Electrical Energy already constitutes more than 50 % of all energy usage on Earth. A large part of the electrical energy production on earth is used to be converted into mechanical energy by different electric motors like DC Motors, Synchronous Motors and Induction Motors.

Induction Motors are termed as “Workhorse of the Industry”. The reason behind is that it is one of the mostly used motors in the world. It has wide application in transportation and industries, and also in household appliances, and laboratories.

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The reasons behind the popularity of the Induction Motors are:
I. IM compared to other motors like DC MOTORS and SYNCHRONOUS Motors are cheap.

II. Its economy of procurement, installation and use, makes the Induction Motor first choice for an operation.

III. Its robustness enables them to be used in all kinds of environments and for long durations of time.

IV. High efficiency of energy conversion made IM very reliable for use.

V. Costs of maintenance is very low
VI. Starting torque is very high therefore made useful in applications where load is applied before starting the motor.

VII. The ease with which its speed is controlled adds IM one of its major advantages.

The main objective behind this project is to develop a model to implement V/f control of an induction motor among all other methods of speed control and do a comparison results between closed loop and open loop V/f method of speed control using PI controller. Transient response during starting is also analyzed so that one should have clear idea about rotor, stator current, speed and torque before comparing closed loop and open loop.

1. Development of a Simulink model of 3 phase induction motor.

2. Run an Induction Motor at load, at rated load and at no load and obtain its uncontrolled speed, torque, and current characteristics.

3. V/f Control scheme development for controlling both Open Loop and Closed Loop IM using PI controller.

Chapter 1 deals with motivation towards use of induction motors and objective of the project.

Chapter 2 deals with the basic of the Induction Motor drive and its working and gives an information of its efficient useful needs.

Chapter 3 deals with methods of speed control of induction motor, torque speed characteristics with constant, variable rotor resistance and variable stator voltage.

Chapter 4 deals with torque speed characteristics for closed and open loop and analysis of other methods of control like vector method control.

Chapter 5 deals with simulation results and analysis of three phase IM during starting and comparison of graph of closed loop and open loop control methods.

Chapter 6 summarizes all the results obtained and lists the conclusions based on those results and also made a focused on the future work.

2.1 Introduction
The induction machine, mostly the cage rotor type, is commonly used in industry. These machines are very cheap and rugged in operation and available from fractional of horsepower to high-megawatt capacity, both in single-phase and poly-phase. In this thesis, the basic fundamentals of its, operation and speed control of induction motors are presented with explanation and simulation model and graph.

Three phase induction motor is basically a constant speed motor therefore it’s somewhat difficult to control its speed. The speed control is done at the cost of decrease in efficiency and low electrical power factor.

Controlling Speed is the necessity in Induction Motors because of the following factors:
I. It smooth operation.

II. It provides torque control and acceleration control.

III. Different processes require the motor to run at different speeds.

IV. It compensates the fluctuating process of current and voltage
V. Slow running of the motors is required during installation. These factors present a strong implementation of variable speed drives in Induction Motors.

Before the implementation of IM only dc motors were employed for drives requiring variable speeds due to their ease of speed control methods. The conventional methods of controlling speed of an induction motor were either expensive or too inefficient therefore restricting their application to constant speed drives only. Although new modern trends and development of speed controlling methods increased the use of induction motors in electrical drives very extensively. In this thesis, we will study the various speed control methods of a 3-Phase induction motor and compare their speed using their simulation graph and Torque-Speed characteristics. The transients analysis during the starting of 3-phase IM will be focussed and the effects of various machine parameters such as rotor, stator resistances and inductances will be analyzed.

Some of the recent development of IM drives:
i. Analytical models for design and research purposes.

ii. Better Magnetic materials, Insulating materials and cooling systems
iii. Availability of designing optimization tools.

iv. IGBT based PWM Inverters for efficient frequency changing property with low loss and high power density.

v. New methods for manufacturing and testing.

vi. Applications with high power and high speed and widespread presence in all kinds of industries, households and in transportation, hence the Induction Motor is called the Racehorse of the Industry.

Whenever the stator winding is energized with a 3 phase supply, there is a production of rotating magnetic field which rotates around the stator at synchronous speed Ns. This rotating flux cuts the stationary rotor and induces an electromotive force in the rotor windings. Since the rotor windings are short-circuited there is a flow of current in them. As these conductors are placed in stator’s magnetic field this exerts a mechanical force on them by Lenz’s law which state that the rotor current direction will be such that it will try to oppose the cause which produces them. Hence a torque production reduces relative speed between rotor and magnetic field. Hence the rotor will rotate in same direction as that of the flux. Thus the relative speed between the rotor and the speed of magnetic field is responsible for driving the rotor. Therefore the rotor speed Nr always remains less than Ns the synchronous speed.

Various methods for the speed control of an Induction Motor are
i. Pole changing method
ii. Variable supply frequency control
iii. Variable supply voltage control
iv. Variable Rotor Resistance Control
v. V/f method control
vi. Slip Recovery
vii.Vector control
However, we shall not be analyzing the pole changing and the variable supply frequency methods as these are very rarely used. This thesis deals with the basic theory of several methods of speed control. Hereafter, they are discussed one after the other.

This controlling method is applicable only to wound rotor motor as external resistance
can be added to it through the slip rings. External resistance can be connected in the
rotor circuit during operation.This increases the starting torque and reduces the starting current.By making use of appropriate value of resistors, the maximum torque can be made to appear during starting. This can be used in applications requiring high starting torque. Once the motor starts, the external resistance can be cut out for obtaining high torque throughout the accelerating range. As external resistance are connected, most of the heat loss is dissipated through them thus the rotor temperature rise during starting is limited.


In this the development of torque varies as square of the voltage applied to its stator windings terminals, hence on varying the applied voltage, the electromagnetic torque developed by the motor can be varied. This method of varying stator voltage is generally used for small squirrel-cage motors where cost is an important criterion and not efficiency.This method of operation has rather limited range of speed control.On decreasing supply voltages, the value of maximum torque also decreases. However it still occurs at the same slip as earlier. Even the starting torque and the overall torque reduced. Thus the machine is highly underutilized and so this speed controlling method has very limited applications.

From the above mentioned methods V/f Control is the most popular one which is found as widespread use in industrial and domestic applications because of its ease of implementation.It has inferior dynamic performance compared to vector control and therefore in areas where precision is required, V/f control are not used.

Some of the advantages are
It gives good running and transient performance
It provides good range of speed operation.

Voltage and frequencies reach rated values at base speed.

It is easy and easy to implement.

It has low starting current requirement.

It has a wider stable operating region.

Voltage and frequencies reach rated values at base speed.

On controlling accelaration the rate of change of supply frequency is controlled

Figure 1: Equivalent Circuit of an Induction Motor
Where Xm= Magnetizing reactance
Xs= Stator Reactance
Xr= Rotor Reactance
Rs= Stator Resistance
Rr= Rotor Resistance
s=slip of Induction Motor so slip is given as ? = (?????)/ ?s…………………….1
where Ns = Synchronous Speed
Nr=Rotor speed
The following expresson derived is
Rotor Current ?2 =??/(??+ ??/? )+? (??+?? )……………………………….………2
Torque ? = ± ( 3??^2 ??/ ? )/ ?? (??+ ??/ ?) ^2+( ??+??) ^2 ………………….3 ^……..

Figure 2: Torque and Speed Curves for an Induction Motor
Figure 2 shows the ideal torque speed characteristics of an Induction motor. The X axis shows speed slip while the Y axis shows torque current. When the motor is started it draws a very large current to the tune of seven times the rated current which is a result of the stator and rotor flux. Also the starting torque is around 1.54 times the rated value for the motor. Increase of speed reduces current slightly and then drops significantly when the speed reaches close to 80% of the rated speed. At the base speed the rated current flows in the motor and rated torque is delivered. At the base speed if the load is increased beyond the value for the torque rated the speed drops and the slip increases. Thereby increase in load further causes the torque to fall down rapidly and the motor stalls.


Figure 3: Torque Speed characteristics of a 3 phaseIM with variable rotor resistance

Figure 4: torque speed characteristics with variable stator voltage
By varying the supply frequency synchronous speed can be controlled. Voltage induced in stator windings is E1 which is directly proportional to air gap flux and frequency supply. By neglecting the stator voltage drop we can obtain terminal voltage V1 which also directly proportional to flux and frequency therefore reducing frequency without changing voltage supply leads to increase in air gap flux which is not a desirable condition. Whenever hence frequency is varied in order to control the speed, there is also variation in the terminal voltage as to maintain V/f ratio constant.

So by maintaining ratio of constant v/f the torque maximum of the motor becomes constant for change in speed. The torque developed by the motor is directly proportional to magnetic field which is produced by the stator and flux produced is proportional to the ratio of voltage applied and supply frequency. So by the variation of voltage and frequency by a same ratio, flux and torque can be kept as a constant throughout the range of speed. This function makes the V/f method of control a most common one among others method of control.

In the figure below of closed loop of V/f method of control the rotor speed is measured by using a sensor which is compared to the reference speed. Difference between the speed is taken as error and this error is fed to PI controller which is known as Proportional Integral controller. This proportional Integral controller set the inverter frequency which is taken as a input for the VSI (voltage source Inverter) that does the modification in the terminal voltage accordingly as to keep the constant V/f ratio.

Synchronous speed obtained by the addition of actual speed wf and the slip speed wsldetermines the frequency of inverter and this frequency is responsible for the generation of reference signal for the closed loop control. Voltage is also varied along with frequency to make constant voltage frequency ratio so that the maximum torque and airgap flux remains constant.

Fig 5 Block Diagram of closed loop V/f method control
This method of control is one of the most common method of speed control. These types of motor are widely used in industry because of its simplicity. Some of the advantages of this types of motor are:
Low costs, simplicity in operation and immunity to error of feedback signal. Most probably induction motor with 50 Hz power supply has been used with open loop control for constant speed of applications. Frequency control is natural for adjustable speed drive applications but voltage needs to be proportional to frequency so that stator flux remains constant. However, voltage is required to be proportional to frequency so that the stator flux remains constant.

Fig 6 Block diagram of open loop control
Problems in this operation are
Motor speed cannot be controlled as rotor speed will be slightly less than the synchronous speed and in this the stator frequency and synchronous speed is the only controlled variable.

Therefore this makes the stator current to exceed the rated current by a large amount. Hence the speed of slip cannot be maintained due to the differences between rotor speed and Ns the synchronous speed.

Input data 🙁 machine details)
a) Vratedph=240V
b) P=4
c) Rs= 0.075ohm
d) Rr=0.1ohm
e) Xs=0.45mH
f) Xr=0.45mH
Figure 7 Torque-Speed Characteristics with Starting Load Torque 1.5 Nm and Reference Speed 500 rpm

Figure 8 torque speed characteristic with starting load 11Nm and ref sped 1200rpm
Input machine details
RMS Value of line-to-line supply voltage= 415 V
No. of poles= 4
Stator Resistance= 0.075?
Rotor Resistance= 0.1?
Frequency= 50 Hz
Stator Reactance = 0.45?
Rotor Reactance = 0.45?

Figure 9 Torque vs Speed Curves for various frequencies
For analyzing vector control, development of a dynamic model of Induction motor is needed and that can be done by the conversation of 3phase quantities into 2 axis system which is known as d axis and q axis and this type of conversation is known as axes transformation.

One of the major disadvantages of per phase equivalent circuit analysis is that it is valid if the 3 phase system is balanced only. Therefore any imbalance in the system made the analysis erroneous and even this problem is eradicated if d- q model is used.

1. d-q equivalent circuit
In most of the cases induction motors analysis with space vector model is very much complicated because in this we have to deal with variables of complex of space vector model. Let for any space vector Y let define two real quantities ie Sq and Sd as:
S=Sq-jSdIn other words Sq=Re(S)
and Sd = -Im(S).

which shows the relationship between d-q axis and stationary frame a-b-c.There is a point to note that d axis and q axis which is defined on rotating reference frame at the speed of wa w.r.t fixed frame a-b-c
.2. Axis transformation

Substituting wa=0
Above equation can be written as below

When the calculation is made in rotor reference frame one of the frame is attached to the rotor windings at wo.

In that case wa=wo and hence the matrix equation is changed as

Also we have
Vqs = Rs Iqs + pqs +s ds………………………………………………………..5
Vds = Rs Ids + p ds – s qs ……………………………………………………….6
0 = Rr Iqr + pqr + r dr …………………………………………………………7
0 = Rr Idr + p dr – r qr …………………………………………………………8
where flux linkage variables are defined by
?qs = Ls Iqs + Lm Iqr…………………………………………………………..……9
?ds = Ls Ids + Lm Idr……………………………………………………………….10
?qr = Lm Iqs + Lr Iqr……………………………………………………………….11
?dr = Lm Ids + Lr Idr……………………………………………………………….12
3- quantities converted into d-q quantities can be expressed as:
Sqs = (2/3) Re{exp(-ja) (Sa + Sb + ^2 Sc)}…………….13
Sds = – (2/3) Im{exp(-ja) (Sa +Sb + ^2Sc)}……………14

its inverse transformation gives equation as

In terms of space vector instantaneous for any frame of referce input power can be written as
Pi = (3/2) Re(Vs Is’ )
Pi = (3/2) Vds Ids + Vqs Iqs ………………………………………………………15
The reactive power Qi can also be defined as
Qi = (3/2) Im(Vs Is’ )
Qi = (3/2) Vqs Ids – Vds Iqs ………………………………………………………16

Figure 10 variation of d axis stator current with change in stator voltage

Fig 11 variation of q axis stator current with change in stator voltage
Parameter of machine details is below:
Motor rating Stator resistance Stator inductance Rotor resistance Rotor inductance
400V,50Hz,1430rpm 1.405ohm 0.00583H 1.395ohm 0.00839H

Fig 12 Parameter of 3 phase machine details
3 phase Asynchronous machine model is below:

Fig 13 Simulink model of 3 phase asynchronous machine
Simulation result: Note- always consider x axis as time

Fig 14 Rotor speed vs Time graph for machine parameter

Fig 15 Torque vs Time graph for machine parameter

Fig 16 Rotor current vs Time graph
For Parameter of machine details2
Motor rating Stator resistance Stator inductance Rotor resistance Rotor inductance
215HP,400V,50Hz 0.01379ohm 0.000152H 0.0077281ohm 0.000152H

Fig 17 Rotor speed vs Time graph for machine parameters2

Fig 18 Torque vs Time graph for machine parameters2

Fig 19 Rotor current vs Time graph for machine parameters2
On the basis of the above outcomes, the following observations were made:
The transient lasted for longer period on increasing rotor inductance and stator inductance as the machine takes longer time for achieving its steady state current speed and torque. Apart from this the start of the motor is bit jerky.

There was no any effect on the steady state time if the value of rotor resistance is increased but the machine starts with fewer jerks. In this the maximum torque occurred at lower speed, fluctuation during the transient period is reduced.

But if the value of stator resistance is increased the steady state time as well as the machine starts with more jerks therefore we must keep stator resistance as low as possible.

This model is created for analyzing closed loop V/f method control using PI controller and to plot a graph of stator current, electromagnetic torque and Rotor Speed against time.

Fig 20 Simulink model of 3 phase IM using PI controller
Simulation result

Fig 21 Rotor current vs Time response for machine details

Fig 22 Torque vs Time response for machine details
Fig 23 Variation of Rotor Speed vs. time response for machine details

Fig 24 Simulink model of a open loop V/f method control using PI
Simulation result
At rate load condition T=1Nm, time=0.5 sec, speed=1500rpm

Figure 25 Stator current vs Time response at rated load

Fig 26 Speed response vs Time graph at rated load

Fig 27 Torque response vs Time graph at rated load
At no load condition
2. Figures (29) and (30) show the speed and torque responses of IM when the speed is varied from 1000 to 1500 rpm at time .5sec
A-At No load Condition. In figure (30) shows that the starting torque is high reach to 2.5N.m less than case 1. when change the speed ,the response take more time to reach for reference speed and the torque also change due to speed change or change input voltage and after that back to zero and the current stays without change as shown in fig.(29)
Fig 28 Current response vs time graph at no load

Fig 29 Speed response vs Time graph at no load

Fig 30 Torque response vs Time graph at no load
B.At torque =1Nm from fig (32) it can be seen that the rotor speed cannot reach the required speed due to the load condition.fig (33) shows that torque has normally dynamic performance under these changes.

Fig 31 Rotor current response vs time graph at load

Fig 32 Speed response vs Time graph at load

Fig 33 Torque response vs Time graph at load
While developing Matlab simulink model analysis of torque speed characteristics for different speeds control methods were done and I concluded from the following that:
1. In the case of rotor resistance controlling methods starting torque can be varied by varying rotor resistance, however the maximum torque remains unaffected i.e for the operation requiring for high starting torque, the resistance can be varied to obtain the maximum torque during starting but one may also note that increasing resistance increase the copper loss so this method cannot be used throughout the operation as this method is highly inefficient.

2. In the case of variable supply voltage controlling methods, with the decrease of supply voltage the maximum torque decreases therefore the motor is underutilized so even this method cannot be used for good performance.

3. In constant controlling methods we can vary the supply voltages as well as frequency by using PWM inverter and rectifier such that the ratio of V/f as well as flux remains constant. By this, different operating zone for various speed and torque can be obtained. Even though different synchronous speed with same maximum torque can also be obtained. Thus the motor is completely utilized in this case and good range of speed can be achieved.

4. From simulink model for the starting of an induction motor it was deduced that the transient lasted for longer period on increasing rotor inductance and stator inductance as the machine takes longer time for achieving its steady state current, speed and torque. Apart from this the start of the motor is bit jerky.

5. There was no any effect on the steady state time if the value of rotor resistance is increased but the machine starts with less jerks. In this the maximum torque occurred at lower speed, fluctuation during the transient period is reduced. But if the value of stator resistance is increased the steady state time as well as the machine starts with more jerks therefore we must keep stator resistance as low as possible. Any imbalance in the system leads to erroneous analysis and dynamic response of the motor cannot be obtained from per phase equivalent circuit.

In this thesis the work done could be further extended by the consideration of advanced machine tools, both in hardware as well as software. As research work has no end its keep going on according to the development of latest technology and inventions.
Future work can be done on some interfacing cards like TMSDSP, Dspace, NI cards technology for controlling of various machine parameter in combination with fuzzy logic technique. Use of genetic algorithm with fuzzy logic and neural network for speed control can be one of the important future scope in the field of research.

Apart from this some of the fast sampling feedback, periodic output feedback can also be a better option for controlling speed of induction motor. Along with hybrid controller, the control technique for robust free i.e. H(infinity) control scheme could be used for removing robustness issue in controlling speed of motor which could be one of the future options.


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