembered

that any electromagnetic device must draw a magnetizing current from the AC source to
produce the required working flux. This magnetizing current lags by almost 90o to the supply
voltage. In other words, the function of this magnetizing current or lagging VA drawn by the
electromagnetic device is to set up the flux in the magnetic circuit of the device.The
synchronous motor is doubly fed electrical motor Synchronous converts electrical energy to
mechanical energy via magnetic circuit. Hence, it comes under electromagnetic device. It
receives 3 phase AC electrical supply to its armature winding and DC supply is provided to
rotor winding.

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Synchronous motor excitation refers to the DC supply given to rotor which is used to
produce the required magnetic flux.
One of the major and unique characteristics of this motor is that it can be operated at
any electrical power factor leading, lagging or unity and this feature is based on the excitation
of the synchronous motor. When the synchronous motor is working at constant applied
voltage V, the resultant air gap flux as demanded by V remains substantially constant. This
resultant air gap flux is established by the co operation of both AC supply of armature
winding and DC supply of rotor winding.
CASE 1: When the field current is sufficient enough to produce the air gap flux, as
demanded by the constant supply voltage V, then the magnetizing current or lagging reactive
VA required from ac source is zero and the motor operate at unity power factor. The field
current, which causes this unity power factor is called normal excitation or normal field
current.
CASE 2: If the field current is not sufficient enough to produce the required air gap flux as
demanded by V, additional magnetizing current or lagging reactive VA is drawn from the AC
source. This magnetizing current produces the deficient flux (constant flux- flux set up by dc
supply rotor winding). Hence in this case the motor is said to operate under lagging power
factor and the is said to be under excited.
CASE 3: If the field current is more than the normal field current, motor is said to be over
excited. This excess field current produces excess flux (flux set up by DC supply rotor
winding – resultant air gap flux) which must be neutralized by the armature winding.
Hence the armature winding draws leading reactive VA or demagnetizing current leading
voltage by almost 90o from the AC source. Hence in this case the motor operate under
leading power factor.
This whole concept of excitation and power factor of synchronous motor can be summed up
in the following graph. This is called V curve of synchronous motor.

Conclusion: An overexcited synchronous motor operate at leading power factor, under-

excited synchronous motor operate at lagging power factor and normal excited synchronous
motor operate at unity power factor.
11. The synchronous reactance per phase of a three phase star connected 6600 V
synchronous motor is 20Ω. For a certain load input, the input is 915 KW at
normal voltage and the induced line emf is 8942 V. Neglect resistance
determine the current and powerfactor. (Nov 2019)
Given:
V= 6600 V
Xs = 20Ω.
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Input power = 900 KW
Back EMF = 8942 V
Solution:
Applied Voltage / phase = 6600/√3 = 3810 V
Back EMF/phase = 8942//√3 = 5162.67 V
Input = √3VI cosΦ = 915000
I cosΦ =80.04 A
20 I cosΦ = 1600.8V
5162.672 = 1600.82+AC2
Therefore AC =4908.2V
OC = 4908.2-3810 = 1098.2V
tanΦ = 1098.2/1600.8 =0.686
Φ =34.45
cos Φ =0.825(leading)
Therefore I = 80.04/0.825 =97.06 A

UNIT III THREE PHASE INDUCTION MOTOR

PART A
1. State the principle of 3 phase IM?
While starting, rotor conductors are stationary and they cut the revolving
magnetic field and so an emf is induced in them by electromagnetic induction. This
induced emf produces a current if the circuit is closed. This current opposes the cause
by Lenz’s law and hence the rotor starts revolving in the same direction as that of the
magnetic field.
2. Why an induction motor is called a rotating transformer'?
The rotor receives electric power in exactly the same way as the secondary of a
two-winding transformer receiving its power from the primary. That is why an
induction motor can be called as a rotating transformer i.e. one in which primary
winding is stationary but the secondary is tree to rotate.
3. Why an induction motor will never run at its synchronous speed?
If the rotor runs at synchronous speed, then there would be no relative speed
between the two; hence no rotor EMF, no rotor current and so no rotor torque to
maintain rotation. That is why the rotor runs at a speed, which is always less than
synchronous speed.
4. Why are the slots on the cage rotor of induction motor usually skewed?
(Nov/Dec 2011,Nov/Dec 2015,May/June 2016, Nov/Dec 2016& April/May 2017)
 It reduces humming and hence quite running of motor is achieved.
 It reduces magnetic locking of the stator and rotor.
5. State the condition at which the starting torque developed in a slip-ring
induction motor is maximum.
R2=X2 ; R2 = rotor resistance; X2 = Rotor reactance;
6. What are the effects of increasing rotor resistance on starting current and
starting torque?
 The additional external resistance reduces the rotor current and hence the
current drawn from the supply.
 It improves the starting torque developed by improving the power factor in
high proportion to the decrease in rotor current.
7. What is slip of an induction motor? (Nov/Dec 2011)& (Nov/Dec 2012) )&
(Nov/Dec 2013 & 2014)
The slip speed is defined as the ratio of relative speed to synchronous speed is
expressed as
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% slip = ( N s  N ) N s *100
8. What are the advantages of slip-ring IM over cage IM?
(i) Rotor circuit is accessible for external connection.
(ii) By adding external resistance to the rotor circuit the starting current is
reduced with the added advantage of improving starting torque.
(iii) Additional speed control methods can be employed with the accessibility
in the rotor circuit..
9. Name the tests to be conducted for predetermining the performance of 3-phase
induction machine.
(a) No load test (b) Blocked rotor test
10. What are the information’s obtained from no-load test in a 3-phase I M?
(i) No –load input current per phase, Io (ii) No load power factor and hence
no load phase angle (iii) Iron and mechanical losses together (iv) Elements of
equivalent circuit shunt branch
11. What are the information’s obtained from blocked rotor test in a 3-phase I
M?
(i)Blocked rotor input current per phase at normal voltage
(ii) Blocked rotor power factor and hence phase angle
(iii) Total resistance and leakage reactance per phase of the motor as referred to
the stator.
12. What is circle diagram of an IM?
When an IM operates on constant voltage and constant frequency source, the
loci of stator current phasor is found to fall on a circle. This circle diagram is used to
predict the performance of the machine at different loading conditions as well as mode
of operation.
13. What are the advantages and disadvantages of circle diagram method of
predetermining the
performance of 3 –phase IM?
Advantages, the performance can be evaluated with acceptable accuracy from
tests without shaft load, through use of a circle diagram. The only disadvantage is,
being a geometrical solution; errors made during measurements will affect the
accuracy of the result.
14. What are the advantages and disadvantages of direct load test for 3 –phase
IM?
Advantages
 Direct measurement of input and output parameters yield accurate results
 Aside from the usual performance other performances like mechanical
vibration, noise etc can be studied.
 By operating the motor at full load for a continuous period, the final steady
temperature can be measured.
Disadvantages
 Testing involves large amount of power and the input energy and the entire
energy delivered is wasted.
15. What is an induction generator? (April/May 2012)
An induction generator does not differ in its construction from an induction motor.
Whether the induction, machine acts as generator or motor depends solely upon its
slip. Below synchronous speed it can operate only as motor, above synchronous speed
it operates as generator and is now called as induction generator.
16. What do you mean by slip speed?
The difference between the synchronous speed and the rotor speed N is called as
slip speed. The rotor speed will be always less than synchronous speed.
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17. Explain why an induction motor, at no-load, operates at very low power
factor.
The current drawn by an induction motor running at no load is largely a
magnetizing current. So, no-load current lags behind the applied voltage by a large
angle. Therefore the power factor of a lightly loaded induction motor is very low.
18. What is cogging of induction motor?
When the number of teeth in stator and rotor are equal, the stator and rotor
teeth have a tendency to align themselves exactly to minimum reluctance position. In
such case the rotor may refuse to accelerate. This phenomenon is called "magnetic
locking, or cogging.
19. What are the advantages of double squirrel cage induction motor. (Nov/Dec
2012 & 2014)(April/May 2019)
1. Improves the starting torque 2. Low I2R loss under running conditions
and hence high efficiency.
20. How the direction of rotation of a three phase induction motor can be
reversed?(May 2012, Nov/Dec 2016)
The direction of rotation of three phase induction motor can be changed by
interchanging any two terminal of input supply (R&Y,R&B, etc.,). The direction of
the synchronously rotating field reverses and hence the direction of rotor reverses.
21. How do change in supply voltage and frequency affect the performance of a 3
phase induction motor?(May/June 2014)
(i)This large change in voltage will result in a large change in the flux density
thereby seriously disturbing the magnetic conditions of the motor.
(ii)If the supply frequency is changed,the value of air gap flux also gets
affected.This may results in to saturation leads to the sharp rise in the noload current
of the motor.
22. State the condition at which the torque developed in a 3 phase induction
motor is maximum under running. (Nov/Dec 2015,May/June 2016)
R2=SX2; R2 = rotor resistance; X2 = Rotor reactance; s = slip
23. What is meant by synchronous watts?
The torque developed in an induction motor is proportional to rotor input. By
defining a new unit of torque (instead of the force at radius unit) we can say that the
rotor torque equals rotor input. The new unit is synchronous watts. Synchronous
wattage of an induction motor equals the power transferred across the air-gap to the
rotor.
24. How much is the developed torque in an induction motor at synchronous
speed? Explain.(May/June 2015)
The torque developed in an induction motor at synchronous speed is zero. If the
rotor runs at synchronous speed, then there would be no relative speed between the
two; hence no rotor EMF, no rotor current and so no rotor torque to maintain rotation.
That is why the rotor runs at a speed, which is always less than synchronous speed.
25. State a method by which starting torque of the induction motor can be
increased. (May/June 2015)
By adding external resistance to the rotor circuit to improve the strating torque
of induction motor.
26. What measure can be taken for minimizing the effect of crawling in a 3-phase
induction motor? (Nov/Dec 2017)
 By proper selection stator and rotor slots.
 By providing skewing arrangement in the rotor or stator.
27. Draw the torque-slip characteristic of double-cage induction motor. (Nov/Dec
2017)

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28.Classify the two types of 3-phase induction motor.(Nov 2018)

1.Squrriel cage induction motor 2.Slip ring induction motor
29. A 3-phase induction motor is wound for 4 poles and is supplied from 50 Hz
system. Calculate the speed at which the magnetic field of the stator is
rotating.(April/May 2019)
Speed of stator magnetic field=Sysnchronous speed(Ns)=120f/P=(120*50)/4
=1500RPM
30. A three phase 6 pole 50 HZ induction motor has a slip of 1% at noload. Find
the synchronous speed and frequency of rotor current at standstill.
PART B
1. (i)Explain the construction and working of three phase induction motor. (Nov/Dec
2011, Apr 2012, Nov/Dec 2012, Nov/Dec 2013, Nov/Dec 2014, Nov/Dec 2015 &
Nov/Dec 2017)(April/May 2019)
Three Phase Induction Motor:
The three phase induction motors are the most widely used electric motors in
the industry.They run at essentially constant speed from no-load to full-load.However, the
speed is frequency dependent and consequently, these motors are not easily adapted to speed
control.We usually prefer dc motors when large speed variations are required.
Nevertheless, the 3-phase induction motors are simple, rugged, low-priced, easy to
maintain and can be manufactured with characteristics to suit most industrial requirements.In
this, we shall discuss working principle of 3-phase induction motors.
Like any electric motor, a 3-phase induction motor has a stator and a rotor.The stator carries
a 3-phase winding (called stator winding) while the rotor carries a short-circuited winding
(called rotor winding). Only the stator winding is fed from 3-phase supply.The rotor winding
derives its voltage and power from the externally energized stator winding through
electromagnetic induction and hence the name.
The induction motor may be considered to be a transformer with a rotating secondary
and it can, therefore, be described as a “transformer type” ac machine in which electrical
energy is converted into mechanical energy.
Construction of Three Phase Induction Motor:
Figure 8.1 shows the construction of three phase induction motor. A 3 phase
induction motor has two main parts (i) stator and (ii) rotor.The rotor is separated from the
stator by a small air-gap which ranges from 0.4 mm to 4 mm, depending on the power of the
motor.
1. Stator :

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It consists of a steel frame which encloses a hollow, cylindrical core made up of thin
laminations of silicon steel to reduce hysteresis and eddy current losses. A number of evenly
spaced slots are provided on the inner periphery of the laminations.[See Fig.(8.1)].The
insulated connected to form a balanced 3-phase star or delta connected the circuit.
The 3-phase stator winding is wound for a definite number of poles as per requirement
of speed.Greater the number of poles, lesser is the speed of the motor and vice-versa.When 3-
phase supply is given to the stator winding, a rotating magnetic field(See Sec. 8.3) of constant
magnitude is produced.This rotating field induces currents in the rotor by electromagnetic
induction.
2.Rotor:
The rotor, mounted on a shaft, is a hollow laminated core having slots on its outer
periphery.The winding placed in these slots (called rotor winding) may be one of the
followingtwotypes:
(i) Squirrel cage type (ii) Wound type
(i) Squirrel cage rotor: It consists of a laminated cylindrical core having parallel slots on its
outer periphery.One copper or aluminum bar is placed in each slot.All these bars are joined at
each end by metal rings called end rings.
This forms a permanently short circuited winding which is indestructible. The entire
construction (bars and end rings) resembles a squirrel cage and hence the name.The rotor is
not connected electrically to the supply but has current induced in it by transformer action
fromthestator.
Those induction motors which employ squirrel cage rotor are called squirrel cage
induction motors.Most of 3 phase induction motors use squirrel cage rotor as it has a
remarkably simple and robust construction enabling it to operate in the most adverse
circumstances.
However, it suffers from the disadvantage of a low starting torque.It is because the
rotor bars are permanently short-circuited and it is not possible to add any external resistance
to the rotor circuit to have a large starting torque.

(ii) Wound rotor: It consists of a laminated cylindrical core and carries a 3-phase winding,
similar to the one on the stator [See Fig. (8.3)].The rotor winding is uniformly distributed in
the slots and is usually star-connected.The open ends of the rotor winding are brought out and
joined to three insulated slip rings mounted on the rotor shaft with one brush resting on each
slipring.
The three brushes are connected to a 3-phase star-connected rheostat as shown in Fig.
(8.4).At starting, the external resistances are included in the rotor circuit to give a large
starting torque.These resistances are gradually reduced to zero as the motor runs up to speed.

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The external resistances are used during starting period only. When the motor attains
normal speed, the three brushes are short-circuited so that the wound rotor runs like a squirrel
cage rotor.
Working Principle of Three Phase Induction Motor:
Speed of rotating magnetic field:
The speed at which the rotating magnetic field revolves is called the synchronous
speed (Ns).Referring to Fig. (8.6 (ii)), the time instant 4 represents the completion of one-
quarter cycle of alternating current Ix from the time instant 1.During this one-quarter cycle,
the field has rotated through 90°. At a time instant represented by 13 or one complete cycle of
current Ix from the origin, the field has completed one revolution.
Therefore, for a 2-pole stator winding, the field makes one revolution in one cycle of
current.In a 4-pole stator winding, it can be shown that the rotating field makes one
revolution in two cycles of current.In general, fur P poles, the rotating field makes one
revolution in P/2 cycles of current.

The speed of the rotating magnetic field is the same as the speed of the alternator that
is supplying power to the motor if the two have the same number of poles.Hence the
magnetic flux is said to rotate at synchronous speed.
Three Phase Induction Motor Advantages:
(i) It has simple and rugged construction.
(ii) It is relatively cheap.
(iii) It requires little maintenance.
(iv) It has high efficiency and reasonably good power factor.
(v) It has self starting torque.
Three Phase Induction Motor Disadvantages:
(i) It is essentially a constant speed motor and its speed cannot be changed
easily.
(ii) Its starting torque is inferior to dc shunt motor.
(ii)Explain the torque slip characteristics of 3 phase induction motor. (Nov/Dec 2011
& 2012,Nov/Dec 2015,Nov/Dec 2016 & April/May 2017)(Nov 2018)
Torque Slip Characteristics of Three Phase Induction Motor
The torque slip curve for an induction motor gives us the information about the variation of
torque with the slip. The slip is defined as the ratio of difference of synchronous speed and
actual rotor speed to the synchronous speed of the machine. The variation of slip can be
obtained with the variation of speed that is when speed varies the slip will also vary and the
torque corresponding to that speed will also vary.

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The curve can be described in three modes of operation-

The torque-slip characteristic curve can be divided roughly into three regions:
 Low slip region
 Medium slip region
 High slip region
MotoringMode
In this mode of operation, supply is given to the stator sides and the motor always rotates
below the synchronous speed. The induction motor torque varies from zero to full load
torque as the slip varies. The slip varies from zero to one. It is zero at no load and one at
standstill. From the curve it is seen that the torque is directly proportional to the slip.
That is, more is the slip, more will be the torque produced and vice-versa. The linear
relationship simplifies the calculation of motor parameter to great extent.
GeneratingMode
In this mode of operation induction motor runs above the synchronous speed and it should be
driven by a prime mover. The stator winding is connected to a three phase supply in which it
supplies electrical energy. Actually, in this case, the torque and slip both are negative so the
motor receives mechanical energy and delivers electrical energy. Induction motor is not much
used as generator because it requires reactive power for its operation.
That is, reactive power should be supplied from outside and if it runs below the synchronous
speed by any means, it consumes electrical energy rather than giving it at the output. So, as
far as possible, induction generators are generally avoided.
BrakingMode
In the Braking mode, the two leads or the polarity of the supply voltage is changed so that the
motor starts to rotate in the reverse direction and as a result the motor stops. This method of
braking is known as plugging. This method is used when it is required to stop the motor
within a very short period of time. The kinetic energy stored in the revolving load is
dissipated as heat. Also, motor is still receiving power from the stator which is also dissipated
as heat. So as a result of which motor develops enormous heat energy. For this stator is
disconnected from the supply before motor enters the braking mode.
If load which the motor drives accelerates the motor in the same direction as the motor is
rotating, the speed of the motor may increase more than synchronous speed. In this case, it
acts as an induction generator which supplies electrical energy to the mains which tends to
slow down the motor to its synchronous speed, in this case the motor stops. This type of
breaking principle is called dynamic or regenerative breaking.

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2. (i)Develop an equivalent circuit for three phase induction motor. State the
difference between exact and approximate equivalent circuit. (Nov/Dec
2011,Nov/Dec 2012,Nov/Dec 2016)
An induction motor is a well-known device which works on the principle of transformer. So
it is also called the rotating transformer. That is, when an EMF is supplied to its stator, then
as a result of electromagnetic induction, a voltage is induced in its rotor. So an induction
motor is said to be a transformer with rotating secondary. Here, primary of transformer
resembles stator winding of an induction motor and secondary resembles rotor.
The induction motor always runs below the synchronous or full load speed and the relative
difference between the synchronous speed and speed of rotation is known as slip which is
denoted by s.
Where, Ns is synchronous speed of rotation which is given by-
Where, f is the frequency of the supply voltage.
P is the number of poles of the machine.
Equivalent Circuit of an Induction Motor
The equivalent circuit of any machine shows the various parameter of the machine such as its
Ohmic losses and also other losses.
The losses are modeled just by inductor and resistor. The copper losses are occurred in the
windings so the winding resistance is taken into account. Also, the winding has inductance
for which there is a voltage drop due to inductive reactance and also a term called power
factor comes into the picture. There are two types of equivalent circuits in case of a three-
phase induction motor-
Exact Equivalent Circuit

Here, R1 is the winding resistance of the stator.

X1 is the inductance of the stator winding.
Rc is the core loss component.
XM is the magnetizing reactance of the winding.
R2/s is the power of the rotor, which includes output mechanical power and copper loss of
rotor.
If we draw the circuit with referred to the stator then the circuit will look like-

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Here all the other parameters are same except-

R2’ is the rotor winding resistance with referred to stator winding.
X2’ is the rotor winding inductance with referred to stator winding.
R2(1 – s) / s is the resistance which shows the power which is converted to mechanical power
output or useful power. The power dissipated in that resistor is the useful power output or
shaft power.
Approximate Equivalent Circuit
The approximate equivalent circuit is drawn just to simplify our calculation by deleting one
node. The shunt branch is shifted towards the primary side. This has been done as the voltage
drop between the stator resistance and inductance is less and there is not much difference
between the supply voltage and the induced voltage. However, this is not appropriate due to
following reasons-
1. The magnetic circuit of induction motor has an air gap so exciting current is larger
compared to transformer so exact equivalent circuit should be used.
2. The rotor and stator inductance is larger in induction motor.
3. In induction motor, we use distributed windings.
This model can be used if approximate analysis has to be done for large motors. For smaller
motors, we cannot use this.
Power Relation of Equivalent Circuit

1. Input power to stator- 3 V1I1Cos(Ɵ). Where, V1 is the stator voltage applied.

I1 is the current drawn by the stator winding.
Cos(Ɵ) is the stator power stator.
2. Rotor input =Power input- Stator copper andiron losses.
3. Rotor Copper loss = Slip × power input to the rotor.
4. Developed Power = (1 – s) × Rotor input power.
(ii) Describe the principle of synchronous induction motor (Nov/Dec 2014)
(April/May 2019)
In the applications where high starting torque and constant speed are desired then
synchronous induction motor can be used. It has the advantages of both synchronous motor
and induction motor. The synchronous motor gives constant speed whereas induction motors can be
started against full load torque.
Consider a normal slip ring induction motor having three phase winding on the rotor as shown in the
figure.
The motor is connected to the exciter which gives d.c. supply to the rotor through slip rings. One
phase carries full d.c. current while the other two carries half the full d.c. current as they are
connected in parallel. Due to this d.c. excitation, permanent poles (N and S) formed on the rotor.
Initially it is run as a slip ring induction motor with the help of starting resistances. When the
resistances are cut out the motor runs with a slip. Now the connections are changed and the exciter is
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connected in series with the rotor windings which will remain in the circuit permanently.
As the motor is running as induction motor initially high starting torque (up to twice full load value)
can be developed. When the d.c. excitation is provided it is pulled into synchronism and starts running
at constant speed. Thus synchronous induction motor provides constant speed, large starting torque,
low starting current and power factor correction.
3. (i)A 6 pole, 50Hz, 3 phase, induction motor running on full load develops a useful
torque of 160Nm. When the rotor emf makes 120 complete cycle per minute.
Calculate the shaft power input. If the mechanical torque lost in friction and that for
core loss is 10 Nm, compute i. The copper loss in the rotor windings. ii. The input
of motor. iii.The efficiency. The total stator loss is given to be 800W. (Nov/Dec
2011)

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(ii) A 746 KW,3-phase,50 Hz, 16-pole induction motor has a rotor impedance of
(0.02+j0.15)Ω at standstill.Full load torque is obtained at 360 rpm.Calculate (i)
The ratio of maximum to full-load torque (ii) The speed at maximum torque and
(iii) The rotor resistance to be added to get maximum starting torque. (May/June
2014)

4. A 15KW,400V,50Hz,3 phase star connected induction motor gave the following

test results:
No load test: 400V,9A,1310W; Blocked rotor test: 200V,50A,7100W; Stator and
rotor ohmic losses at standstill are assumed equal. Draw the induction motor circle
diagram and calculate (i)Line current (ii)Power Factor (iii)Slip (iv)Torque and
efficiency at full load. (May/June 2014)

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5. A three phase induction motor has a starting torque of 100% and a maximum
torque of 200% of the full load torque. Determine (Nov/Dec 2015)
i.slip at which maximum torque occurs
ii.full load slip
iii.rotor current at starting in per unit of ful-load rotor current.

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6. (i)Draw the equivalent circuit and derive expressions for maximum
torque and power of a three phase induction motor. (May/June2016)
The torque produced by three phase induction motor depends upon the following three
factors:
Firstly the magnitude of rotor current, secondly the flux which interact with the rotor of
three phase induction motor and is responsible for producing emf in the rotor part of
induction motor, lastly the power factor of rotor of the three phase induction motor.
Combining all these factors, we get the equation of torque as-

Where, T is the torque produced by the induction motor,

φ is flux responsible for producing induced emf,
I2 is rotor current,
cosθ2 is the power factor of rotor circuit.
The flux φ produced by the stator is proportional to stator emf E1.
i.e φ ∝ E1
We know that transformation ratio K is defined as the ratio of secondary voltage (rotor
voltage) to that of primary voltage (stator voltage).

Rotor current I2 is defined as the ratio of rotor induced emf under running condition , sE2 to
total impedance, Z2 of rotor side,

and total impedance Z2 on rotor side is given by ,

Putting this value in above equation we get,

s = slip of induction motor

We know that power factor is defined as ratio of resistance to that of impedance. The power
factor of the rotor circuit is

Putting the value of flux φ, rotor current I2, power factor cosθ2 in the equation of torque we
get,

Combining similar term we get,

Removing proportionality constant we get,

Where, ns is synchronous speed in r. p. s, ns = Ns / 60. So, finally the equation of torque

becomes,
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Derivation of K in torque equation.

In case of three phase induction motor, there occur copper losses in rotor. These rotor copper
losses are expressed as
Pc = 3I22R2
We know that rotor current,

Substitute this value of I2 in the equation of rotor copper losses, Pc. So, we get

The ratio of P2 : Pc : Pm = 1 : s : (1 – s)
Where, P2 is the rotor input,
Pc is the rotor copper losses,
Pm is the mechanical power developed.

Substitute the value of Pc in above equation we get,

On simplifying we get,

The mechanical power developed Pm = Tω,

Substituting the value of Pm

We know that the rotor speed N = Ns(1 – s)

Substituting this value of rotor speed in above equation we get,

Ns is speed in revolution per minute (rpm) and ns is speed in revolution per sec (rps) and the
relation between the two is

Substitute this value of Ns in above equation and simplifying it we get

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Comparing both the equations, we get, constant K = 3 / 2πns

Equation of Starting Torque of Three Phase Induction Motor
Starting torque is the torque produced by induction motor when it starts. We know that at the
start the rotor speed, N is zero.

So, the equation of starting torque is easily obtained by simply putting the value of s = 1 in
the equation of torque of the three phase induction motor,

The starting torque is also known as standstill torque.

Maximum Torque Condition for Three-Phase Induction Motor
In the equation of torque,

The rotor resistance, rotor inductive reactance and synchronous speed of induction motor
remain constant. The supply voltage to the three phase induction motor is usually rated and
remains constant, so the stator emf also remains the constant. We define the transformation
ratio as the ratio of rotor emf to that of stator emf. So if stator emf remains constant, then
rotor emf also remains constant.
If we want to find the maximum value of some quantity, then we have to differentiate that
quantity concerning some variable parameter and then put it equal to zero. In this case, we
have to find the condition for maximum torque, so we have to differentiate torque concerning
some variable quantity which is the slip, s in this case as all other parameters in the equation
of torque remains constant.
So, for torque to be maximum

Now differentiate the above equation by using division rule of differentiation. On

differentiating and after putting the terms equal to zero we get,

Neglecting the negative value of slip we get

So, when slip s = R2 / X2, the torque will be maximum and this slip is called maximum slip
Sm and it is defined as the ratio of rotor resistance to that of rotor reactance.
NOTE: At starting S = 1, so the maximum starting torque occur when rotor resistance is
equal to rotor reactance.
Equation of Maximum Torque
The equation of torque is

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The torque will be maximum when slip s = R2 / X2
Substituting the value of this slip in above equation we get the maximum value of torque as,

In order to increase the starting torque, extra resistance should be added to the rotor circuit at
start and cut out gradually as motor speeds up.
Conclusion
From the above equation it is concluded that
1. The maximum torque is directly proportional to square of rotor induced emf at the
standstill.
2. The maximum torque is inversely proportional to rotor reactance.
3. The maximum torque is independent of rotor resistance.
4. The slip at which maximum torque occur depends upon rotor resistance, R2. So, by
varying the rotor resistance, maximum torque can be obtained at any required slip.
ii)A 6-pole, 50 Hz, 3-phase induction motor running on full load
develops a useful torque of 160 Nm when the rotor emf makes 120
complete cycles per minute. Let, the mechanical torque lost in friction and
core-loss is 10 Nm. Determine the following,
(1) shaft power output.
(2) input to the motor, and
(3) Efficiency.Let the total stator loss be 800W.(May/June 2015)

Refer Q.no 3. i
7. (i) Draw the torque slip characteristics of an induction motor for
varying frequency,stator voltage and rotor resistance.(May/June 2015)
Refer Q.No 1.(ii)
(ii) A 400 V, 6-pole, 3-phase, 50 Hz star-connected induction motor
running light at rated voltage takes 7.5A with a power input of 700 W.
With the rotor locked and 150 V applied to the stator, the input current
is 35 A and power input is 4000 W; the stator resistance/phase
being 0.55 ohms under these conditions. The standstill reactances of
the stator and rotor as seen on the stator side are estimated to be in
the ratio of 1:0.5.Determine the parameters of the equivalent circuit.
(May/June 2015)

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8. (i)Derive the expression for torque, slip and draw speed-torque characteristics of 3-
phase induction motor. (Nov/Dec 2013)

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The torque produced by three phase induction motor depends upon the following three
factors:
Firstly the magnitude of rotor current, secondly the flux which interact with the rotor of three
phase induction motor and is responsible for producing emf in the rotor part of induction
motor, lastly the power factor of rotor of the three phase induction motor.
Combining all these factors, we get the equation of torque as-

Where, T is the torque produced by the induction motor,

φ is flux responsible for producing induced emf,
I2 is rotor current,
cosθ2 is the power factor of rotor circuit.
The flux φ produced by the stator is proportional to stator emf E1.
i.e φ ∝ E1
We know that transformation ratio K is defined as the ratio of secondary voltage (rotor
voltage) to that of primary voltage (stator voltage).

Rotor current I2 is defined as the ratio of rotor induced emf under running condition , sE2 to
total impedance, Z2 of rotor side,

and total impedance Z2 on rotor side is given by ,

Putting this value in above equation we get,

s = slip of induction motor

We know that power factor is defined as ratio of resistance to that of impedance. The power
factor of the rotor circuit is

Putting the value of flux φ, rotor current I2, power factor cosθ2 in the equation of torque we
get,

Combining similar term we get,

Removing proportionality constant we get,

Where, ns is synchronous speed in r. p. s, ns = Ns / 60. So, finally the equation of torque

becomes,

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Derivation of K in torque equation.
In case of three phase induction motor, there occur copper losses in rotor. These rotor copper
losses are expressed as
Pc = 3I22R2
We know that rotor current,

Substitute this value of I2 in the equation of rotor copper losses, Pc. So, we get

The ratio of P2 : Pc : Pm = 1 : s : (1 – s)
Where, P2 is the rotor input,
Pc is the rotor copper losses,
Pm is the mechanical power developed.

Substitute the value of Pc in above equation we get,

On simplifying we get,

The mechanical power developed Pm = Tω,

Substituting the value of Pm

We know that the rotor speed N = Ns(1 – s)

Substituting this value of rotor speed in above equation we get,

Ns is speed in revolution per minute (rpm) and ns is speed in revolution per sec (rps) and the
relation between the two is

Substitute this value of Ns in above equation and simplifying it we get

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Comparing both the equations, we get, constant K = 3 / 2πns

Equation of Starting Torque of Three Phase Induction Motor

Starting torque is the torque produced by induction motor when it starts. We know that at the
start the rotor speed, N is zero.

So, the equation of starting torque is easily obtained by simply putting the value of s = 1 in
the equation of torque of the three phase induction motor,

The starting torque is also known as standstill torque.

Maximum Torque Condition for Three-Phase Induction Motor
In the equation of torque,

The rotor resistance, rotor inductive reactance and synchronous speed of induction motor
remain constant. The supply voltage to the three phase induction motor is usually rated and
remains constant, so the stator emf also remains the constant. We define the transformation
ratio as the ratio of rotor emf to that of stator emf. So if stator emf remains constant, then
rotor emf also remains constant.
If we want to find the maximum value of some quantity, then we have to differentiate that
quantity concerning some variable parameter and then put it equal to zero. In this case, we
have to find the condition for maximum torque, so we have to differentiate torque concerning
some variable quantity which is the slip, s in this case as all other parameters in the equation
of torque remains constant.
So, for torque to be maximum

Now differentiate the above equation by using division rule of differentiation. On

differentiating and after putting the terms equal to zero we get,

Neglecting the negative value of slip we get

So, when slip s = R2 / X2, the torque will be maximum and this slip is called maximum slip
Sm and it is defined as the ratio of rotor resistance to that of rotor reactance.
NOTE: At starting S = 1, so the maximum starting torque occur when rotor resistance is
equal to rotor reactance.

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(ii)Explain in detail the construction of circle diagram of an induction
motor.(May/June2016 & April/May 2017)

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9. A 40KW, 3-phase, slip-ring induction motor of negligible stator impedance runs at
a speed of 0.96 times synchronous speed at rated torque. The slip at maximum
torque is four times the full-load value. If the rotor resistance of the motor is
increased by 5 times, determine:
(a)The speed, power output and rotor copper loss at rated torque.
(b)The speed corresponding to maximum torque.(May/June2016)

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10.(i)Explain the operation of induction machine as a generator with neat

diagram.(Nov/Dec 2016 & Nov/Dec 2017)
Just like a DC Machine, a same induction machine can be used as an induction motor as well
as an induction generator, without any internal modifications. Induction generators are also
called as asynchronous generators.
Before starting to explain how an induction (asynchronous) generator works, I
assume that you know the working principle of an induction motor. In an induction motor,
the rotor rotates because of slip (i.e. relative velocity between the rotating magnetic field and
the rotor). Rotor tries to catch up the synchronously rotating field of the stator but never
succeeds. If rotor catches up the synchronous speed, the relative velocity will be zero, and
hence rotor will experience no torque.
But what if the rotor is rotating at a speed more than synchronous speed?
How Induction Generators Work?
 Consider, an AC supply is connected to the stator terminals of an induction machine.
Rotating magnetic field produced in the stator pulls the rotor to run behind it (the machine is
acting as a motor).
 Now, if the rotor is accelerated to the synchronous speed by means of a prime mover, the
slip will be zero and hence the net torque will be zero. The rotor current will become zero
when the rotor is running at synchronous speed.
 If the rotor is made to rotate at a speed more than the synchronous speed, the slip becomes
negative. A rotor current is generated in the opposite direction, due to the rotor conductors
cutting stator magnetic field.
 This generated rotor current produces a rotating magnetic field in the rotor which
pushes (forces in opposite way) onto the stator field. This causes a stator voltage which
pushes current flowing out of the stator winding against the applied voltage. Thus, the
machine is now working as an induction generator (asynchronous generator).

Induction generator is not a self-excited machine. Therefore, when running as a generator, the
machine takes reactive power from the AC power line and supplies active power back into
the line. Reactive power is needed for producing rotating magnetic field. The active power
supplied back in the line is proportional to slip above the synchronous speed.
Self-Excited Induction Generator

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It is clear that, an induction machine needs reactive power for excitation, regardless whether
it is operating as a generator or a motor. When an induction generator is connected to a grid,
it takes reactive power from the grid. But what if we want to use an induction generator to
supply a load without using an external source (e.g. grid)?
A capacitor bank can be connected across the stator terminals to supply reactive power to the
machine as well as to the load. When the rotor is rotated at an enough speed, a small voltage
is generated across the stator terminals due to residual magnetism. Due to this small
generated voltage, capacitor current is produced which provides further reactive power for
magnetization.

Applications of induction generators: Induction generators produce useful power even at

varying rotor speeds. Hence, they are suitable in wind turbines.
Advantages: Induction or asynchronous generators are more rugged and require no
commutator and brush arrangement (as it is needed in case of synchronous generators).
ne of the major disadvantage of induction generators is that they take quite large amount of
reactive power.

(ii)Explain the speed torque characteristics of double cage induction motor with a
neat diagram.

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UNIT IV - STARTING AND SPEED CONTROL OF THREE PHASE

INDUCTION MOTOR
PART A
1. What is the need of starter for induction motor? (April/May 2012,
Nov/Dec 2016)
The plain induction motor is similar in action to polyphase transformer with a
short-circuited rotating secondary. Therefore, if normal supply voltage is applied to
the stationary motor, then, as in case of a transformer, a very large initial current about
5-7 times full load current is drawn taken by the stator.
2. What is the magnitude of starting current and torque for induction
motor?(Nov/Dec 2014)
Induction motors, when direct-switched take five to seven times the full load
current and develop only 1.5 to 2.5 times their full- load torque.
3. Name the different types of starters used for induction motor. (Nov/Dec 2013,
Nov/Dec 2016)
1. Primary resistor. 2. Autotransformer starter. 3. Star-delta starter 4. Rotor
rheostat.
4. Brief the over –load protection of autotransformer starter.
When the load on the motor is more than the rated value the supply to motor
will be cut off.
5. How the starting current is reduced using rotor resistance starter. (Nov/Dec
2011)
The controlling resistance is in the form of a rheostat, connected in star. The
resistance being gradually cut-out of the rotor circuit as the motor gathers speed.
Increasing the rotor resistance, not only in the rotor current reduced at starting, but at
the same time starting torque is also increased due to improvement in power factor.
6. Mention the methods of speed control on stator side of induction motor.
(Nov/Dec 2011, (Nov/Dec 2012 & Nov/Dec 2015)
1. By changing the applied voltage ; 2. By changing the applied frequency; 3.
By changing the number of stator poles.
7. Mention the methods of speed control from rotor side of induction motor.
(Nov/Dec 2011)& (Nov/Dec 2012)
1. Rotor rheostat control, 2. By operating two motors in concatenation or
cascade. 3. By injecting an e.m.f in the rotor circuit.
8. Why speed control by changing the applied voltage is simpler?
A large change in voltage is required for a relatively small change in
speed.This large change in voltage will result in a large change in the flux density
thereby seriously disturbing the magnetic conditions of the motor.
9.What are the limitations of speed control of induction motor by changing the
supply frequency?
This method could only be used in cases where the induction motor happens to
be the only load on the generators.
10.What are the applications of speed control of induction motor by pole
changing method?
Elevator motors, Traction motors Small motors driving machine tools.
11.How the speed control is achieved by changing the number of poles.
Synchronous speed of induction motor could also be changed by changing the
number of stator poles. This change of number of poles is achieved by having two or
more entirely independent stator windings in the same slots.
12.What are the limitations of rotor rheostat speed control of induction motor?

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2
With increase in rotor resistance, I R losses also increase which decrease the
operating efficiency of the motor. In fact, the loss is directly proportional to the
reduction in the speed. Double dependence of speed, not only on R2 but also on load
as well.
13. Brief the method of speed control by injecting emf in the rotor circuit.
The speed of an induction motor is controlled by injecting a voltage in the rotor
circuit. It is necessary or the injected voltage to have the same frequency as the slips
frequency
14. What are the advantages of slip power scheme?
Advantages
1. Easier power control. 2. Higher efficiency.
Disadvantage
1. Reactive power consumption. 2. Low power factor at reduced speed.
15. Mention types of slip power recovery schemes.
Scherbius system and Kramer drive.
16. What is effect of increasing rotor resistance in starting current and torque.
(Nov/Dec 2012)(April/May 2019)
Staring current can be reduce and starting torque can be increase by increasing
the rotor resistance of an induction motor.
17. Why are most of the three phase induction motors constructed with delta
connected stator
winding? (April/May 2012)
Squirrel cage induction motor started with star to delta starter, therefore stators
winding in delta connection.
18. What is meant by slip power recovery scheme? (Nov/Dec 2013)
Some amount of power is wasted in the rotor circuit .wasted power is
recovered by using converter.
19. What is meant by plugging? (May/June 2014)
The reversal of direction of rotation of motor is the main principle in plugging
of motor.In case of an induction motor,it can be quickly stopped by interchanging any
two stator leads.Due to this,the direction of rotating magnetic field gets reversed and
this produces a torque in reverse direction and the motor tries to rotate in opposite
direction.
20.While controlling the speed of an induction motor, how is super-synchronous
speed achieved?(Nov/Dec 2014)
In the super synchronous speed operation,the power flow is from supply to the
transformer and the slip power is injected in to the rotor circuit.
21. How the tandem operation of induction motor start?
When the cascaded set is started, the voltage at frequency f is applied to the
stator winding of main motor. An induced emf of the same frequency is produced in
main motor (rotor) which is supplied to the auxiliary motor. Both the motors develop
a forward torque. As the shaft speed rises, the rotor frequency of main motor falls and
so does the synchronous speed of auxiliary motor. The set settles down to a stable
sped when the shaft speed become equal to the speed of rotating field of Auxiliary
motor.
22. What is the effect of change in supply voltage on starting torque of induction
motor? (Nov/Dec 2015,May/June 2016 & April/May 2017)
Starting torque of an induction motor will becomes double when slight change
in the supply voltage.
23. State an important distinguishing factor of induction generator and
alternator. (May/June 2015)
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Induction Generator Alternator

Induction machine is single excited.Alternator is doubly excited machine.
Induction Generator, the field is induced in
Alternators use a separate excitation
the rotor. field.
Induction Generator the rotor speed need
The alternator output frequency is
only be above rated synchoronus speed.
intimately connected to rotor rpm and
poles.
24. Draw the torque speed characteristics of an induction motor
whose rotor resistance is very large compared to rotor inductance.
(May/June 2015)

25. Why is rotor rheostat starter unsuited for a squirrel cage motor? (Nov/Dec
2017)
In an squirrel cage induction motor, the rotor conductors are short circuited
through end rings. There is no slipring, no provision to connect external resistantce to
rotor circuit.
26. What are the conditions for regenerative braking of an induction motor to be
possible? (Nov/Dec 2017)
Whenever the motor has a tendency to run faster than the rotating
field, regenerative braking occurs.It is also possible with a pole change motor when
the speed is changed from high to low.
27.State two advantages of speed control of induction motor by injecting an emf
in the rotor circuit. (April/May 2017)
 Wide range of speed control is possible, whether it is above normal or below
normal speed.
 Slip power loss can be recovered and supplied back in order to improve the
overall efficiency of the three-phase induction motor.
28. Name the two windings of a single-phase induction motor(Nov 2018)
1.Main winding 2.Auxiliary winding
29.Specify the use of single phase IM(Nov 2018)
1.Air-conditioner and refrigerator 2.Ceiling Fan and Blowers
3.Machine Tool Drive 4.Pump Drive
30.What type of braking is employed during deceleration of an induction motor?
(April/May 2019)
 Regenerative braking
 Dynamic braking

PART B
1. (i)With neat diagrams explains the working of any two types of starters used for
squirrel cage type 3 phase induction motor. (Nov/Dec 2013) (Nov/Dec 2019)
TYPES OF INDUCTION MOTOR STARTERS
 Direct online starter
 Squirrel cage motor
• Primary resistor (or) rheostat starter

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• Auto transformer starter
• Star to delta starter
 Slip ring motor
• Rotor rheostat starter

Auto Transformer starter

This method also aims at connecting the induction motor to a reduced supply at starting and
then connecting it to the full voltage as the motor picks up sufficient speed. shows the circuit
arrangement for autotransformer starting. The tapping on the autotransformer is so set that
when it is in the circuit, 65% to 80% of line voltage is applied to the motor. At the instant of
starting, the change-over switch is thrown to "start" position. This puts the autotransformer in
the circuit and thus reduced voltage is applied to the circuit. Consequently, starting current is
limited to safe value. When the motor attains about 80% of normal speed, the changeover
switch is thrown to "run" position. This takes out the autotransformer from the circuit and puts
the motor to full line voltage. Autotransformer starting has several advantages viz low power
loss, low starting current and less radiated heat. For large machines (over 25 H.P.), this
method of starting is often used. This method can be used for both star and delta connected
motors.

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Stator resistance starter:
Stator resistance starting In this method, external resistances are connected in series with each
phase of stator winding during starting. This causes voltage drop across the resistances so that
voltage available across motor terminals is reduced and hence the starting current. The starting
resistances are gradually cut out in steps (two or more steps) from the stator circuit as the motor
picks up speed. When the motor attains rated speed, the resistances are completely cut out and
full line voltage is applied to the rotor see This method suffers from two drawbacks. First, the
reduced voltage applied to the motor during the starting period lowers the starting torque and
hence increases the accelerating time. Secondly, a lot of power is wasted in the starting
resistances.
Relation between starting and F.L. torques. Let V be the rated voltage/phase. If the voltage is
reduced by a fraction x by the insertion of resistors in the line, then voltage applied to the motor
per phase will be xV. So, Thus while the starting current reduces by a fraction x of the rated-
voltage starting current (Isc), the starting torque is reduced by a fraction x2 of that obtained by
direct switching. The reduced voltage applied to the motor during the starting period lowers the
starting current but at the same time increases the accelerating time because of the reduced value
of the starting torque. Therefore, this method is used for starting small motors only.

ii) Discuss the various starting methods of induction motors. (April / May 2012, May / June
2019)
Refer Q.No 1 (i)

2. (i)Explain the speed control of 3 phase squirrel cage induction motor by pole
changing and its applications.(Nov/Dec 2014 & Nov/Dec 2017)

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2.(ii) Describe with a neat sketch, the principle and working of a stator resistance
starter and auto transformer starter. (Nov/Dec 2011,Nov/Dec 2012,Nov/Dec
2014,Nov/Dec 2016 & Nov/Dec 2017) (April/May 2019)
Refer Q.no. 1

3. (i)Explain the speed control methods of a three phase induction motor. (Nov/Dec
2016,May/June2016) (April/May 2019)

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3. ii. Explain in detail the scherbius system of speed control.(May/June2016)

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4. Explain in detail the slip power recovery scheme.(Nov/Dec 2011, Nov/Dec 2012,
Nov/Dec 2013, May/June 2014,Nov/Dec 2015 & April/May 2017)

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5. Explain the various techniques of speed control of induction motor from rotor side
control. (April/May 2012,May/June 2014) Refer Q.no. 4
6. Describe a starter available for slip ring induction motor. (April/May 2012,
Nov/Dec 2015, May/June2016)
Refer Q.no. 4

7. A small squirrel-cage induction motor has a starting current of six times the full
load current and a full-load slip of 0.05. Find in pu of full-load values, the

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current(line) and starting torque with the following methods of starting ((a) to(d)). (a)
Direct switching,(b) Stator-resistance starting with motor current limited to 2p.u,(c)
auto-transformer starting with motor current limited to 2p.u, and (d) Y-delta
starting.(e) What auto transformer ratio would give 1p.u starting
torque?(May/June2016)

8. Explain the speed control of -3 phase wound rotor induction motor by the rotor
resistance method (Nov/Dec2013) Refer Q.No 5

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9. A small squirrel-cage induction motor has a starting current of six times The full-
load current and a full-load slip of 0.05. Find in p. u of full-load values, the current
(line) and starting torque with the following methods of starting. i. direct switching,
ii. autotransformer starting with motor current limited to 2 p. u and iii. star-delta
starting.(May/June 2015)
refer Q.No. 7

10. i) Illustrate the phenomena of Cogging and Crawling in induction

motor.(May/June 2015)(Nov 2018)
Crawling of Induction Motor
It has been observed that squirrel cage type induction motor has a tendency to run at very low
speed compared to its synchronous speed, this phenomenon is known as crawling. The
resultant speed is nearly 1/7th of its synchronous speed. Now the question arises why this
happens? This action is due to the fact that harmonics fluxes produced in the gap of the stator
winding of odd harmonics like 3rd, 5th, 7th etc. These harmonics create additional torque fields
in addition to the synchronous torque. The torque produced by these harmonics rotates in the
forward or backward direction at Ns/3, Ns/5, Ns/7 speed respectively. Here we consider only
5th and 7th harmonics and rest are neglected. The torque produced by the 5th harmonic rotates
in the backward direction.
This torque produced by fifth harmonic which works as a braking action is small in quantity,
so it can be neglected. Now the seventh harmonic produces a forward rotating torque at
synchronous speed Ns/7. Hence, the net forward torque is equal to the sum of the torque
produced by 7th harmonic and fundamental torque. The torque produced by 7th harmonic
reaches its maximum positive value just below 1/7 of Ns and at this point slip is high. At this
stage motor does not reach up to its normal speed and continue to rotate at a speed which is
much lower than its normal speed. This causes crawling of the motor at just below 1/7
synchronous speed and creates the racket. The other speed at which motor crawls is 1/13 of
synchronous speed.
Cogging of Induction Motor
This characteristic of induction motor comes into picture when motor refuses to start at all.
Sometimes it happens because of low supply voltage. But the main reason for starting
problem in the motor is because of cogging in which the slots of the stator get locked up with
the rotor slots. As we know that there is series of slots in the stator and rotor of the induction
motor. When the slots of the rotor are equal in number with slots in the stator, they align
themselves in such way that both face to each other and at this stage the reluctance of the
magnetic path is minimum and motor refuse to start. This characteristic of the induction
motor is called cogging. Apart from this, there is one more reason for cogging. If the
harmonic frequencies coincide with the slot frequency due to the harmonics present in the
supply voltage then it causes torque modulation. As a result, of it cogging occurs. This
characteristic is also known as magnetic teeth locking of the induction motor.
Methods to overcome cogging
This problem can be easily solved by adopting several measures. These solutions are as
follows:
 The number of slots in rotor should not be equal to the number of slots in the stator.
Skewing of the rotor slots, that means the stack of the rotor is arranged in such a way that
it angled with the axis of the rotation.
ii. The impedances at standstill of the inner and· outer cages of a
double-cage rotor are (0.01 + j 0.5) nand (0.05 +j 0.1) n respectively. The
stator impedance may be assumed to be negligible. Determine the ratio of
the torques due to the two cages (1) at starting, and (2) running with a
Slip of 5%.(May/June 2015)

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11. A three phase induction motor takes a starting current which is 5 times full load
current at normal voltage.Its full load slip is 4 percent.What auto-transformer ratio
would enable the motor to be started with not more than twice the full load current
drawn from the supply? What would be the starting torque under this conditions?
(May-2014) (Nov/Dec 2019)
Refer Q.No. 7
12. A 3-phase 440 V distribution circuit is designed to supply not more than 1200 A.
Assuming that a 3-phase squirrel cage induction motor has full load efficiency of 0.85
and a full load power factor of 0.8 and that the starting current at rated voltage is 5
times the rated full load current. What is the maximum permissible kW rating of the
motor if it is to be started using an auto-transformer stepping down the voltage to
80%. (Dec-2014),(May 17), (Nov/Dec 2019)
Refer Q.No. 7

UNIT V SINGLE PHASE INDUCTION MOTORS AND SPECIAL MACHINES

PART A
1. Name the two windings of a single-phase induction motor.
i. Running winding (main winding) ii. Starting winding
(auxiliary winding)
2. What are the various methods available for making a single-phase motor self-
starting? (Nov/Dec 2012, Nov/Dec 2015& April/May 2017)
i. By splitting the single phase. ii. By providing shading coil in the
poles
iii. Repulsion start method. iv. Capacitor start capacitor run.
3. Differentiate between "Capacitor start" and "Capacitor start capacitor run"
induction motors.
In "capacity, start" motor capacitor is connected in series with the starting
winding. But it will be disconnected from the supply when the motor picks up its
speed. But in capacitor start, capacitor-run motor the above starting winding and
capacitor are not disconnected, but always connected in the supply. So it has high
starting and running torque.
4. Why single-phase induction motor has low power factor?
The current through the running winding lags behind the supply voltage by a
very large angle. Therefore power factor is very low.
5. Why a capacitor run type motor is considered as superior one?
i. It has high starting and running torques.
ii. Current drawn is less because of higher power factor
iii. It can be started with some load.
6. How can a universal motor rotation be reversed?
i. The direction of rotation of the concentrated-pole (or salient-pole) type
universal motor may be reversed by reversing the flow of current through either the
armature or field windings.
ii The direction of rotation of the distributed field compensating type universal
motor may be reversed by interchanging either the armature or field leads and shifting
the brushes against the direction in which the motor win rotate.
7. What is the function of centrifugal switch in a single phase - induction motor?
(April/May 2012)
Its function is to automatically disconnect the starting winding from the supply
when the motor has reached 70 to 80 percent of its full speed is reached.
8. Explain why a single-phase induction motor is not self-starting? (Nov/Dec
2015,May/June 2016 & April/May 2017)(Nov/Dec 2019)
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When the motor is fed from a single-phase supply, its stator winding produces an
alternating or pulsating flux, which develops no torque. That is why a single-phase
motor is not self-starting.
9. Why should a motor be named as universal motor?
The available supply in the universe is both A.C and D.C. So the rotor, which
works on both A.C and D.C, is called universal motor.
10. What is the role of magnetic bridges in the operation of shaded pole induction
motor?(April/May2019)
The shading coil(magnetic bridge) causes the flux in the shaded portion to lag
behind the flux in unshaded portion of pole. This gives in effect a rotation of flux
across the pole face and under the influence of this moving flux a starting torque is
developed.
11. State the advantages of using capacitor start motor over a resistance split
phase motor.(May 12)
i. The starting current of capacitor start motor is less than resistance split
phase motor. ii. Starting torque of the capacitor motor is twice that of resistance
start motor.
12. How will you change the direction of rotation of a split phase induction
motor?(Nov/Dec 2014)
By changing the direction of current either in the starting winding or in the
running winding the direction of rotation can be changed.
13. State double revolving field theory.(Nov/Dec 2013 & April/May 2017)
Double revolving theory, formulated by Ferrari, states that a single pulsating
magnetic field  m as its maximum value can be resolved into two rotating magnetic
fields of  m/ 2 as their magnitude rotating in opposite direction as synchronous speed
proportional to the frequency of the pulsating field.
14. What type of motor is used for ceiling fan? (Nov/Dec 2011,May/June
2014,May/June 2016)(Nov 2018)
Singe phase induction motor.
15. State the application of shaded pole motor. (Nov/Dec 2011, Nov/Dec 2016)
Low power household application because the motors have low starting torque
and efficiency ratings. Hair dryers, humidifiers and timing devices.
16. What is meant by single phasing? (Nov/Dec 2012)
Induction motor can operate in single phase supply is called as single phasing.
17.What is the principle of reluctance motor?(Nov/Dec 2014)
A reluctance torque is the torque produced in a motor in which the reluctance
of the airgap is a function of angular position of the rotor,with respect to stator coils.A
motor which develops torque only due to the difference in reluctance in two axes is
known as reluctance motor.
18. What could be the reasons if a split-phase motor runs too slow?
(i) Short-circuited or open winding in field circuit. (ii) Over load. (iii)
Grounded starting and running winding. (iv) Wrong supply voltage and
frequency.
19. What is the main basic difference between the principle of operation of a 3-
phase and single phase induction motors?
When three-phase supply is given to 3-phase induction motor, a rotating
magnetic field is produced and the rotor-starts rotating. But when single-phase supply
is given to single-phase motor only a pulsating flux is produced. So motor is not self-
starting. Therefore to make it self-starting split-phase arrangement is made by
providing an auxiliary winding.

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20. What is a universal motor?
A universal motor is defined as a motor, which may be, operated either on
direct current or single phase A.C supply, at approximately, the same speed and
output.
21. State some applications of universal motor.
Used for sewing machines, table fans, vacuum cleaners, hair driers, blowers
and kitchen appliances etc.
22. How can the direction of a capacitor run motor be reversed? (Nov/Dec 2015
&May/June 2016)
The direction of rotation of capacitor run motor can be reversed by reversing
the connection of any one of the winding.
23. Distinguish the terms rotating and pulsating magnetic fields.
(May/June 2015)
Rotating magnetic field Pulsating magnetic field
Three phase induction motor produce Single phase induction motor produce
rotating magnetic field. pulsating magnetic field.
Field strength is high Field strength is low
Resultant flux will be 1.5 times the Resultant flux will be zero at starting.
maximum flux at starting.
24. State the limitations of shaded pole motors. (May/June 2015)
 Low power factor.
 The starting torque is very poor.
 The efficiency is very low as, the copper losses are high due to presence of
copper band.
 The speed reversal is also difficult and expensive as it requires another set of
copper rings.
25. Define the term step angle in a stepper motor.(Nov/Dec 2016)
Step angle is defined as the angle which the rotor of a stepper motor moves when
one pulse is applied to the input of the stator.The positioning of a motor is decided by
the step angle and is expressed in degrees. The resolution or the step number of a
motor is the number of steps it makes in one revolution of the rotor. Smaller the step
angle higher the resolution of the positioning of the stepper motor.

26. How is the direction of rotation of a single phase induction motor reversed?
(Nov/Dec 2017)
The direction of rotation of single induction motor can be reversed by reversing
the connection of either starting winding or main winding.
27. What is the principle of operation of a linear induction motor? (Nov/Dec
2017)
When the primary of an linear induction motor is excited by a balanced three
phase power supply, a traveling flux is induced in the primary instead of rotating 3 φ
flux, which will travel along the entire length of the primary. Electric current is
induced into the aluminum conductors or the secondary due to the relative motion
between the traveling flux and the conductors. This induced current interacts with the
traveling flux wave to produce linear force or thrust.
28. Application of linear induction motor(Nov 2018)
 The main application of the LIM is in transportation and in electric traction
system. The primary is mounted on the vehicle and the secondary is laid on the
track.
 It is used in the cranes
 Pumping of liquid metals
 Actuators for the movement of doors
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 Used in High voltage circuit breakers and also in accelerators.

29.What is the necessity of having laminated yoke in an ac series
motor?(April/May 2019)
Necessity of laminated yoke in AC series motor is to reduce eddy current loss and
temperature.
30. Mention the advantages of the stepper motor. (NOV 2019)
First, stepper motors have full torque at standstill, and the rotation angle of the motor
is proportional to the input pulse. Essentially, stepper motors offer excellent speed
control, precise positioning, and repeatability of movement.
Additionally, stepper motors are highly reliable since there are no contact brushes in
the motor. This minimizes mechanical failure and maximizes the operation lifespan of
the motor. These motors can be used in a wide range of environments, as many
different rotational speeds can be achieved because the speed is proportional to the
frequency of pulse inputs.
PART – B
1. Give the classification of single phase motors .Explain any two types of single
phase induction motors.(Nov 2013)
The single phase induction motor are classified according to the starting methods,
 Resistance start (split phase) induction motor
 Capacitor start induction motor
 Capacitor run induction motor
 Capacitor start capacitor run motor
 Shaded pole induction motor
CAPACITOR START AND RUN MOTOR
CAPACITOR-START, CAPACITOR-RUN MOTORS As discussed earlier, one capacitor-
start, induction-run motors have excellent starting torque, say about 300% of the full load
torque and their power factor during starting in high. However, their running torque is not
good, and their power factor, while running is low. They also have lesser efficiency and
cannot take overloads. CONSTRUCTION AND WORKING The aforementioned problems
are eliminated by the use of a two valve capacitor motor in which one large capacitor of
electrolytic (short duty) type is used for starting.capacitor of oil filled (continuous duty) type is
used for running, by connecting them with the starting winding.
This motor also works in the same way as a capacitor-start, induction-run motor, with
exception, that the capacitor C1 is always in the circuit, altering the running performance to a
great extent. The starting capacitor which is of short duty rating will be disconnected from the
starting winding with the help of a centrifugal switch, when the starting speed attains about
75% of the rated speed.
This motor has the following advantages:
• The starting torque is 300% of the full load torque
• The starting current is low, say 2 to 3 times of the running current.
• Starting and running power factor are good.
• Highly efficient running.
• Extremely noiseless operation.
• Can be loaded upto 125% of the full load capacity.
APPLICATIONS
• Used for compressors, refrigerators, air-conditioners, etc.
• Higher starting torque.
• High efficiency, higher power factor and overloading.
• Costlier than the capacitor-start — Induction run motors of the same capacity.
SHADED POLE SINGLE PHASE MOTOR
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2. Explain the double field revolving theory for operation of single phase induction
motor.(May 2012, Nov 2012, May 2014, Nov 2014, May/June 2015, Nov/Dec
2016, April/May 2017& Nov/Dec 2017) (April/May 2019)

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3. Explain the operation of shaded pole induction motor with diagram. (May 2012,
Nov 2012, Nov/Dec 2016)(Nov 2018) (NOV 2019)
Refer Q.No 1

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4. (i)Develop equivalent circuit of a single phase induction motor. (April/May
2017)

(ii)Explain the working principle of single phase induction motor. Mention its four
applications.

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Applications:
 Fans
 Blowers
 Centrifugal pumps
 Washing machines
 Refrigerators
 Conveyors
Hair driers
5. What is the principle and working of hysteresis motor and AC series motor?
Explain briefly. (Nov/Dec2011, Nov/Dec 2012, April/May 2014, Nov/Dec 2014,
Nov/Dec 2015, Nov/Dec 2016, May/June 2016 , April/May 2017& Nov/Dec 2017)
Hysteresis Motor:

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AC series motor:

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6. Explain the principle of operation and applications of reluctance motor and

repulsion motor. (May 2012)
Reluctance Motor

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7. (i)Explain about no load and blocked rotor test of single phase induction motor.
(Nov 2014& Nov/Dec 2017) (April/May 2019)
No Load Test
The efficiency of large motors can be determined by directly loading them and by
measuring their input and output powers. For larger motors it may be difficult to arrange
loads for them. Moreover power loss will be large with direct loading tests. Thus no load
and blocked rotor tests are performed on the motors. As the name suggest no load test is
performed when rotor rotates with synchronous speed and there is no load torque. This
test is similar to the open circuit test on transformer. Actually, to achieve synchronous
speed in an induction motor is impossible. The speed is assumed to be synchronized. The
synchronous speed can be achieved by taking slip = 0 which creates infinite impedance in
the rotor branch.
This test gives the information regarding no-load losses such as core loss, friction loss
and windage loss. Rotor copper loss at no load is very less that its value is negligible.
Small current is required to produce adequate torque. This test is also well-known as
running light test. This test is used to evaluate the resistance and impedance of the
magnetizing path of induction motor.
Theory of No Load Test of Induction Motor
The impedance of magnetizing path of induction motor is large enough to obstruct
flow of current. Therefore, small current is applied to the machine due to which there is a
fall in the stator-impedance value and rated voltage is applied across the magnetizing
branch. But the drop in stator-impedance value and power dissipated due to stator
resistance are very small in comparison to applied voltage. Therefore, there values are
neglected and it is assumed that total power drawn is converted into core loss. The air gap
in magnetizing branch in an induction motor slowly increases the exciting current and the
no load stator I2R loss can be recognized. One should keep in mind that current should
not exceed its rated value otherwise rotor accelerates beyond its limit.
The test is performed at poly-phase voltages and rated frequency applied to the stator
terminals. When motor runs for some times and bearings get lubricated fully, at that time
readings of applied voltage, input current and input power are taken. To calculate the
rotational loss, subtract the stator I2R losses from the input power.

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Calculation of No Load Test of Induction Motor

Let the total input power supplied to induction motor be W0 watts.

Blocked Rotor Test:

The induction motors are widely used in the industries and consume maximum
power. To improve its performance characteristics certain tests have been designed
like no-load test and block rotor test, etc. A blocked rotor test is normally performed
on an induction motor to find out the leakage impedance. Apart from it, other
parameters such as torque, motor, short-circuit current at normal voltage, and many
more could be found from this test. Blocked rotor test is analogous to the short circuit
test of transformer. Here shaft of the motor is clamped i.e. blocked so it cannot move
and rotor winding is short circuited. In slip ring motor rotor winding is short circuited
through slip rings and in cage motors, rotors bars are permanently short circuited.
The testing of the induction motor is a little bit complex as the resultant value of
leakage impedance may get affected by rotor position, rotor frequency and by
magnetic dispersion of the leakage flux path. These effects could be minimized by
conducting a block rotor current test on squirrel-cage rotors. Process of Testing of
Blocked Rotor Test of Induction Motor
In the blocked rotor test, it should be kept in mind that the applied voltage on
the stator terminals should be low otherwise normal voltage could damage the
winding of the stator. In block rotor test, the low voltage is applied so that the rotor
does not rotate and its speed becomes zero and full load current passes through the
stator winding. The slip is unity related to zero speed of rotor hence the load resistance
becomes zero. Now, slowly increase the voltage in the stator winding so that current

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reaches to its rated value. At this point, note down the readings of
the voltmeter, wattmeter and ammeter to know the values of voltage, power and
current. The test can be repeated at different stator voltages for the accurate value.

Calculations of Blocked Rotor Test of Induction Motor

Resistance and Leakage Reactance Values
In blocked rotor test, core loss is very low due to the supply of low voltage and
frictional loss is also negligible as rotor is stationary, but stator cupper losses and the rotor
cupper losses are reasonably high.
Let us take denote copper loss by Wcu

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8. Explain with a neat diagram the following types of single phase induction motor.
(a). Split phase induction run motor. (b).Capacitor start and induction run motor and
also draw the slip torque characteristics.(Nov/Dec 2013, May/June 2016)

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9. Explain the operating principle of Linear Induction Motor with neat diagram.
(Nov/Dec 2015, May/June 2016)(NOV 2019)
Linear Induction motor abbreviated as LIM, is basically a special purpose motor that is in
use to achieve rectilinear motion rather than rotational motion as in the case of conventional
motors. This is quite an engineering marvel, to convert a general motor for a special purpose
with more or less similar working principle, thus enhancing its versatility of operation. Let us
first look into the construction of a LIM.
Construction of a Linear Induction Motor
Construction wise a LIM is similar to in more ways than one as it has been depicted in the
figure below.

In LIM stator and rotor are called primary and secondary respectively. If the stator of the poly
phase shown in the figure is cut along the section aob and laid on a flat surface, then it
forms the primary of the LIM housing the field system, and consequently the rotor forms
the secondary consisting of flat aluminum conductors with ferromagnetic core for
effective flux linkage.

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There is another variant of LIM also being used for increasing efficiency known as the
double sided linear or DLIM, as shown in the figure below.
Working of a Linear Induction Motor
When the primary of an LIM is excited by a balanced three phase power supply, a traveling
flux is induced in the primary instead of rotating 3 φ flux, which will travel along the entire
length of the primary. Electric is induced into the aluminum conductors or the secondary due
to the relative motion between the traveling flux and the conductors. This induced interacts
with the traveling flux wave to produce linear force or thrust F. If the secondary is fixed and
the primary is free to move, the force will move the primary in the direction of the force,
resulting in the required rectilinear motion. When supply is given, the synchronous speed of
the field is given by the equation :
Where, fs is supply frequency in Hz, and p = number of poles, ns is the synchronous speed of
the rotation of in revolutions per second.The developed field will results in a linear traveling
field, the velocity of which is given by the equation,
where, vs is velocity of the linear traveling field, and t is the pole pitch. For a slip of s, the
speed of the LIM is given by
Application of Linear Induction Motor
A linear is not that widespread compared to a conventional motor, taking its economic
aspects and versatility of usage into consideration. But there are quite a few instances where
the LIM is indeed necessary for some specialized operations.

Few of the applications of a LIM have been listed below.

1. Automatic sliding doors in electric trains.

2. Mechanical handling equipment, such as propulsion of a train of tubs along a certain
route.
3. Metallic conveyor belts.
Pumping of liquid metal, material handling in cranes, etc.

10. A 220V, 6-pole, 50Hz, single-winding single-phase induction motor has

the following equivalent circuit parameters as referred to the
stator.(May/June 2015)
Rlm=3.0Ω, Xlm=5.0 Ω, R2 = 1.5 Ω, X2= 2.0 Ω
Neglect the magnetizing current. When the motor runs at 97% of the
synchronous speed, compute the following:
i. The ratio Emf/Emb.
ii.The ratio Tf/Tb.
iii.The gross total torque
Solution:
Tf = Pf = (I2f)2 * (r2/s)
Tb = Pb = (I2b)2 * (r2/2-s)
I2f = Vf / ( (r2 / s)+jx2 )
I2b = Vb / ( (r2 / 2-s)+jx2 )
Vf= I1*Zf
Vb= I1*Zb
Net Torque = Tf - Tb
i.Emf/Emb=23.38
ii. Tf/Tb=65.668.

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11. The resistance and inductive reactance of each winding of a 50 Hz split phase induction
motor are 75Ω and 230 Ω respectively . Additional resistance R and condenser C are in series
with one winding .Calculate their values to give the same current in each winding with a
phase difference of 90 degrees. ( Nov 2019)
Solution:
Z= 75+230j =241.9∟72º
Im =Ia =V/Z = V∟0º/241.9∟72º =
Auxillary winding current Ia’ will make an angle 90-72 = 18º
COS 18º = 75+R/Z
R = ZCOS18º -75
= 241.9COS18º -75
R = 155.1Ω
Sin 18º = XC-XL/Z
XC = 230+ 241.9* Sin 18º= 304.75Ω
Therefore C =1.044*10-5 F.

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