Modeling and Testing of Induction Motor: A Review

Modeling and Testing of Induction Motor: A Review

Aditya Narayan, Birju Besra, Manish Bakhla, Nitesh Thapa, Raju Ranjan

Dept. of Electrical and Electronics Engg., RVS College of Engineering and Technology, Jamshedpur-831012, INDIA.

Abstract This paper is a review of the working of induction motors and its mathematical modelling. It also covers the basic terms involved in the study of the induction motor and also the speed control of induction motor is presented. The various performance characteristics are studied for torque slip characteristics and no load and blocked rotor test are performed on an induction motor and the results are presented here.

Keywords Induction motor; slip; rotor torque; speed control; mathematical modeling

1. INTRODUCTION

   The three phase induction motors shown in Fig. 1. are widely used in industries where a constant speed is essential. These motors are almost constant speed motors as they run at constant speed from no load to full load. As we shall see that the speed of these motors is frequency dependent, the speed control of these motors is a tedious job. However, the speed control of induction motor has been and is even now the center of interest for many engineers as induction motors are robust, need less maintenance, can operate at hazardous locations therefore it will be beneficial to use induction motors if the speed can be controlled.

   Fig. 1. Induction Motor

2. CONSTRUCTION DETAILS

A three phase induction motor mainly consists of two main parts:

1. Stator

2. Rotor

1. Stator:The stator 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(fig1). The insulated conductors are placed in the stator slots and are connected to form a balanced three phase star or delta connection circuit.

2. Rotor:The rotor is rotating part of an induction motor. It is a hollow laminated core having slots on its outer periphery. The rotor winding may be one the following types.

   1. Squirrel cage type

   2. Wound type

1. Squirrel cage type: It

   consists of laminated cylindrical core having parallel slots on its outer periphery, in these slots one copper or aluminum bar is placed. All these bars are connected at

   each end by metal rings, called end rings. These bars, therefore, are permanently short circuited and therefore no external resistance can be connected.

2. Wound type: These consist of laminated cylindrical core and carries a three phase winding as in the stator. The open ends of the rotor winding is brought out and connected to three insulated slip rings mounted on the rotor shaft with one brush resting on each slip ring. The three brushes are connected to a three phase star connected rheostat. These resistances are included at starting to limit high circulating current in the short circuited rotor winding and to give a large starting torque. These resistances are gradually reduced to zero as the rotor attains its normal speed.

3. PRINCIPLE OF OPERATION

   Fig. 2. Principle of Operation

   When a three phase induction motor is energized by a three phase supply a rotating magnetic field is produced. This rotating magnetic field cuts the rotor conductors which are yet stationary. Due to the relative speed between rotating magnetic field and stationary rotor, an E.M.F is induced in the rotor conductors. Since the rotor circuit is short circuited, current starts flowing in the rotor conductors.

   Ns 120 f

   P

   where, P Number of poles,

   f Frequency

   In an induction motor the change in slip from no load to full load is of the order of 0.1% – 0.3%. Therefore an induction motor is essentially a constant speed motor.

4. MATHEMATICAL MODELING

   1. Rotor Torque

      The torque developed in an I.M. is directly proportional to the followings:

      • Rotor current

      • Rotor emf

      • Power factor of the rotor circuit

        As the current carrying rotor conductors are placed in the magnetic field produced by the stator. As a result, mechanical force acts on the rotor conductors. The sum of this mechanical force on each of the rotor conductors produces a torque, which tends to move the rotor in the same direction as the rotating field. The fact that the rotor tends to move the same direction as that of the rotor can be explained by the Lenz's law. According to this law, the direction of the rotor current will be such that it tends to oppose the very cause of the current. Now the cause producing the rotor current is the

        Therefore,

        where,

        T E 2I 2 cos 2

        T KE 2I 2 cos

        I 2 =rotor current at standstill

        E2 =rotor emf at standstill

        cos 2 =rotor p.f at standstill

        relative speed between the rotating magnetic field and the rotor conductors. Hence, to reduce the relative speed, the rotor starts running in the same direction as that of the

   2. Starting Torque(Ts)

      rotating magnetic field.

      In practice the rotor can never reach the speed of stator field. If it does so, there will be no relative speed between the stator field and the rotor and hence no induced emf and no current in the rotor circuit and therefore no torque to drive the rotor. Practically, the friction and windage would immediately slow down the rotor speed. Hence the rotor speed (N) is always less than that of rotating magnetic field

      Let,

      I 2 =rotor current at standstill

      E2 =rotor emf at standstill

      cos 2 =rotor p.f at standstill

      X 2 =rotor reactance per phase at standstill R2 =rotor resistance per phase at standstill

      (RMF) known as synchronous speed of the stator (Ns).

      The difference between the synchronous speed (Ns)

      Rotor impedance/phase, Z 2

      R22 X 22

      E2 E 2

      and the rotor speed (N) is known as slip. It is usually

      Rotor current/phase,

      I 2

      expressed as percentage of synchronous speed i.e.,

      Z 2 R22 X 22

      %slip, s Ns N 100

      Rotor p.f.,

      cos R2 R2

      2

      2

      Ns Z 2

      R2 X 2

      When the motor is stationary the rotor is stationary (N=0),therefore,

      Starting torque,

      Ts KE 2I 2 cos 2

      %slip, s Ns 0 100

      Ns

      KE2

      E2

      R22 X 22

      R2

      R22 X 22

      Ns 100 Ns

      100%

      E 2R2

      K 2 2

      2 2

      2 2

      R2 X 2

      Rotor speed,

      or s 1

      The supply voltage is generally constant, so that flux per pole

      set up by the stator is also fixed. This means the emf

      Nr Ns(1 s)

      and synchronous speed is given by,

      E2 induced is also constant.

      Ts

      K R2 K1 R2 R2 X 2 Z 2

      where K 2 is another constant.

      1

      1

      2 2 2

      3

      3

      where K1 is another constant.

      The value of K is, K Ns

      2

      Here Ns is in r.p.s.

   3. Torque Under Running Condition:

5. TORQUE SLIP CHARACTERISTICS

   The curve drawn between the torque and the slip for a particular value of rotor resistance is known as torque-slip characteristics.

   The following points may be noted by the torque-slip characteristics:

   1. At s=0, T =0 so that the torque – slip curve starts from the origin.

      Let,

      I 2 =rotor current at standstill

      E2=rotor emf at standstill

   2. At normal speed, slip is small, so that sX 2 is negligible as compared to,

      cos 2 =rotor p.f at standstill

      X 2 =rotor reactance per phase at standstill

      T s R2

      R2 =rotor resistance per phase at standstill

      Rotor emf/phase, E 2 ' sE 2

      Rotor reactance/phase, X 2 ' sX 2

      Hence a torque slip curve is a straight line from zero slip to a slip that corresponds to full load.

   3. As the slip increases beyond the full load slip, the torque increases and becomes maximum

      R2

      Rotor

      at s . This maximum torque is known as a pull out

      2 2 X 2

      impedance/phase, Z 2 '

      Rotor current/phase,

      R2 X 2

      torque or breakdown torque. Its value is almost twice that of full load torque when the motor operates at its rated voltage and frequency.

      I 2 ' E2 ' sE2

   4. When the slip increases beyond the maximum torque, the

   2

   2

   Z 2 '

   R22 (sX 2)2

   term

   s2 X 2

   increases very rapidly, so that

   R2 may be

   Rotor p.f.,

   neglected as compared to.

   cos ' R2

   T s

   2 2 2 s2 X 2

   Running torque,

   R (sX 2) 2

   1

   Tr E 2 ' I 2 ' cos 2 '

   I 2 ' cos 2 '

   ( E 2 ' )

   s

   as X 2 is constant

   Thus the torque is now inversely proportional to slip. Hence the torque slip characteristics are a rectangular parabola.

   sE 2 '

   R22 (sX 2)2

   R2

   R22 (sX 2)2

6. TESTS ON THE INDUCTION MOTOR

   1. No Load Test:

      sE 2R2

      2

      2

      R2 (sX 2)2

      2

      2

      KsE 2R2

      2

      2

      R2 (sX 2)2

      2

      2

      K1sE 2R2

      2

      2

      R2 (sX 2)2

      No load test is performed to determine the no load current, no load power factor, windage and friction losses, no load resistance and reactance. Since there is no power output on no load, the power supplied to the stator furnishes its core loss and the friction and windage losses in the rotor. The circuit diagram for the no load test is shown in Fig. 3.

      ( E 2 )

      If the supply voltage V is constant, then stator flux and hence E2 will be constant,

      Tr

      K 2sR2

      2

      2

      R2 (sX 2)2

      Fig. 3. No Load Test

      Procedure for no load test:

      1. The three phase Variac is kept at '0' position and switched on the main supply.

      2. The voltage is increased slowly through the variac upto the rated voltage of induction motor.

      3. Readings of voltmeter, ammeter, and voltmeter was taken at different value of voltages.

   2. Blocked Rotor test:

      0.26 1.58 0.144

      0.2275A

      Ia Iph sin

      1.58 1 (0.144)2

      1.56 A

      The blocked rotor test is also known as locked rotor test or short circuit test. This test is employed to find the short circuit current of the rotor circuit. This test is performed at

      Ro Vo

      Iw

      400

      0.2275

      1758

      the rated current of the induction motor. The circuit diagram for blocked rotor test is shown in Fig. 4.

      Xo Vo 400 256.14

      Ia 1.56

      Zo

      Ro 2 Xo 2

      17582 256.142

      1776.56

      2. For Block Rotor Test:

      Fig. 4. Blocked Rotor Test

      I 01

      Isc 5

      2.88 A

      Procedure for blocked rotor test:

      3 3

      P / 3

      369

      1. The three phase Variac is kept at '0' position before switching "ON" the main supply.

      2. Block the rotor by applying external load or by any means.

      3. Increase the voltage through Variac slowly up to the rated current of the induction motor is reached.

         R01 4.85

         Isc2 3 52

         Z 01 V 01 76 26.38

         I 01 2.88

      4. Take one or maximum of two readings of all the

         X 01

         Z 0 2 R0 2

         (26.38)2 (4.85)2 25.93

         1 1

         instruments..

      5. Switch off the main supply.

   3. Calculations:

      1. For no load test:

   VI cos

7. SPEED CONTROL OF INDUCTION MOTOR

   An induction motor essentially runs at constant speed as the load is varied. Some industrial drives, however, require

   Wattmeter constant =

   Fullscale

   600 5 0.2 150

   4

   several different speeds or even continually variable speeds The induction motor, being most rugged motor with almost negligible maintenance, has been and even now the center of interest for electrical engineers to make it run successfully at different speeds.

   The operating speed of a 3-phase induction motor is

   P

   276

   3VI cos

   3 V 2.75 cos

   given by,

   Nr Ns(1 s)

   cos 0.144

   or,

   Nr 120 f

   (1 s)

   Iph Io 2.75 1.58A P

   3 3

   Vph 400V

   Iw Iph cos

   From above equations, it can be noted that, the speed of an induction motor depends on synchronous speed which depends on the number of poles, frequency, and slip. Hence, the speed of an induction motor can be controlled by controlling the number of poles, frequency and slip of the motor.

   Methods of speed control of induction motor:

   1. Pole changing method:

      A change in the number of poles, changes the

      V 4.44N mF

      where N is the number of the turns per phase, m

      is the

      synchronous speed and therefore, the induction motor operating speed. Since three numbers of poles can be changed only by even numbers, the speed control is not continuous but a stepped one. With pole-amplitude modulation, a finer control in the number of poles and, therefore, the speed can be controlled.

      Sometimes induction machines have a special stator winding capable of being externally connected to form two different number of pole numbers. Since the synchronous speed of the induction machine is given by:

      Ns Fs

      P

      where p is the number of pole pairs, this would correspond to changing the synchronous speed. With the slip now corresponding to the new synchronous speed, the operating speed is changed. This method of speed control is a stepped variation and generally restricted to two steps. If the changes in stator winding connections are made so that the air gap flux remains constant, then at any winding connection, the same maximum torque is achievable. Such winding arrangements are therefore referred to as constant-torque connections. If however such connection changes result in air gap flux changes that are inversely proportional to the synchronous speeds, then such connections are called constant-horsepower type.

   2. Stator frequency control:

      The expression for the synchronous speed indicates that by changing the stator frequency the rotor speed can be changed. This can be achieved by using power electronic circuits called inverters, which convert DC to AC of desired frequency. Depending on the type of control scheme of the inverter, the AC generated may be variable-frequency-fixed- amplitude or variable-frequency-variable-amplitude type. Power electronic control achieves smooth variation of voltage and frequency of the AC output. This when fed to the machine is capable of running at a controlled speed. However, consider the equation for the induced emf in the induction machine.

      peak flux in the air gap and F is the frequency. Note that in order to reduce the speed, frequency has to be reduced. If the frequency is reduced while the voltage is kept constant, thereby requiring the amplitude of induced emf to remain the same, flux has to increase. This is not advisable since the machine likely to enter deep saturation. If this is to be avoided, then flux level must be maintained constant which implies that the voltage must be reduced along with frequency. The ratio is held cnstant in order to maintain the flux level for maximum torque capability.

   3. Line voltage control:

   The electromagnetic torque of an induction motor is approximately proportional to the stator terminals. The stator voltage and consequently the torque and speed of an induction motor, can be varied by inserting rheostat, a saturable reactor or an auto transformer in the supply mains. More recently, thyristors in series with the supply mains are used to control the voltage across the stator winding.

8. CONCLUSIONS

The construction of Induction motor is studied and performed no load and blocked rotor test on it and torque slip curve is studied, observation table of no load and blocked rotor test is studied. It is observed from the rotor speed equation that the speed of an inaction motor can be controlled by pole changing, stator frequency control, line voltage control methods.

REFERENCES

1. Fitzgerald, A. E., Charles Kingsley, and Stephen D. Umans. Electric Machinery. Boston, Mass: McGraw-Hill, 2003.

2. P. S. Bimbhra. Electrialc Machinery.Khanna Publishers, 2003.

Table.1 Observation Table(For No Load Test)

Table.2 Observation Table For Blocked Rotor Test: