Speed Control of Induction Motor

This research work provides a detailed explanation of the different working principles of the induction motors as well as general methods of speed control for these devices. The key features for the common control methods of induction motor speeds have also been discussed.

Electric Machines 1
ELECTRICAL MACHINES
By Name
Course
Instructor
Institution
Location
Date

Electric Machines 2
Speed control of Induction motor
Abstract
Several induction motors are currently being used general purposes within the surroundings to
perform different activities. Their usage range from household machines to equipment to tools
used in several industrial activities. The induction motors are slowly becoming a vital and a
source of power that cannot be dispensable within several industries. There is a wide range of
performance capabilities that are needed for these induction motors. On the speed control
segment of the induction motors, it presents a very important functional organ for the induction
motors that generally requires a lot of attention and knowledge on how to achieve. Despite being
traditionally used in the services of fixed speed, its usage has evolved over the years and is
currently being used together with variable frequency drives (VFDs) in services of variable
speed. The VFDs provide necessary opportunities of energy savings for the already existing
induction motors as well future motors in applications such as compressor load, pump and torque
centrifugal fan. This research work provides a detailed explanation of the different working
principles of the induction motors as well as general methods of speed control for these devices.
The key features for the common control methods of induction motor speeds have also been
discussed.

Electric Machines 3
Table of Contents
Abstract...................................................................................................................................................2
1. Introduction.....................................................................................................................................4
1.1. Synchronous speed......................................................................................................................4
1.2. Operating principle of the induction motor..................................................................................5
2. Literature review..............................................................................................................................6
2.1. The equivalent circuit and control of speed of induction motor...................................................6
2.2. Induction motor and their torque speed analysis........................................................................12
2.3. Analysis of various methods for speed control of induction motors..........................................15
2.3.1. By changing stator Voltage....................................................................................................15
2.3.2. By changing stator Frequency................................................................................................19
2.3.3. By changing stator Voltage/Frequency Ratio.........................................................................20
3. Efficient Method of speed control.................................................................................................21
4. Methodology..................................................................................................................................22
4.1. Operation of inductors...............................................................................................................22
4.2. Slip............................................................................................................................................23
5. Conclusion.....................................................................................................................................24
References.............................................................................................................................................26

Electric Machines 4
1. Introduction
An induction motor basically represents a speed motor, implying that for the whole range of
loading, the change in speed for the induction motor is relatively low. It also commonly referred
to as asynchronous motor due to its ability to propel at a speed that is lower than its synchronous
speed (Barrero et al, 2012). It is an alternating current electric motor where the rotor electric
motor required in order to produce the torque is attained through electromagnetic induction from
the stator winding magnetic field. This implies that induction motors can be designed without
any electrical links to the rotor. The rotor of an induction motor can either be squirrel cage type
or the wounded type. The mostly used induction motors in most industrial drives are the 3-phase
squirrel cage type of induction motors. This is mainly due to the fact that they are more reliable,
self-starting and are generally economical.
1.1. Synchronous speed
Synchronous speed can be defined as the rotation speed for the magnetic field in any given rotary
machine. Synchronous speed often relies on the number of poles as well as the frequency of the
machine. The induction motor often operates at a speed that is generally lower than the
synchronous speed (Ben-Brahim, Tadakuma & Akdag, 2017). The rotating magnetic field is
produced in the stator. It will develop a flux in the rotor and thus enabling the rotor to rotate. As
a result of the lagging of the flux current in the rotor with the current of the flux in the stator, it
will be impossible for the rotor to attain its speed for the rotating magnetic field. This speed is
the synchronous speed.
The synchronous speed, ns for an AC motor basically represents the rate of rotation of the
magnetic field of the stator. It is given by the below expression;

Electric Machines 5
Where; f- the power supply frequency
p- number of magnetic poles
ns – synchronous speed for the machine
the formula can be expanded as;
1.2. Operating principle of the induction motor
In both the synchronous motors and the induction motors, the alternating power that is supplied
to the stator of the motor is able to generate a magnetic field that will rotate in synchronous
manner to the oscillations of the AC. While the rotor of a synchronous motor rotates at a similar
rate to that of the stator field, the rotor of an induction motor on the other hand rotates at a speed
that is somehow slower than the stator field (Chen & Sheu, 2012). The stator magnetic field of
the induction motor is therefore rotating or changing with regard to the motor. The rotation
induces an opposing current in the rotor of the induction motor, in effect the secondary winding
of the motors rotor whenever the winding is short-circuited or is closed by impedance that occurs
externally. The rotating magnetic flux will induce the currents in the rotors windings in a manner
that is same to the induced currents in the secondary windings of a transformer.
The currents that are induced in the windings of the rotor will in turn generate magnetic fields in
the rotor that will further react against the field of the stator. According to Lenz’s laws, the

Electric Machines 6
magnetic field direction that is developed will exist in such a way that it opposes current change
through the windings of the rotor. What causes the induced current in the windings of the rotor is
the stator magnetic field that is rotating. In order to oppose the change in rotor winding currents,
the rotor will begin to rotate in the direction of the magnetic field for the rotating stator (Feng,
Liu & Huang, 2014). The rotor will continue to accelerate up to a point where the magnitude of
the torque and the induced rotor current will balance to the mechanical load that is applied to the
rotor rotation. Given that the rotation at a synchronous speed will lead to no induced current of
the rotor, the operation of the induction motor will always be at a speed that is lower than the
synchronous speed. The slip or difference between the synchronous and the actual sped ranges
from about 0.5% to 5.0%. This is always for the standard design B torque induction motors
curves. Induction motor have an essential character of being solely developed by the process of
induction and not being excited independently as in DC or synchronous machines or even being
self-magnetized as in the case of magnetic motors that are permanent (Garces, 2010).
2. Literature review
2.1. The equivalent circuit and control of speed of induction motor
In order to understand the way the induction motor behaves in various conditions of operation, it
is important to develop an equivalent circuit for the motor. The equivalent circuit should be
developed the conditions of sinusoidal steady state operations. In the instance of a balanced three
phase operation, the equivalent circuit for any given phase will suffice. The equivalent circuit for
the induction motor is as shown below (Holtz & Quan, 2012).

Electric Machines 7
Figure 1: equivalent circuit for the induction motor (Kim et al, 2011)
The current that is drawn by the circuit from the per-phase induction motor equivalent circuit is
given as below;
The air gap power is also expressed as below;
Mechanical output power is expressed by;
The mechanical torque is therefore given by the following equation;

Electric Machines 8
A plot graph of the torque in relation to the speed or slip achieves a torque- speed feature for the
motor.

Electric Machines 9
Figure 2: torque speed curve for variable voltage (Kim et al, 2011)
Figure 3: torque speed curve for normal operation(Kim et al, 2011)
For the positive values of the slip, the curve for the torque speed attains a peak. This represents
the maximum torque that the motor produces. It is generally called the stalling torque or the
breakdown torque. The value for the produced maximum torque can be achieved by
differentiating the expression of the torque with respect to the slip. It is then set to zero in order
to achieve ŝ. This represents the slip at maximum torque (Kim et al, 2014). The expression of
attaining the slip at maximum torque is given by the equation below;
Slip at maximum torque

Electric Machines 10
Maximum torque
From the initial equations, it can be observed that the torque appears proportional to the applied
voltage square. The graphs showing the variation of the torque speed curves as well as the
changing voltages have been shown as below;
Figure 4: torque speed curves for constant Eag/f (Krzemiński, 2017)

Electric Machines 11
Figure 5: torque speed curves for constant V/f (Krzemiński, 2017)
In order to prevent saturation within the motor, the air gap flux has to be maintained at a constant
value. In order to maintain Qag constant, it is prper to vary Eag proportionate to f. the developed
torque is expressed as shown below (Kubota, Matsuse & Nakano, 2013);
Slip at maximum torque
Maximum torque
The equations prove that the maximum torque does not depend on the frequency thus remains
constant for each E/f. the maximum similarly happens when it is at a speed that is lower than the
synchronous speed for each E and f combination. There is however a slightly different curve for

Electric Machines 12
constant V/f. this implies that for any fixed V, the E is changed with the operating slips hence the
maximum torque is reduced (Lascu, Boldea & Blaabjerg, 2010).
2.2. Induction motor and their torque speed analysis
Standard torque
The typical relationship between the speed and torque for a standard NEMA design B polyphase
induction motor can be described by the curves below;
Figure 6: Typical speed torque curve for NEMA design B induction motor (Li, Xu &
Zhang, 2015)
The design B motors are highly suitable for several low performance loads including fans and
centrifugal pumps. The motors are usually constrained by these ranges of typical torque;
 Pull-torque (65-190% of the rated torque)
 Breakdown torque (175- 300% of rated torque). Also called the peak torque
 Locked- rotor torque (75- 275% of rated torque)

Electric Machines 13
Within the normal load range of the motor, the slope of the torque is proportional to slip or is
relatively linear to slip due to the rotor resistance value divided by the slip dominating the torque
in a linear manner (Maes & Melkebeek, 2010). Whenever the load increases beyond the rated
load, the leakage reactance factors for the rotor and stator slowly becomes more relevant in
relation to the Rr/ s such that the torque will curve gradually towards the breakdown torque. The
monitor will ultimately stall as the torque load rises past the breakdown torque.
The following curves represent the speed-torque curves for 4 different types of induction motors
(Marino, Peresada & Valigi, 2013).
Figure 7: single-phase motor (Nash, 2016)

Electric Machines 14
Figure 8: Multi-phase motors with single squirrel cage (Nash, 2016)
Figure 9: Multi-phase motors with squirrel cage bar deep (Nash, 2016)

Electric Machines 15
Figure 10: multi-phase motors with double squirrel cage (Nash, 2016)
2.3. Analysis of various methods for speed control of induction motors
It is possible to vary the speed of a direct current motor by the use of a good frequency but for
the induction motors, reduction of speed is always associated with a corresponding efficiency
loss as well as a poor power factor. Given that induction motors are largely used for different
functions, it is proper to have efficient speed controls for the different applications (Ohtani,
Takada & Tanaka, 2012). The following represents some of the major speed controls for the
induction motors;
2.3.1. By changing stator Voltage
Considering the torque equation for the induction motor,
,

Electric Machines 16
Rotor resistance R2 is a constant. Whenever the slip is small, then the (SX2)2 is also considered
very tiny such that it is possible to neglect it. This implies that T ∝ sE22 where E2 represents the
rotor induced emf and E2 ∝ V. hence T ∝ sV2. This means that whenever the supplied voltage is
reduced, the torque that is developed also decreases. In order to provide a similar torque load
torque, the slip should increase as the voltage decreases. The speed will consequently be
decreasing (Ortega et al, 2016).
This method of inductor motor speed control represents the cheapest and the simplest method of
speed control. It is however not commonly used due to the following reasons;
 A greater change in the voltage supplied is often needed for a change in speed that is
relatively small.
 A greater change in the voltage supply will definitely lead to a greater change in the flux
density. This implies that it will disrupt the magnetic conditions of the motor (Peng &
Fukao, 2014).
The torque sspeed features for a 3-phase induction motor that follows a varying voltage supply
as well as fan load has been expressed in the graph below;

Electric Machines 17
Figure 11: Torque-speed characteristics (Schauder, 2012)
The most preferred voltage controller when performing variation of the voltage is the Thyristor
voltage controller. The connection for a single phase supply is connected as shown with 2
Thryristors in back to back connection.

Electric Machines 18
Figure 12: Single phase supply (Shin et al, 2012)
In a 3-phase induction motor, 3 pairs of the Thyristor are connected back to back. Each pair of
the Thyristor comprises of thyristors as shown in the diagram below.

Electric Machines 19
Figure 13: Thyristor Voltage Controller (shin et al, 2012)
2.3.2. By changing stator Frequency
The equation for a synchronous speed of an induction motor rotating magnetic field is always
expressed as below;
Where; p- number of stator poles
f- Supply frequency
Therefore, changes in the synchronous speed will result to a change in the frequency that is
supplied. The actual speed for an induction motor can be determined by the expression below
(Shyu & Shieh, 2016);

Electric Machines 20
This method is however not commonly used. The formula is mainly applied where the induction
motor has a supply from a dedicated generator such that it is easier to vary the frequency by
changing the prime mover speed (Tajima & Hori, 2013). Similarly, at lower frequency, the
current from the motor can also be very high as a result of the reactance that is reduced.
Whenever the frequency is raised past its rated value, the maximum torque that is developed will
fall whereas the speed will rise.
Figure 14: torque speed curves (Tursini, Petrella & Parasiliti, 2010)

Electric Machines 21
2.3.3. By changing stator Voltage/Frequency Ratio
This is basically the widely used method of controlling the speed of an induction motor. From
the above methods, whenever the frequency supplied is lowered while maintaining the rated
voltage supply, the air gap flux will appear to saturate. This will result to a possible excessive
stator current as well as the disruption of the stator flux wave. The stator voltage should therefore
be lowered in a proportional way to the frequency such that it is able to maintain a constant air
gap flux. The stator flux magnitude is also proportional to the ratio of the stator frequency and
voltage. This implies that whenever the voltage to ratio frequency is kept constant, the flux will
equally be kept constant (Uddin, Radwan & Rahman, 2012). When the voltage to frequency ratio
is also kept constant, the torque that is developed is also kept approximately constant. This
method of induction motor speed control achieves a greater run-time efficiency implying that
most of the alternating current speed drives makes use of a constant voltage to frequency ratio
method in the control of speed for the induction motors. The variable voltage to the variable
frequency method could similarly be used. This method has a wide range of controlling speed
and equally provides a capability that is soft start.
3. Efficient Method of speed control
The use of V/F method is basically the most effective method of controlling the speed of an
induction motor. V/F simply means voltage/frequency. This represents a speed control method
that ensures the output voltage is kept proportional to the frequency such that it is able to
maintain a constant motor flux. This process is able to avoid weak magnetic saturation and
magnetic phenomenon from actually occurring (Yan, Jin & Utkin, 2010).
The control principle for this method is to generate a circuit with the frequency oscillator
commonly referred to as the voltage controller oscillator. It involves a capacitance that is

Electric Machines 22
dependent on the voltage and when it is subjected to a voltage change, the capacity will change
which further results to changes in the frequency of oscillation thus the frequency becomes
variable. The controlled frequency is useful in controlling the frequency of the output voltage
that makes it attain the changes in speed of the electric motors.
Figure 15: V/F Control (Yang & Chin, 2013)
Several general purpose induction motors are currently using this method of speed control.
4. Methodology
4.1. Operation of inductors
The application of a 3- phase balanced set of sinusoidal voltages to an induction motor stator; it
results to the production of constant amplitude within the air gap which subsequently rotates by

Electric Machines 23
the use of a constant speed. The constant speed is often known as the synchronous speed. The
synchronous speed for a p pole machine is described as shown below;
(Revolutions per minute)
Where; f represents the frequency of the currents and voltages that are applied
As a result of the rotating air-gap flux, a counter emf, basically known as the air gap voltage, is
induced into all the phases of the stator at a specified frequency, f. the production of an electric
motor torque occurs through the interaction of the rotor currents and the air gap flux. In case
there is the rotation of the rotor at a synchronous speed, there will be no relative motion between
rotor and the air gap flux. This therefore implies that there will be no induced currents, torque
and voltages in the rotor (Yang & Chin, 2013). At any other rotor speed in a similar direction of
the rotation of the air gap flux, the motor moves in relation to the air gap flux. The movement is
at a relative speed commonly known as the slip speed. Whenever the slip speed is normalized by
the synchronous speed, the slip generates the following equation;
4.2. Slip
Slip can be defined as the difference between the operating speed and the synchronous speed at a
similar frequency often expressed in rpm. The illustration of the slip can be given as below;
Where; ns – electrical speed of the stator

Electric Machines 24
NT –mechanical speed of the rotor
Figure 16: typical torque curve as a function of slip (Yang & Chin, 2013)
Slip often ranges between 0 at synchronous speed and 1 whenever the rotor is at rest. Slip can
therefore be used to determine torque of the motor. Given that the rotor windings that are short
circuited have a generally lower resistance, even a tiny slip will be able to induce a large current
to the rotor and subsequently resulting to a significant torque. Whenever there is a load that is
full rated, the slip will be ranging from 5% or more for tiny or motors designed for special
functions to lower than 1% for large motors. The variations in speed can lead to problems of load
sharing motors that are differently sized are connected mechanically (Yan, Jin & Utkin, 2010).
There currently exist several methods of lowering the slip. The most favored solution for
reducing slip has always been the concept of VFDs.

Electric Machines 25
5. Conclusion
Induction motors are generally constant speed motors implying that for the whole range of
loading, there are very small changes in sped for the motor. Induction motors have been largely
used in several electric applications. It is therefore important to properly understand the
functionality of these devices in order to improve their effectiveness. One most important factor
for the induction motors operation is to understand the different methods of control. This study
has presented the common methods of controlling the speeds of the induction motors. An
illustration of how each method operates has also been explained.

Electric Machines 26
References
Barrero, F., Gonzalez, A., Torralba, A., Galvan, E. and Franquelo, L.G., 2012. Speed control of
induction motors using a novel fuzzy sliding-mode structure. IEEE Transactions on
Fuzzy Systems, 10(3), pp.375-383.
Ben-Brahim, L., Tadakuma, S. and Akdag, A., 2017. Speed control of induction motor without
rotational transducers. IEEE Transactions on Industry Applications, 35(4), pp.844-850.
Chen, T.C. and Sheu, T.T., 2012. Model reference neural network controller for induction motor
speed control. IEEE Transactions on Energy Conversion, 17(2), pp.157-163.
Feng, G., Liu, Y.F. and Huang, L., 2014. A new robust algorithm to improve the dynamic
performance on the speed control of induction motor drive. IEEE Transactions on Power
Electronics, 19(6), pp.1614-1627.
Garces, L.J., 2010. Parameter adaption for the speed-controlled static ac drive with a squirrel-
cage induction motor. IEEE Transactions on Industry Applications, (2), pp.173-178.
Holtz, J. and Quan, J., 2012. Sensorless vector control of induction motors at very low speed
using a nonlinear inverter model and parameter identification. IEEE Transactions on
industry applications, 38(4), pp.1087-1095.
Kim, S.H., Park, T.S., Yoo, J.Y. and Park, G.T., 2011. Speed-sensorless vector control of an
induction motor using neural network speed estimation. IEEE Transactions on industrial
electronics, 48(3), pp.609-614.
Kim, Y.R., Sul, S.K. and Park, M.H., 2014. Speed sensorless vector control of induction motor
using extended Kalman filter. IEEE Transactions on Industry Applications, 30(5),
pp.1225-1233.

Electric Machines 27
Krzemiński, Z., 2017. Nonlinear control of induction motor. IFAC Proceedings Volumes, 20(5),
pp.357-362.
Kubota, H., Matsuse, K. and Nakano, T., 2013. DSP-based speed adaptive flux observer of
induction motor. IEEE transactions on industry applications, 29(2), pp.344-348.
Lascu, C., Boldea, I. and Blaabjerg, F., 2010. A modified direct torque control for induction
motor sensorless drive. IEEE Transactions on industry applications, 36(1), pp.122-130.
Li, J., Xu, L. and Zhang, Z., 2015. An adaptive sliding-mode observer for induction motor
sensorless speed control. IEEE Transactions on Industry Applications, 41(4), pp.1039-
1046.
Maes, J. and Melkebeek, J.A., 2010. Speed-sensorless direct torque control of induction motors
using an adaptive flux observer. IEEE Transactions on Industry Applications, 36(3),
pp.778-785.
Marino, R., Peresada, S. and Valigi, P., 2013. Adaptive input-output linearizing control of
induction motors. IEEE Transactions on Automatic control, 38(2), pp.208-221.
Nash, J.N., 2016. Direct torque control, induction motor vector control without an encoder. IEEE
Transactions on Industry Applications, 33(2), pp.333-341.
Ohtani, T., Takada, N. and Tanaka, K., 2012. Vector control of induction motor without shaft
encoder. IEEE Transactions on Industry Applications, 28(1), pp.157-164.
Ortega, R., Nicklasson, P.J. and Espinosa-Pérez, G., 2016. On speed control of induction motors.
Automatica, 32(3), pp.455-460.
Peng, F.Z. and Fukao, T., 2014. Robust speed identification for speed-sensorless vector control
of induction motors. IEEE Transactions on Industry Applications, 30(5), pp.1234-1240.

Electric Machines 28
Schauder, C., 2012. Adaptive speed identification for vector control of induction motors without
rotational transducers. IEEE Transactions on Industry Applications, 28(5), pp.1054-1061.
Shin, M.H., Hyun, D.S., Cho, S.B. and Choe, S.Y., 2010. An improved stator flux estimation for
speed sensorless stator flux orientation control of induction motors. IEEE Transactions
on Power Electronics, 15(2), pp.312-318.
Shyu, K.K. and Shieh, H.J., 2016. A new switching surface sliding-mode speed control for
induction motor drive systems. IEEE transactions on Power Electronics, 11(4), pp.660-
667.
Tajima, H. and Hori, Y., 2013. Speed sensorless field-orientation control of the induction
machine. IEEE Transactions on Industry Applications, 29(1), pp.175-180.
Tursini, M., Petrella, R. and Parasiliti, F., 2010. Adaptive sliding-mode observer for speed-
sensorless control of induction motors. IEEE Transactions on Industry Applications,
36(5), pp.1380-1387.
Uddin, M.N., Radwan, T.S. and Rahman, M.A., 2012. Performances of fuzzy-logic-based
indirect vector control for induction motor drive. IEEE Transactions on Industry
Applications, 38(5), pp.1219-1225.
Yan, Z., Jin, C. and Utkin, V., 2010. Sensorless sliding-mode control of induction motors. IEEE
Transactions on Industrial Electronics, 47(6), pp.1286-1297.
Yang, G. and Chin, T.H., 2013. Adaptive-speed identification scheme for a vector-controlled
speed sensorless inverter-induction motor drive. IEEE Transactions on Industry
Applications, 29(4), pp.820-825.