Speed Control of Induction Motor
using V/f Technique
(Phase I)
A thesis submitted in partial fulfillment of the requirements for the degree of
Bachelor of Technology
Submitted by
Jeetesh Kumar (08010815)
Kamakhya Prasad Basumatary (08010817)
Supervisor
Professor A. K. Gogoi
(Professor, Department of Electronics and Electrical Engineering, IIT Guwahati)
Certificate
This is to certify that the work contained in this thesis entitled “Speed Control of Induction Motor using
V/f technique”, is a bonafide work of Jeetesh Kumar (08010815) and Kamakhya Prasad Basumatary
(08010817) , carried out in the Department of Electronics and Electrical Engineering, IIT Guwahati under
my supervision and it has not been submitted elsewhere.
Date:
Place:
(Supervisor’s Signature)
A.K.Gogoi
Proffesor,
Department of Electronics and Electrical Engineering
IIT Guwahati
Contents:
1. Introduction ……………………………………………………………………………1
2. Operation of induction motors…………………………………………………………2
2.1 Equivalent circuit and control of speed of induction motor……………………….2
2.2 Pulse Width Modulated Inverter…………………………………………………..5
2.3 Three phase harmonic filter………………………………………………………..6
3. Basic features of the project……………………………………………………………7
3.1 Determining the parameters of induction motor…………………………………..7
3.2 Modeling of 3-phase voltage source inverter in MATLAB Simulink……………11
3.3 Harmonic Distortion in the motor………………………………………………...12
4. Potential Applications………………………………………………………………...13
5. Future work/ Plan for overall thesis…………………………………………………..14
1 Introduction:
It is very important to control the speed of induction motors in industrial and engineering
applications. Efficient control strategies are used for reducing operation cost too. Speed control
techniques of induction motors can be broadly classified into two types – scalar control and vector
control. Scalar control involves controlling the magnitude of voltage or frequency of the induction motor.
Figure1. Torque-Speed characteristic of induction Motor
Having known the Torque-speed characteristic of the motor, its speed can be controlled in three ways:
i)
ii)
iii)
Changing the number of poles
Varying the input voltage at fixed frequency
Varying both the input voltage and frequency accordingly
To maintain torque capability of the motor close to the rated torque at any frequency, the air gap flux, φag
is maintained constant. Any reduction in the supply frequency without changing the supple voltage will
increase the air gap flux and the motor may go to saturation. This will increase the magnetizing current,
distort the line current and voltage, increase the core loss and copper loss, and it makes the system noisy.
The air gap voltage is related to φag and the frequency f as,
Eag =k1 φag f
(1)
Input voltage, Vs≈k1 φag f
or, φag = constant ≈
where k1 is a constant.
1
Vs
f
(2)
(3)
We shall be concentrating on the third method throughout the project, beginning with analyzing the
parameters of the induction motor and the harmonic contents.
2 Operation of induction motors:
When a balanced set of three-phase sinusoidal voltages is applied to the stator of an induction
motor, a constant amplitude flux is produced in the air-gap which rotates with a constant speed called the
synchronous speed. For a p pole machine, the synchronous speed is given as
Ns =
120f
p
(revolutions per minute)
(5)
where, f is the frequency of the applied voltages and currents. Due to the rotating air-gap flux, a counteremf, called the air-gap voltage is induced in each of the stator phases at frequency f. The torque in an
induction motor is produced by the interaction of the air-gap flux and the rotor currents. If the rotor
rotates at synchronous speed, there is no relative motion between the air-gap flux and the rotor, and hence
there is no induced voltages, currents and torque in the rotor. At any other speed ωr of the rotor in the
same direction of the air-gap flux rotation the motor moves with respect to the air-gap flux at a relative
speed called the slip speed ωsl ,where
ωsl = ωs - ωr
(6)
The slip speed normalized by the synchronous speed gives the slip :
=
�
ℎ
�
�
=
ω s−ω r
ωs
(7)
2.1 The equivalent circuit and control of speed of induction motor:
To study the behavior of the induction motor at various operating conditions, it is convenient to
derive an equivalent circuit of the motor under sinusoidal steady state operating conditions. For a
balanced 3 phase system, equivalent circuit for any one phase will suffice.
Figure 2. Equivalent circuit of the induction motor
From the per-phase equivalent circuit of the induction motor, the current drawn by the circuit is,
2
Vs
R s+R r ′ +j(X ls+X lr ′ )
Is =
(8)
The air-gap power is given as,
Pag = 3 | Is |2
R r′
(9)
s
3V s2
=
R s+R r ′
2+j
X ls+X lr ′
2
.
R r′
s
(10)
Mechanical output power is given as,
Pm = (1-s)Pag
(11)
Hence, the mechanical torque is given as,
Pm
Te = ω
(12)
m
=
=
1−s P ag
(13)
(1−s)ωs
3 Is 2Rr '
3
sωs
=ω .
s
R r′
R s+
s
(14)
V 2s
2+
X ls+X lr ′
.
2
R r′
s
(15)
Plotting the torque against slip or speed gives us the torque-speed characteristic of the motor.
Figure 3. Torque-speed curve for normal operation
Figure 4. Torque-speed curve for variable voltage
3
For positive values of slip, the torque-speed curve has a peak. This is the maximum torque
produced by the motor and is called the breakdown torque or the stalling torque. Its value can be
calculated by differentiating the torque expression with respect to slip and then setting it to zero to get ŝ,
the slip at the maximum torque.
Slip at maximum torque,
Maximum torque,
Rr ′
ŝ=±
R r ′ 2+ X ls+X lr ′
1
3V s2
.
2ω s R s± R 2s+ X ls+X lr ′
Temax =
(16)
2
2
(17)
From equation (15) we observe that the torque is proportional to the square of applied voltage. Figure 4
shows the variation of torque-speed curves with changing applied voltage.
Figure 5. Torque-speed curves for constant Eag /f
Figure 6. Torque-speed curves for constant V/f
To avoid saturation in the motor, the air-gap flux must be kept constant. From equation (1), to
keep φag constant, we vary Eag proportionate to f. The developed torque is given as,
TE/f =
k 2f 2
R r′
s
2+
ωL lr ′
2
Rr ′
. sω
(18)
Slip at maximum torque,
�r′
ŝ = ± ��
4
lr
′
(19)
Maximum torque,
TE/f =
2
8� 2�lr ′
(20)
Equation (20) shows that the maximum torque is independent of frequency and hence remains the same
for each E/f and the maximum torque occurs at a speed lower than the synchronous speed for each
combination of E and f . However, we get a slightly different set of curves for constant V/f, so for fixed
V, E changes with operating slip and the maximum torque is reduced, as shown in figure 6.
2.2 Pulse-Width-Modulated inverter:
For obtaining variable speed/ voltage control of induction motors, various DC-AC
converters (inverters) are used to drive the motors. The function of the inverter is to change a DC
input voltage to a symmetric AC output of desired magnitude and frequency. A typical threephase inverter is shown in the figure below. A balanced set of sinusoidal voltages are fed as input
to the inverter to obtain a constant rectified DC voltage, which is again smoothed through the DC
link capacitor(s). The semiconductor switches are eventually driven by the smoothed DC
voltage.
The output voltage may be fixed or variable at a fixed or variable frequency. Variable
voltage can be obtained by varying the gain of the inverter, which is usually done by using Pulse
Width Modulation (PWM) control within the inverter.
Figure 7. A variable frequency 3-phase motor drive ( inverter)
In PWM inverters the gating signals for the 6 switches are generated by comparing a
sinusoidal reference signal with a triangular wave. The frequency of the reference signal
determines the inverter output frequency and its peak amplitude controls the modulation index,
which in turn controls the rms output voltage. Figure 8 shows the typical process of generating a
sinusoidal PWM signal. Vcontrol_A, Vcontrol_B, Vcontrol_C are the reference signals equally shifted
away from one another (120º) and these are compared with the instantaneous points of the carrier
5
signal Vtri . The gating pulses are hence obtained which drive the switches and we get the Pulse
Width Modulated signals as the output of the inverter.
Figure 8. Generation of PWM signals and inverter output signals.
Vtri = carrier signal; Vcontrol_A, Vcontrol_B, Vcontrol_C are the 3 phases of the balanced sinusoidal input
voltage; VA0,VB0,VC0 are the output phase voltages; VAB is the line-line output voltage.
2.3 Three Phase Harmonic Filter:
Three phase harmonic filters are used in power system to decrease voltage distortion and
for power factor correction. Non–linear elements like power electronic converters generate
harmonic currents and voltages. The resulting distorted currents flowing through the system
impedance produces harmonic voltage distortion. Harmonic filters reduce distortion by diverting
harmonic currents in low impedance paths. Harmonic filters are designed to be capacitive at
fundamental frequency, so that they also produce reactive power required by converters and for
power factor correction. Here, we use a double-tuned harmonic filter which consists of RLC
elements and it is essentially a bandpass filter. The filter basically filters the lowest order
harmonics( 5th, 7th, 11th, 13th).
Figure 9. Double tuned harmonic filter (MATLAB Simulink)
6
3 Basic features of the project:
We start off with finding the parameter variations of the induction motor during its operation,
particularly the variations in rotor resistance and reactance due to the variations in frequency of the motor.
We also look into the harmonic contents of the electrical quantities (voltages and currents) at different
stages of the drive set-up and make proper adjustments to minimize the effects of harmonics to get a
better control of the motor.
3.1 Determining the parameters of the induction motor:
The most widely used tests for determining the motor parameters are:
i)
ii)
iii)
DC test: To find the stator resistance.
No-Load test: To find the magnetizing branch inductance and core loss resistance.
Locked- rotor test: To find the rotor resistance and reactance.
DC test:
A DC voltage is applied to the stator. In this case the equivalent circuit will consist only of the
stator resistance. For motors with star connected stator terminals (as used in the simulations) the circuit
for DC test is given as:
Figure 10. Equivalent circuit for DC test.
The stator voltage can be found out as,
Rs =
V dc
2I dc
No-Load test:
Figure 10.is the equivalent circuit for the No-Load test.
7
(21)
Figure 11. Equivalent circuit for No-Load test
Figure 12. Equivalent circuit for locked-rotor test
Here the rotor circuit is kept open and the slip is zero. The magnetizing branch impedance is large
compared to the stator impedance. Hence the voltage drop across the stator impedance is neglected and
the total power drawn is assumed to be entirely consumed as core loss.
The no-load power factor is given by
P1
s I0
where, P1 is the input power per phase.
cos φ0 = V
(22)
Im = I0 sin φ0
(23)
Ic = I0 cos φ0
(24)
Magnetizing current is calculated as,
and the core-loss current is given by,
The magnetizing inductance is found as,
Vs
Lm = 2π f
s Im
(25)
The core-loss resistance is given by,
Rc =
Vs
Ic
(26)
Locked-Rotor test:
The rotor is blocked and kept at standstill. For this test the slip is unity and the equivalent
circuit looks like a secondary-shorted transformer. The magnetizing branch impedance is higher
compared to the rotor impedance and so the magnetizing branch is neglected in the equivalent
circuit.
8
The short-circuit power factor obtained from the equivalent circuit is given by,
Psc
cos φsc= V
(27)
sc Isc
where , Vsc snd Isc are the short-circuit voltage and current respectively.
The short-circuit impedance is given by,
Zsc =
V sc
(28)
I sc
The rotor resistance is given as,
Rr = Zsc cos φsc – Rs
(29)
The total leakage reactance is given as,
Xeq = Zsc sin φsc
(30)
Xeq is the sum of the stator and referred-rotor leakage reactance
Xeq = Xls+ Xlr
(31)
Usually the value of stator reactance is taken same as that of the referred rotor leakage reactance. For
accurate results, the following pattern can be followed for various motors:
Motor
Stator inductance (% of Xeq) Rotor inductance (% of Xeq)
Squirrel Cage Class A
50
50
Squirrel Cage Class B
40
60
Squirrel Cage Class C
30
70
Squirrel Cage Class D
50
50
Wound Rotor
50
50
Table 1. Standard stator and rotor inductances for induction motors
For the simulations we have used a squirrel-cage induction motor with the following parameters:
Nominal Power= 5 hp ; Nominal Line-line Voltage = 460 V ; Frequency= 60 Hz
We run the simulation for different values of input frequency and observe the induction motor
parameters:
Frequency(Hz)
60
50
40
30
20
Lm
Rc
Rr
Xeq
0.208
582.692
1.017
4.45
0.207
728.86
1.018
3.726
0.209
906.4
1.020
2.982
0.211
898.73
1.018
2.257
0.210
549.48
0.411
2.132
Table 2. Motor parameters at different frequencies.
Rs
1.115
1.115
1.115
1.115
1.115
The variation of parameters with frequency is due to the skin effect and other non-linear imperfections
such as heating and main flux path saturation. This analysis of parameters is important for vector control
9
schemes. The changes in the magnetizing parameters are critical for obtaining self-excitation in selfexcited induction machines. Measuring data at zero and synchronous speed is very difficult. At zero speed
the machine is switched on with full voltage, due to which a transient current is produced , the peak value
of which may be substantially higher than the steady-state current. This problem can be solved by rotating
the motor in reverse direction, reversing the phase sequence and start sampling as soon as the speed
reaches zero. At synchronous speed, the induction motor will not normally run at synchronous speed.
This can be solved by coupling the induction motor with a synchronous motor with the same number of
poles, such that the measured data is taken at exact synchronous speed[14].
The control scheme used in the project is an open loop control (manual control) in which
controlling parameters are fixed or set by a user and the system finds its own equilibrium state. In the case
of a motor the desired operating equilibrium may be the motor speed or its angular position. The
controlling parameters such as the supply voltage or the load on the motor may or may not be under the
control of the user. If any of the parameters such as the load or the supply voltage are changed then the
motor will find a new equilibrium state, in this case it will settle at a different speed. The actual
equilibrium state can be changed by forcing a change in the parameters over which the user has control.
Frequency(Hz)
20
25
30
35
40
45
50
55
60
Speed(rpm)
594
731
871
1045
1165
1298
1443
1578
1708
Torque(Nm)
21.06
20.87
18.04
25.86
20.42
20.36
21.34
20.16
21.8
Table3. Motor speed and torque at different frequencies, at load 19.78 pu [speed up test]
The double tuned harmonic filter used to filter harmonic distortion ( Figure 9) consists of a series
LC circuit and a parallel RLC circuit. If f1 and f2 are the tuning frequencies, the filter is tuned
approximately the geometric mean frequency fm=√f1f2.
Tuned harmonic order,
n=
fm
f1
XC
XL
=
(32)
The quality factor of the double tuned filter is defined as the quality factor of the parallel L, R elements at
the mean frequency fm, and is given by,
R
Q = L×2πf
10
(33)
m
3.2 Modeling a 3-Phase voltage source inverter in MATLAB Simulink:
A 3-phase voltage source inverter is designed in Simulink using MOSFETs as switching
devices.
Figure 13. 3-phase sinusoidal PWM inverter
Figure 14a. Line current without filter at no-load; THD= .7366
Figure 14b. Line current without filter at load 19.78 pu; THD= 0.4009
Figure 14c. Line current with filter at no-load; THD= 0.2612
11
Figure 14d. Line current with filter at load 19.78 pu; THD= 0.0818
From the simulation results (Figures 14a – 15d, 15, 16) we observe,
i)
ii)
iii)
iv)
THD of line current in the system with filter is lower than the system without
filter.
THD of line current in the system is lower if system is loaded than the system
without load.
Similar results are obtained in case of line voltages, rotor and stator currents, and
the fluxes.
The steady state fluctuation in torque and speed is also reduced after application
of filter and mechanical load.
3.3 Harmonic distortion in the induction motor:
The induction motor has been assumed to be driven by ideal 3 phase, balanced, and sinusoidal set
of voltages. But practically the supply phases are not perfectly sinusoidal and these contain higher
frequency components that are harmonics of the fundamental frequency [3]. Harmonics also appear due
to the non-linear load connected to the supply in the form of inverters and motors. Generally the
harmonics generated by 3-phase PWM 6-pulse inverters, like the one used here, are the odd harmonics
excluding the multiples of 3rd harmonic ( 5,7,11, 13, etc.) [3]. The most prominent among these
harmonics are the 5th, 7th, 11th and 13th . As the order of harmonic gets higher, their magnitude becomes
negligible and these are easier to eliminate using filters.
The harmonic distortion present in any signal is measured by the Total Harmonic Distortion
(THD) and is given by,
THD =
∞
An 2
=2 A 1
(34)
where, An are the rms values of the non-fundamental harmonic components and A1 is the rms value of the
fundamental component.
The drive model is first simulated without using any filter and we get the following responses
from the motor:
12
Figure 15. Simulation graphs of motor parameters without harmonic filter
The drive model is simulated again, for the same time period and with the same specifications,
with a 3-phase harmonic filter at the inverter output. Following are the results:
Figure 16. Simulation graphs of motor parameters with harmonic filter
13
Figure 17a. FFT of Vab without filter
Figure 17b. FFT of Vab with filter
The effect of filtering can be clearly seen from the FFT analysis of the line voltage Vab
as shown in Figure 17a and 17b. The lower order harmonics, mainly 5th and 7th harmonics are
eliminated.
4 Potential Applications:
Voltage-source induction motor drives find their uses in applications like fans, pumps,
packaging, conveyors, hand tools, and appliances. The motors driven by the control loop used here is
capable of producing torque even at zero speed. Such feature is useful in applications where a starting
torque needs to be produced, like robotics.
5 Future work / Plan for overall thesis:
The open loop control scheme followed in this phase of our project is not responsive to
subsequent changes or disturbances in the system operating environment such as temperature and
pressure, or to varying demands on the system such as power delivery or load conditions. For
continual monitoring and control over the operating state of a system without operator
intervention, for more precision or faster response, automatic control systems are needed. In the
next phase of the project, we shall work on vector control method which is a closed loop
scheme. We shall also try to implement this closed loop scheme on hardware.
14
References:
[1] Muhammad H. Rashid, “Power Electronics- Circuits , Devices and Applications”, Third Edition,
Pearson 2004
[2] Bimal K. Bose, “Modern Power Electronics and AC Drives”, Pearson 2002
[3] Ned Mohan, Tore M. Undeland, and William P. Robbins, “Power Electronics- Converters,
Applications and Design”, Wiley India Edition 2010
[4] R. Krishnan, “ Electric Motor Drives, Modeling, Analysis, and Control”, Pearson 2001
[5] Thida Win, Nang Sabai, and Hnin Nandar Maung , “Analysis of Variable Frequency Three Phase
Induction Motor Drive”, World Academy of science, Engineering and Technology 42 (2008) pp. 647651.
[6] Mehmet Akbaba, “Motor Input Voltage and Rectifier Firing Angle Variation With Load Torque in
Constant Current Operated Induction Motors”, Mathematical and Computational Applications, Vol. 14,
no.1, pp. 73-84, 2009.
[7]
[8] K. L. Shi, T. F. Chan, Y. K. Wong, and S. L. Ho, “Modelling and Simulation of the Three Phase
Induction Motor Using Simulink”, International Journal of Electrical Engineering Education, Vol. 36, pp.
163-172, Manchester U.P., 1999.
[9] A. A. Ansari and D. M. Deshpande, “Mathematical Model of Asynchronous Machine in Matlab
Simulink”, International Journal of Engineering Science and Technology, Vol.2(5), pp. 1260-1267, 2010.
[10] P. Pillay and V. Levin, “ Mathematical Models for Induction Machines”, pp. 606-616, IEEE, 1995.
[11] “Technical Guide- Induction Motors fed by PWM frequency inverters”, http://www.weg.net
[12] M.A.A. Younis, N.A. Rahim and S. Mekhilef, “Harmonic Reduction in Three- Phase Parallel
Connected Inverter”, World, Academy of Science, Engineering and Technology, 50, pp. 944-949 (2009).
[13] C. Grantham and D.McKinnon, “Rapid parameter Determination of Induction Motor analysis and
Control”,
[14] D.J. McKinnon,D. Seyoum, and C. Grantham, “INVESTIGATION OF PARAMETER
CHARACTERISTICS FOR INDUCTION MACHINE ANALYSIS AND CONTROL”, The Institution
of Electrical Engineers, IEE, Michael Faraday House, Six Hills Way, Stevenage, SG1 2AY, pp. 320-325,
2004
15