Electrical Technology UNIT-IV Visvodaya Technical Academy
UNIT-IV 3-PHASE INDUCTION MOTORS
Syllabus:Polyphase Induction Motors-Construction Details of Cage and Wound Rotor
Machines- - Principle of Operation – Slip- Rotor emf and Rotor Frequency - Torque Equation-
Torque Slip Characteristics.
POLY PHASE INDUCTION MOTORS:
Advantages of 3-Ph Induction Motor:
The Induction motor is an ac machine which converts ac electrical energy into
mechanical energy. The 3-Ph induction motor is commonly used ac motor for
industrial/commercial applications because of the following advantages:
i. It is cheaper in cost
ii. Its construction is simple and robust i.e mechanically strong.
iii. It has more Effiency and more reliable.
iv. It requires less maintenance and has more overload capacity.
v. Its starting (Tst) torque is more.
Construction of 3-Ph Induction Motor:
The 3-Ph induction motor mainly consists of two parts: (i) Stator (ii) Rotor
Stator: Stator is a stationary part. It is made-up of high grade steel
laminations to reduce eddy current losses. The laminations are
insulated from each other and slots are provided as shown in fig (i)
to place the 3-ph stator winding in the stator slots. The stator
winding is made of copper material and the stator winding may be
star or delta connection. Here the stator poles are created by
providing the stator slots. When the 3-ph ac supply is given to the
stator, a 3-ph alternating flux will setup in stator core and this
120 f
stator flux is running with synchronous speed ( N s ) along
P
with stator core.
Rotor: Rotor is rotating part. The rotor is in cylindrical shape and is laminated to reduce the eddy
current losses. The rotor has rotor slots to house the rotor winding. Constructionally, the rotors
are classified as two types. Those are
(i) Squirrel cage rotor (ii) Phase wound or Slip ring rotor.
Squirrel cage rotor:
The squirrel cage rotor consists of cylindrical laminated core with slots nearly parallel to
shaft as shown in fig fig(2) called skewed. At each end of the rotor, the rotor bar conductors are
short circuited with end rings. The conductors and end rings combinely forms a cage as shown
in fig(2). The skewing of rotor bars offers the following advantages:
(i) The locking tendency of the rotor is reduced.
(ii) More torque produced i.e noise is reduced during the operation.
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Phase wound or Slip ring rotor:
This type of rotor consists of three slip-rings which are mounted on the shaft with brushes
resting on them as shown in fig (3). The brushes are connected to star connected variable
resistor. The main use of brushes and slip-rings are to connect the external resistance to rotor.
The use of connecting external resistance to rotor circuit is
(i) It increases the starting torque and decreases the starting current.
(ii) It controls the speed of the motor.
Comparison between Squirrel cage & Slip ring rotor:
Squirrel cage rotor Slip ring rotor
1. Simple and robust construction 1. Difficult in construction
2. It requires less maintenance because
2. It requires more maintenance.
of absent of brushes.
3. No possibility of connecting 3. Additional resistance can be connected to
external resistance to rotor circuit rotor circuit to increase the starting torque
because the rotor bars are short circuited. and to reduce the starting current.
4. Effiency decreases due to power losses
4. Higher Effiency and higher power factor
in additional resistance in rotor.
5. Its cost is low due to absent of
5. Its cost is more.
brushes, slip-rings etc.
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Production of Rotating Magnetic Field:
When the 3-ph AC supply is given to stator, a rotating magnetic flux is developed and is
rotating with a speed of synchronous speed Ns.
Let Φm = Maximum flux, ΦR , ΦY and ΦB are fluxes due to R, Y
and B phases and are given by
ΦR = Φm Sinwt, ΦY = Φm Sin(wt - 120)
ΦB = Φm Sin(wt - 240)
(i) When wt = 0o i.e
3 3
ΦR = 0, ΦY = m and ΦB = m
2 2
From the vector diagram (fig.a)
Resultant flux Φr = 2B ( Y ) 2 2 B ( Y ) cos(60)
= 2B 2Y 2 B Y cos(60)
3 3 3 3 1
= ( m )2 ( m ) 2 2( m )( m )
2 2 2 2 2
9
= m
4
3
= m
2
Resultant flux Φr = 1.5Φm
(ii) When wt = 60o i.e
3 3
ΦR = m , ΦY = m and ΦB = 0
2 2
From the vector diagram (fig.b)
Resultant flux Φr = 2R ( Y ) 2 2 R ( Y ) cos(60)
= 2R 2Y 2 R Y cos(60)
3 3 3 3 1
= ( m )2 ( m ) 2 2( m )( m )
2 2 2 2 2
9
= m
4
3
= m
2
Resultant flux Φr = 1.5Φm
(ii) When wt = 120o i.e
3 3
ΦR = m , ΦY = 0 and ΦB = m
2 2
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From the vector diagram (fig.c)
Resultant flux Φr = 2R ( B ) 2 2 R ( B ) cos(60)
= 2R 2B 2 R B cos(60)
3 3 3 3 1
= ( m )2 ( m ) 2 2( m )( m )
2 2 2 2 2
9
= m
4
3
m
=
2
Resultant flux Φr = 1.5Φm
(iv) When wt = 180o i.e
3 3
ΦR = 0 , ΦY = m and ΦB = m
2 2
From the vector diagram (fig.d)
Resultant flux Φr = 2Y ( B ) 2 2 Y ( B ) cos(60)
= 2Y 2B 2 Y B cos(60)
3 3 3 3 1
= ( m )2 ( m ) 2 2( m )( m )
2 2 2 2 2
9
= m
4
3
m
=
2
Resultant flux Φr = 1.5Φm
From the above analysis, it is clear that at any instant of time the resultant flux is 1.5 time
the max. flux. The direction of the rotating magnetic field in the stator core is in clockwise
direction and this magnetic field is rotating with a speed of N s = 120f /P
Operating or Working principle or why the 3-ph induction motor is self starting
machine:
When the 3-ph AC supply is given to stator of Induction motor, a rotating magnetic field
of constant magnitude and rotating with synchronous speed is produced. This rotating magnetic
field cuts the stationary rotor conductor and an emf is induced across the rotor conductors. The
magnitude of this emf depends on relative speed between the stator flux and rotor conductors.
Since the rotor conductors forms a closed circuit, current will passes through the rotor
conductors called rotor current. Now around the current carrying rotor conductors a magnetic
field will setup in the form of concentric circles as shown in fig.(a). The direction of the
magnetic field around the rotor conductors is determined by skew rule or right hand thumb rule.
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Now, because of interaction of stator flux and flux
around the current rotor conductors, the flux is strengthens right
and weakens on left of the rotor conductors at top of the rotor
conductors and weakens right and strengthens on left of the
rotor conductors at bottom of the rotor conductors as shown in
fig. (b). This result in movement in the rotor in anti clock wise
direction.
From the above discussion it is clear that an induction
motor is a self starting motor.
Slip: The Slip of the 3-Ph Induction Motor can be defined as ‘it
is the difference between the synchronous speed (Ns) and rotor
speed (Nr) and expressed in terms of synchronous speed (Ns) ’ i.e
Synchronou s speed - Rotor speed Ns - Nr
Slip (s) = or
Synchronou s speed Ns
120 f
Rotor speed (Nr) = Ns (1-s) rpm and Synchronous Speed (Ns) = rpm
P
Practically, at no load the value of slip(s) may be 1% to 2%. and at running, slip(s) may be 4%
to 6 %.
Rotor Frequency (fr) :
At stand still or when the rotor is stationary, the frequency of the rotor current is the same
as the supply frequency (f). But when the rotor is rotating the frequency depends on the slip
120 f Ns P
speed i.e if Synchronous Speed (Ns) = and frequency (f) = ------------------- (1)
P 120
also
(Ns - Nr ) P
Rotor frequency (fr) = ------------------- (2)
120
Dividing (2) by (1), we get
fr Ns - Nr f
s r
f Ns f
Rotor frequency fr = sf Hz
Rotor resistance, reactance and emf:
The rotor resistance R2 = ρl/a, where l = length of rotor conductor, a = area of rotor
conductor. Here the rotor resistance does not depends on frequency, so the rotor resistance under
running and stand still (stationary) is samei.e R2 = Rr.
Let X2s = Rotor reactance under standstill (stationary) = 2π f L2
X2r = Rotor reactance under running = 2π fr L2
= 2π (s f) L2
= s (2π f L2)
= s X2s
Similarly the rotor emf under running is E 2r = S E2s
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Rotor Current and Rotor power factor:
Let R2s = Rotor resistance/ph at stationary, X2s =Rotor reactance/ph at stationary =
2πfL2
f = supply frequency E2s = Rotor emf/ph at stationary,
I2s = Rotor current/ph at stationary
R2r = R2s = Rotor resistance/ph, X2r =Rotor reactance/ph at running
E2r = Rotor emf/ph at running = SE2s, I2r = Rotor current/ph at running
Rotor reactance/ph under running is X2r = 2π (sf) L2 = SX2s where f = supply
frequency
Rotor Impedance under running is Z2r = R 2s 2 X 2 r 2 R 2s 2 (sX 2s) 2
E2r sE 2s
Rotor current/ph under running is I2r =
Z2r R 2s 2 (sX 2s) 2
R2s R 2s
Rotor power factor under running is cosϕ2r =
Z2r R 2s 2 (sX 2s) 2
Similarly at stand still i.e slip (s)) = 1
Rotor reactance/ph at standstill is X2s = 2π f L2 where f = supply frequency
Rotor Impedance at standstill is Z2s = R 2 s 2 ( X 2s ) 2
E2s E 2s
Rotor current/ph at standstill is I2s =
Z2s R 2s 2 X 2s 2
R2s R 2s
Rotor power factor at standstill is cosϕ2 =
Z2s R 2s 2 X 2s 2
Torque developed by 3-ph Induction motor:
120 f
Let Φ = Stator flux in wbs and running with speed of Ns =
P
R2s R 2s
Cosϕ2r = Rotor power factor under running = and
Z2r R 2s 2 (sX 2s) 2
E2r sE 2s
I2r = Rotor current/ph under running =
Z2r R 2s 2 (sX 2s) 2
The torque of the 3-ph induction is proportional to net flux (Φ) due to interaction of the stator
and rotor fluxes, rotor current (Ir) and rotor power factor (cosϕr). i.e Torque (T) Φ Ir cosϕr
3
Torque (under running) T Φ I2r cosϕ2r where K =
2 Ns
3 sE 2s R 2s
= Φ x
2 Ns R 2s 2 (sX 2s) 2 R 2s 2 (sX 2s) 2
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3 sE 2s R 2s
= E2s [ E2s Φ ]
2 Ns R 2s 2 (sX 2s) 2
3 sE 22s R 2s
Torque at running or Full Load Torque (Tfl) = N-m
2 Ns R 2s 2 (sX 2s) 2
Similarly
3 E 22s R 2s
Torque (Stand still or starting) Tst = N-m [ E2s Φ ]
2 Ns R 2s 2 X 2s 2
Torque developed by 3-ph Induction motor:
120 f
Let Φ = Stator flux in wbs and running with speed of Ns =
P
R2s R 2s
Cosϕ2r = Rotor power factor under running = and
Z2r R 2s (sX 2s)
2 2
E2r sE 2s
I2r = Rotor current/ph under running =
Z2r R 2s 2 (sX 2s) 2
The torque of the 3-ph induction is proportional to net flux (Φ) due to interaction of the stator
and rotor fluxes, rotor current (Ir) and rotor power factor (cosϕr). i.e Torque (T) Φ Ir cosϕr
3
Torque (under running) T Φ I2r cosϕ2r where K =
2 Ns
3 sE 2s R 2s
= Φ x
2 Ns R 2s 2 (sX 2s) 2 R 2s (sX 2s) 2
2
3 sE 2s R 2s
= E2s [ E2s Φ ]
2 Ns R 2s 2 (sX 2s) 2
3 sE 22s R 2s
Torque at running or Full Load Torque (T fl) = N-m
2 Ns R 2s 2 (sX 2s) 2
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Torque – Slip Curves/Characteristics:
The expression for torque developed by the 3-Ph induction motor is
sE 22s R 2s
Torque = K N-m ------- (1)
R 2s 2 (sX 2s) 2
The torque – slip characteristics of a 3-ph induction motor can explain as follows:
(i) When the rotor speed is equal to synchronous speed i.e N r = Ns, Slip (s) = 0 and from
equation (1) the torque is zero.
(ii) When the load on the motor is increases, the speed decreases and slip increases. The value
of sX2s is very small compared to R2 and is neglected for constant rotor emf E2.
s R 2s
From equation (1) Torque = K Torque slip(s)
R 2s 2
Hence for low value of slip, the torque – slip curve is represented as a straight line as shown
in fig(5)
As the load increases further, the speed decreases and slip increases. This result in increase
in torque and reaches to maximum when slip = R2s / X2s.
(iii) With the increase load beyond maximum torque (T max), the slip increases further. Now the
value of sX2 is more compared to R2 and R2 is neglected, so
s 1
From equation (1) Torque = K 2 2
or Torque
s X 2s slip(s)
Hence for high value of slip, the torque-slip curve is falling from maximum value as shown
in fig(5).
The figure (5) shows the torque-slip curve of 3-ph induction motor and this curve
represents rectangular hyperbola. The magnitude of the torque at Nr = 0 or slip =1 i.e at stand
still, is called starting torque (Tst). The magnitude of the starting torque and maximum torque
depends on rotor resistance (R2s).
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