CHAPTER 1
INTRODUCTION
1.1 Introduction
In earlier days, the squirrel cage induction motor (SCIM) was used for
essentially constant speed drive, and the wound rotor induction motor (WRIM) was
used for variable-speed drive systems. The wound rotor induction motor (WRIM)
offers a lot of flexibility for wide range of speed control compared to squirrel cage
motor. Although the WRIM is more expensive and less rugged than the SCIM, it has
been used favored for use in high power applications in which a large amount of slip
power could be recovered. Classically, speed of WRIM was changed by mechanically
varying external rotor circuit resistance. The Simplest speed control scheme for
wound-rotor induction motors is achieved by changing the rotor resistance. It has
been established that this rotor resistance control method can provide high starting
torque and low starting current and variation of speed over a wide range below the
synchronous speed of the motor.
Speed-torque curves for rotor resistance control are shown in figure 1.1. While
maximum torque is independent of rotor resistance, speed at which the maximum
torque is produced changes with rotor resistance. For the same torque, speed falls with
an increase in rotor resistance. Advantage of rotor resistance control is that motor
torque capability remains unaltered even at low speeds. Only other method which has
this advantages variable frequency control. However, cost of rotor resistance control
is very low compared to variable frequency control. Because of low cost and high
1
Figure.1.1 Speed-torque curves for rotor resistance control
Slip Speed (rad per sec)
Torque (N-m)
10
Tm
ax R’
,
R1’
R2’ R’ < R1
’
< R2’
torque capability at low speeds, rotor resistance control is employed in cranes, Ward
Leonard Ilgener drives, and other intermittent load applications . Major disadvantage
is low efficiency due to additional loses in resistor connected in the rotor circuit. As
the losses mainly take place in the external resistor they do not-heat the motor.
However, there are certain applications that require enormous variation of the motor
speed . with the increase in availability of high current power electronic devices,
smooth and quick variation of external resistance introduce in the rotor circuit of
wound rotor induction motor to control speed can be accomplished electronically.
Such schemes employing chopper control can be used to obtain a constant speed.
Such circuit are widely used in industrial application where the drive operation is
intermittent such as hoists ,cranes ,conveyers, lifts and high starting torque are more
important with low starting current to avoid voltage dip. The rotor chopper controlled
contains the three phase uncontrolled bridge rectifier and a chopper controlled
external resistance . The rectifier bridge acts as an electronic frequency changer
(EFC), so that the machine will chiefly see the effect of EFC switching at rotor
frequency. This system consequently loses the capacity to control rotor current
waveform by pulse width modulation of electronic switch (ES). The high chopper
frequency tend to improvement the performance of wound rotor induction motor drive
system as, rotor rectified current, rotor phase current, speed smoothing with torque
pulsation and ripple of rotor rectified current.
The principle operation of high chopper frequency drive for wound rotor
induction motor with a resistively loaded rotor chopper is detailed in the consequent
chapters.
1.2 Objectives of the work
The main objectives of this work are as give below,
To develop the dynamic modeling of wound rotor induction motor using
MATLAB/SIMULINK toolbox.
To design and develop the variable speed drive using wound rotor induction
motor controlled by variation of an external rotor resistance by parallel
electronic chopper.
To study the analysis of high chopper frequency, duty cycle on the rotor
current, rotor rectifier current, ripple in rotor rectified current, speed and
torque pulsation for wound rotor induction motor drive with the low value of
filter in rotor side.
2
CHAPTER 2
DYNAMIC MODELING AND SIMULATION OF WOUND
ROTOR INDUCTION MACHINE
2.1 Introduction
In an adjustable speed drive, the machine normally constitutes an element
within a feedback loop, and therefore its transient behavior has to been taken in to
consideration. The dynamic performance of an AC machine is somewhat complex
because the rotor three-phase windings move with respect to the three phase stator
windings. The dynamic model considers the instantaneous effects of varying
voltages/currents, stator frequency, and torque disturbance. The dynamic model of the
induction machine is derived by using a two phase motor in direct and quadrature
axes. This approach is desirable because of the conceptual simplicity obtained with
two sets of windings, one on the stator and the other on the rotor. The concept of
power invariance is introduced: the power must be equal in three phase machine and
its equivalent two phase model. The reference frames are chosen to be arbitrary. The
different possible reference frames are as given below
Stationary reference frame(Stator)
Rotor reference frame
Synchronously rotating reference frame
The differential equations describing the induction motor are non linear. For
stability and controller design studies, it is important to linearize the machine
equations around a steady state operating point.
This chapter contains detailed description to modeling of wound rotor
induction machine (T-Model).
2.2 Real Time Model of a Two Phase Induction Machine
The following assumptions are made to derive the dynamic model:
1) Uniform air gap
2) Balanced rotor and stator windings, with sinusoidally distributed mmf
3) Inductance Vs rotor position is sinusoidal and
4) Saturation and parameter changes are neglected
A two phase machine with stator and rotor windings is shown in figure 2.1. The
windings are placed 90 degrees electrical, and the rotor windings α, is at an angle Ө r
from the stator d axis winding. It is assumed that d axis is leading q axis for clockwise
direction of rotation of the rotor. If the clockwise sequence is dq, the rotating
3
magnetic field will be revolving at the angular speed of the supply frequency but
counter to the phase sequence of the stator supply.
Figure 2.1 Stator and rotor windings of a two phase induction machine
Therefore, the rotor is pulled in the direction of the rotating magnetic field. The
terminal voltages of the stator and rotor windings can be expressed as the sum of
voltage drops in resistance and the rate of change of flux linkages, which is the
product of currents and inductances.
2.3 Axes Transformation
Consider a symmetrical three-phase induction machine with stationary as-bs-cs axes
at 2π/3-angle apart as shown in figure 2.2. our goal is to transform the three-phase
stationary reference frame (as-bs-cs) variables into two-phase stationary reference
frame (ds-qs ) variables and then transform these to synchronously rotating reference
frame( de-qe), and vice versa.
4
Stator
Rotor
Vqs
+
_
d-axis
q-axis
β-axis
iqs
Vα
+_
ids
Vds
Vβ
+
_
_
θr
α-axis
Stator
Rotor
Vqs
+
_
d-axis
q-axis
β-axis
iqs
Vα
+_
ids
Vds
Vβ
+
_
_
θr
Stator
Rotor
Vqs
+
_
d-axis
q-axis
β-axis
iqs
Vα
+_
ids
Vds
Vβ
+
_
_
θr
α-axis
2.3.1 Three -Phase Stationary Reference Frame (as-bs-cs) Variables into Two-
Phase Stationary Reference Frame (ds- qs)
Assume that the ds-qs axes are oriented at θ angle, as shown in figure 2.2. The
voltages and can be resolved into as-bs-cs components and can be represented
in the matrix form as
2.3.2 Two-Phase Stationary Reference Frame Variables (ds- qs) into Three -Phase
Stationary Reference Frame (as-bs-cs)
The corresponding two-phase stationary reference frame variables (ds- qs) in to Three
-Phase Stationary Reference Frame (as-bs-cs) can be written as
Where is added as the zero sequence component, which may or may not be
present. We have considered voltage as the variable.
5
Vas
Vbs
Vcs
Vqss
Vdss
𝜃 qs-axis
ds-axis
as
bs
cs
Figure 2.2 Stationary frame a-b-c to ds-qs axes transformation
It is convenient to set θ = 0, so that the qs-axis is aligned with the as-axis. Ignoring the
zero sequence components, the transformation relations can be simplified as
(2.3)
And inversely
Figure 2.3 shows the synchronously rotating de-qe axes, which rotate at
synchronous speed ωe with respect to the ds-qs axes and angle . The two-
phase ds-qs axes windings are transformed in to the hypothetical windings mounted on
the de-qe axes.
The voltages on the ds-qs axes can be converted in to the de-qe frame as follows:
6
qs
ds
𝜃e
qe
de
𝜃e = ωet
Figure 2.3 Stationary frame ds-qs to synchronously rotating frame axes de-qe transformation
transformation
For convenience, the superscript e has been dropped from now on the synchronously
rotating frame parameters. Again, resolving the rotating frame parameters in to
stationary frame, the relations are
2.4 Equivalent Circuit of T-Model
The equivalent circuit of two phase induction machine (T-Form) for q (quadrature
axis) and d (direct) axis is as shown in the fig 2.4(a) and (b).
iqs iqr
Rs Rr
RsRr
idrids
ωeψds
ωeψqs Llr=Lr-Lm
Lls=Ls-Lm
Lls=Ls-Lm
Llr=Lr-Lm
(ωe – ωr)ψqr
(ωe – ωr)ψdr
Lm
Lm
+
+
+
+
-
-
--
Vqs Vqr
Vds Vdrdsd
dt
drd
dt
qrd
dt
qsd
dt
(b)
(a)
iqs iqr
Rs Rr
RsRr
idrids
ωeψds
ωeψqs Llr=Lr-Lm
Lls=Ls-Lm
Lls=Ls-Lm
Llr=Lr-Lm
(ωe – ωr)ψqr
(ωe – ωr)ψdr
Lm
Lm
+
+
+
+
-
-
--
Vqs Vqr
Vds Vdrdsd
dt
drd
dt
qrd
dt
qsd
dt
iqs iqr
Rs Rr
RsRr
idrids
ωeψds
ωeψqs Llr=Lr-Lm
Lls=Ls-Lm
Lls=Ls-Lm
Llr=Lr-Lm
(ωe – ωr)ψqr
(ωe – ωr)ψdr
Lm
Lm
+
+
+
+
-
-
--
Vqs Vqr
Vds Vdr
iqs iqr
Rs Rr
RsRr
idrids
ωeψds
ωeψqs Llr=Lr-Lm
Lls=Ls-Lm
Lls=Ls-Lm
Llr=Lr-Lm
(ωe – ωr)ψqr
(ωe – ωr)ψdr
Lm
Lm
+
+
+
+
-
-
--
Vqs Vqr
Vds Vdr
iqs iqr
Rs Rr
RsRr
idrids
ωeψds
ωeψqs Llr=Lr-Lm
Lls=Ls-Lm
Lls=Ls-Lm
Llr=Lr-Lm
(ωe – ωr)ψqr
(ωe – ωr)ψdr
Lm
Lm
+
+
+
+
-
-
--
Vqs Vqr
Vds Vdr
iqs iqr
Rs Rr
RsRr
idrids
ωeψds
ωeψqs Llr=Lr-Lm
Lls=Ls-Lm
Lls=Ls-Lm
Llr=Lr-Lm
(ωe – ωr)ψqr
(ωe – ωr)ψdr
Lm
Lm
+
+
+
+
-
-
--
Vqs Vqr
Vds Vdr
Rs RrRs Rr
RsRr
idrids
RsRrRsRr
idrids
ωeψds
ωeψqs Llr=Lr-Lm
Lls=Ls-Lm
Lls=Ls-Lm
Llr=Lr-Lm
(ωe – ωr)ψqr
(ωe – ωr)ψdr
Lm
Lm
+
+
+
+
-
-
--
Vqs Vqr
Vds Vdrdsd
dt
drd
dt
qrd
dt
qsd
dt
(b)
(a)
2.4.1 Stator equations
We can write the following stator equations
Where and are q-axis and d-axis stator flux linkages respectively.
Converting to d e − qe frame
7
Figure 2.4 Dynamic Equivalent circuit (T-Model): (a) q-axis (b) d-axis
are the speed electromagnetic field due to rotation of the axis
2.4.2 Rotor equations
In a similar manner we can write the rotor equations
Case1: rotor not moving (ωr = 0)
Case 2: rotor actually moves at speed ωr
Equivalent circuits of the motor in the synchronously rotating reference frame are
indicated in Figs. 2.4(a) and 2.4(b).
The flux linkage expressions in terms of the currents can be written from Fig. 2.4 as
follows
8
Combining the above expressions with equations (2.12), (2.13), (2.16) and (2.17), the
electrical transient model in terms of voltages and currents can be given in matrix
form as
Where ωr, is the rated frequency in radian/s. and s is the Laplace operator.
The slip s is expressed as
The electromagnetic torque, positive for motor action, may be expressed in
The relation between torque and speed is expressed as
9
CHAPTER 3
CONTROL OF WOUND ROTOR INDUCTION MOTOR DRIVE
3.1 Introduction
The Simplest speed control scheme for wound-rotor induction motors is
achieved by changing the rotor resistance. It has been established that this rotor
resistance control method can provide high starting torque and low starting current
and variation of speed over a wide range below the synchronous speed of the motor.
The rotor resistance is altered manually and discreet steps this mechanical operation is
undesirable the response is slow and speed variation is not smooth. These undesirable
features of the resistance control can be eliminated by using a chopper controlled
external resistance. This chapter presents the complete analysis, design, and control of
wound rotor induction motor drive with a resistively loaded rotor chopper (RLC).
3.1.1 Block diagram for WRIM drive with RLC
10
Va
Vc
Vb
WRIM
Rotor
Stator
EFC
fch
f = 0
f = 0
fr
ES
Rex
Resistively loaded
Figure3.1 Fundamental structure of electronic rotor cascade consisting of WRIM, rotor rectifier and resistively loaded
loaded.
The block diagram of WRIM drive with resistively loaded chopper is shown in
figure 3.1. The wound rotor induction motor (WRIM) offers a lot of flexibility for
wide range of speed control compared to squirrel cage motor. The torque depends on
motor resistance. Therefore, increasing the rotor resistance will at a constant torque
causes a proportionate increase in the motor slip with a result decrease in rotor speed.
Thus, the speed for a given load torque may be varied by varying the rotor resistance.
The function of this resistance is to introduce voltage at rotor frequency, which
opposes the voltage induced in rotor winding.
The main demerit of this method of control is that energy is dissipated in rotor
circuit resistance, internal and external, and this energy is wasted in the form of heat.
Because of the waste-fullness of this method, it is used where speed change are
needed for short duration only. With the recent progress in power semiconductor
technology, these undesirable features of conventional rheostat control scheme can be
eliminated by using a three phase uncontrolled bridge rectifier and a chopper
controlled external resistance. The rectifier bridge acts as an electronic frequency
changer (EFC), so that the machine will chiefly see the effect of EFC switching at
rotor frequency. With the high frequency switching effects of the chopper, which is
power switch electronically monitored by a control module. This system consequently
loses the capacity to control rotor current waveform by pulse width modulation of
electronic switch (ES).
3.1.2 Basic Chopper Circuit
Conventionally, the rotor resistance is controlled manually and in discrete
steps. With the advent of power semiconductors, the conventional resistance control
scheme can be eliminated by using three phase rectifier bridge and chopper controlled
external resistance as shown in Figure 3.2. A chopper is a power switch electronically
monitored by a control circuit. When the chopper is in the "ON" mode all the time the
equivalent external resistance Req in the rotor circuit is Rf. When the chopper is in the
"OFF" mode all the time equivalent external resistance Req in the rotor circuit is (Rf +
Rex).
11
Va
Vc
Vb
WRIM
Rotor
Stator
Rectifier
Rf Lf
Rex
Ideal power switch
Idc
Figure 3.2 Basic chopper circuits with L-R
filter
If the chopper is periodically regulated so that, in each chopper period, it is "ON" for
some time but is "OFF" for the rest, it is possible to obtain variation of Req between Rf
and (Rf + Rex). Thus the chopper electronically alters the external resistance Rex in a
continuous and contactless manner. Effect of ripple in the bridge output on current
waveform is neglected. In this arrangement no external inductor is used. Only
inductance in the circuit is the rotor leakage reactance. This offers very small time
constants during ON and OFF periods. Due to this, current reaches to steady state
during ON and OFF periods. Rex should be chosen as large as possible to obtain lower
speeds. However, this will increase the voltage spike across the switch, which will
require a IGBT with excessively high voltage.
Using such a simple chopper circuit for controlling the average value of
resistance (rotor current) introduces the additional problems such as discontinuity in
the rotor winding currents, and voltage spikes across the chopper IGBT. Highly
distorted waveforms of currents within the rotor cause excessive heating of the
windings. This requires considerable derating of the motor capacity. To certain extent
this heating can be reduced if chopping frequency is much lower than the supply
frequency. However, chopping at such low frequency may cause fluctuations in the
motor speed for low inertia loads. Increasing the chopper frequency will certainly
give speed output without any fluctuations. But this will increase the amplitude of
current harmonics and hence, heating of the motor. This problem can be taken care of
12
Figure 3.3 Rectifier chopper current waveform
by introducing a filter in the rotor circuit as shown in Figures. 3.2. Figure 3.3 shows
the rectifier chopper current waveform. With a filter in the rotor circuit current
waveforms can be made continuous and ripple in DC current can be reduced to a very
small value by selecting the appropriate chopper frequency and corresponding
parameters of the filter circuit. This improvement permits application of motors with a
derating factor of almost 90%. In the next section it will be shown that to reduce the
ripple in the DC current it is necessary that
τoff ≈ τon and τon > T
τon = time constant during "ON" period
τoff = time constant during "OFF" period
and l/T is chopper frequency.
This restricts R 2 to a very small value resulting in not so wide variation in
the speed-torque characteristics. This problem is taken care of if we use 1 st order filter
as shown in Figure 3.2. This will give reduced ripple and also wider variation in the
speed torque characteristics.
3.1.3 Analysis of WRIM drive with RLC
Exact analysis is tedious, involving the phasor calculations for motor
fundamental and harmonic quantities and step-by-step analysis of nonlinearities in the
rectifier-chopper circuitry. However, it has been found possible to develop circuit
models from which a good prediction of the performance characteristics can be made.
Figure 3.4 shows the per-phase equivalent circuit of IM referred to the rotor side. The
DC model is derived for three phase system. If for the given chopping frequency filter
components are chosen such that ripple in the current Id is negligible then rotor
current is composed of alternating square pulse of 2π/3 duration. Rotor RMS current
I2 is given by
Where Id is the average value of the rectified rotor current and Ir is the rotor RMS
phases current. The power loss in the stator and rotor resistance for all three phases is
2Idc2(sR1 +R2) in the DC side. Because of leakage reactance in the motor windings
there is a voltage reduction of 3ω(LI + L2)/π from the terminal voltage of the rectifier
13
voltage. The system is represented by the DC equivalent circuit model as shown in
figure (4).
)
Where
E = Average value of rectified rotor voltage at stand still.
E2 = Rotor voltage per phase in RMS at stand still and the different parameters used in
the figure
L1 + L2 = Total leakage inductance per phase referred to rotor
R1 = Stator resistance/phase referred to rotor
R2 = Rotor resistance/phase
Rf, Rex = External resistances
Lf = External inductor
s = Motor slip
Let τon = ON-period, τoff = OFF period, neglecting the voltage drop due to the
commutation over lap of diode bridge, current during “ON” mode is given by
i1 = I1 + i01
And during “OFF” mode is given by i 2=I2
+i02 )
Where 14
2L1
sE
2L22R1 2R2 RfLf
Rex S
Figure 3.4 DC equivalent circuit model
The i01 and i02 are initial values of current for “ON” and “OFF” mode, respectively. If
the chopper frequency is very high with low value of smoothing inductor such that
It can be shown that
Therefore the equivalent resistance is given by
This equation shows that Req is proportional to the off period of the chopper circuit.
This is show the external resistance in the rotor circuit can be varied by controlling
the duty cycle (D) of the chopper period. If the duty cycle
Then the equation (10) may be written as
Req = Rex (1-D). (3.11)
The rotor copper losses is given by
Where pg is air gap power Irms is rms value of Idc. If the chopper frequency is high,
then Idc ≅ Irms
Therefore
Then the developed torque(T) in N.m
15
Neglecting the voltage drop across the stator resistance (R1), the eq. ) Used to
obtain torque for various slip for different on-off times.
Referring to figure 3.2, using the high switch power transistor such as SIT, IGBT and
power MOSFET for chopper switching permit a high chopper frequency, with
reducing of smoothing inductor
For low value of smoothing inductor the above equation is satisfied if (fch>>fr). Higher
the chopper frequency, lower the ripple in the rotor rectified current and consequently
the torque ripple. Also high values of fch are required to avoid any interaction between
the chopper frequency and the output frequency of rectifier for all slip values. The
smoothing inductor (1mH) is used, but with high chopper frequency to compensate
the minimal value of smoothing inductor. Eliminating or reducing the smoothing
inductor reduces the volume and then the cost of system drives. The minimum value
of external resistance Rex, 50Ω is used, which gives the required operation in the
speed torque characteristics to half of full load speed.
3.2 Open loop speed control of WRIM drive with RLC
16
Slip Speed (rad per sec)
Figure 3.5 Speed-torque characteristics of rotor resistance control
Torque (N.m)
10
Tmax
R1
R11
R21
R1< R11< R2
1
In a slip ring induction motor, a three phase variable resistor R21 can be
inserted in the rotor circuit. Conventionally, the rotor resistance is controlled
manually and in discrete steps. By varying the rotor circuit resistance R21 the motor
torque can be controlled as shown in figure 3.5. The starting torque and starting
current can also be varied by controlling the rotor circuit resistance. The
disadvantages of rotor resistance control method of speed control are: (1) reduced
efficiency at low speeds, (2) speed changes very widely with load variation. These
drawbacks can be eliminated by replacing the three phase resistor by a three phase
diode rectifier, chopper and one resistor as shown in figure 3.6.
17
Vo(desired)
Vo(actual)
Amplifier
+
-
Vcontrol
Comparator
Repetitive waveform
Switch control signal
(a)
Figure 3.7 Pulse-width modulator (a) block diagram (b) comparator signals
Vcontrol
(Amplified error)
(Switching frequency) fs = 1/T
Vcontrol < VstVcontrol > Vst
On
Off
Vst = Saw tooth voltage
Switch control signal
T
Ton Toff
t in secs0
(b)
Figure 3.6 Circuit diagram of the open loop speed control system.
Rf
Rex
Va
Vb
WRIM
Rotor
Stator
Diode Bridge Rectifier
Lf
Controller
Chopper
Vc
Idc
VdcVd
Figure 3.7 shows the block diagram of pulse width modulator for chopper circuit and
comparator signals. Pulse Width Modulation (PWM) is a method of transmitting
information on a series of pulses. The data that is being transmitted is encoded on the
width of these pulses to control the amount of power being sent to a load. In other
words, pulse width modulation is a modulation technique for generating variable
width pulses to represent the amplitude of an input DC. An oscillator is used to
generate a saw tooth waveform. A comparator compares the saw tooth voltage with
the reference voltage. When the saw tooth voltage rises above the reference voltage,
an IGBT is switched on. As it falls below the reference, it is switched off. This gives a
square wave output to the WRIM drive with a RLC. Pulse width modulation is used to
reduce the total power delivered to a load without resulting in loss, which normally
occurs when a power source is limited by a resistive element. The underlying
principle in the whole process is that the average power delivered is directly
proportional to the modulation duty cycle. High frequency pulse width modulation
power control systems can be realized using semiconductor switches. Here, the
discrete ON or OFF state of the modulation itself can be used to control the switches,
thereby controlling the voltage or current across the load. The major advantage with
these types of switches is that the voltage drop across it during conducting and non-
conducting states is ideally zero. Pulse width modulation is widely used in voltage
regulators. It works by switching the voltage to the load with the appropriate duty
cycle; the output will maintain a voltage at the desired level. At low frequencies the
motor speed tends to be jerky, at high frequencies the motor's inductance becomes
significant and power is lost. Frequencies of 30-200Hz are commonly used. The
function of inductor Lf is to smoothen the current Idc a chopper allows the effective
rotor circuit resistance to be varied for the speed control of WRIM drive with a RLC.
Diode bridge rectifier converts slip-frequency input power to DC at its output
18
terminals. When chopper is on, Vdc = Vd = 0 and resistance Rex gets short circuited.
When chopper is off, Vdc = Vd and resistance in the rotor circuit is Rex. The above
circuit topology is realized using Matlab/Simulink tool box. The simulation results are
observed, analyzed, and reported.
3.3 Closed Loop Speed Control of WRIM drive with RLC
The rotor resistance controlled slip ring IM has very poor speed regulation
with open loop control. In many industrial applications, very good speed regulation of
the drive is essential. In such cases it becomes necessary to go for closed loop speed
control. Precision closed loop regulators for conventional rotor resistance control are
impractical. However, with a IGBT chopper, a slip ring IM may now be applied in
closed loop drives, with a good degree of precision. Rotor current Ir and therefore, Id
has a constant value at the maximum torque point, both during motoring and
plugging. If the current limiter is made to saturate at this current, the drive will
accelerate and decelerate at the maximum torque, giving very fast transient response.
For plugging to occur, arrangement will have to be made for reversal of phase
sequence. Compared to conventional rotor resistance control, static rotor resistance
control has several advantages such as smooth and step less control, fast response,
less maintence, compact size, simple closed-loop control and rotor resistance remains
balanced between the three phases for all operating points.
3.3.1 System Description
19
Stator Idc
Figure 3.8 Block diagram of the closed loop speed control system.
Va
Vc
Vb
WRIM
Rotor
Diode Rectifier
Rf Lf
Rex
Power switch
Current controller
Speed sensor
Speed controller
Current limiter
Pulse generation circuitIdc
*
Idc
ωm
ωm*
+
+
Figure 3.8 gives a block diagram of the closed loop speed control system. A chopper
with first order filter is connected on the rotor side of three phase slip ring motor. A
Speed sensor is used to obtain speed feedback signal. The rotor current is sensed by
connecting a small resistance in the DC circuit. The duty cycle of the chopper circuit
(chopper frequency x on time) is controlled by varying the output of speed controller.
A simple arrangement of proportional speed control with current limit will also give
improved speed regulation with protection against excessive currents during starting
and under over load conditions.
However, the scheme shown in the block diagram uses a PI controller to get
almost zero steady state error. Care is taken to make controller response as fast as
possible. The speed controller output has adjustable saturation level. This sets the
reference for current control loop. The current control loop maintains constant current
against disturbances in supply voltage. Moreover, this provides fast response
compared to current limit arrangement. During starting and under overload condition,
output of speed controller limits the rotor current to a preset reference value. The
starting current and hence starting torque can be adjusted by adjusting the saturation
level of output of speed controller.
3.3.2 Speed Controller
A Speed sensor is used to obtain a speed feedback signal from the motor. This
feedback signal is compared with a reference signal and then error signal is generated.
The output of speed controller should be unidirectional and with well defined
saturation level. Besides this, to make current limit adjustable it is desirable to make
this saturation level rather than the feedback factor adjustable. A PI controller was
used to obtain zero steady state error in the speed. Design-procedure is more or less
same as current controller. In ideal case PI controller is supposed to give zero steady
state error. Moreover, it is very difficult to obtain stable DC level as reference source.
Here the reference source is a train of pulses with constant frequency. The scheme of
comparing reference frequency with feedback frequency and giving the DC level
proportional to phase difference as output works as an integrator in the forward path.
This will give absolutely "'zero" steady state error. A comparator compares the saw
tooth voltage with the reference voltage. When the saw tooth voltage rises above the
20
reference voltage, a IGBT is switched on. As it falls below the reference, it is
switched off. This gives a square wave output to the WRIM drive with a RLC. The
closed loop control WRIM drive with a RLC is realized using Matlab/Simulink tool
box. The simulation results are observed, analyzed, and reported.
3.4 Conclusion
The wound rotor induction motor offers a lot of flexibility for wide range of
speed control compared to the squirrel cage motor. Problems associated with simple
chopper circuit such as reduced ripple in rotor rectified current and discontinuity in
the rotor current are eliminated by introducing a filter in the rotor circuit. With high
switching frequency of power electronic devices, the effect of chopper frequency at
different duty cycle of motor performance is studied. The analysis of high chopper
frequency, duty cycle on the rotor current, rotor rectified current, speed and torque
pulsation for wound rotor induction motor drive with resistively loaded chopper is
studied.
CHAPTER 4
SIMULATION RESULTS AND COMPARISON
4.1 Introduction
The Simplest speed control scheme for wound-rotor induction motors is
achieved by changing the rotor resistance. It has been established that this rotor
resistance control method can provide high starting torque and low starting current
and variation of speed over a wide range below the synchronous speed of the motor.
The rotor resistance is altered manually and discreet steps this mechanical operation is
undesirable the response is slow and speed variation is not smooth. These undesirable
features of the resistance control can be eliminated by using a chopper controlled
external resistance. This chapter presents the complete analysis and performance of
different characteristics such as electromagnetic torque, rotor speed, rotor rectified
current and ripple in rotor rectified current, of wound rotor induction motor drive with
a resistively loaded rotor chopper is discussed. The open loop and closed loop control
of WRIM drive with a RLC are discussed.
21
Figure (4.1) Torque -Speed characteristics for different frequencies at D=0.9.
Figure (4.2) Torque -Speed characteristics for different frequencies at D = 0.5.
The computed torque speed curve for different frequencies with the duty cycle fixed
at 0.9 and 0.5 are shown in figure (4.1 and 4.2) respectively. At high chopper
frequency (fch >10 kHz) with 0.9 duty cycle, torque speed curve give essentially the
same results. But for 0.5 duty cycle give the approximately the same results at
chopper frequency greater than 1 kHz.
4.2 Open loop characteristics
4.2.1 Rotor rectified current - Speed characteristics for different frequencies at
D=0.9 and D=0.5.
The low value of smoothing inductor was used. Though, as in other similar
applications, the presence of inductance will have reduced the fluctuations in current.
22
Figure 4.3 (a) and 4.3 (b) show the rotor rectified current against speed for 0.9 and 0.5
duty cycle at different values of chopper frequency. The variation in rotor rectified
current from minimum to maximum current level is larger in 50Hz chopper
frequency.
Figure (4.3) Rotor rectified current -Speed characteristics for different frequencies at D=0.9
Figure (4.4) Rotor rectified current -Speed characteristics for different frequencies at D=0.5
23
4.3 Ripple in rotor rectified current - Speed characteristics for different
frequencies at D=0.9 and D=0.5.
Figure 4.5 Ripple in rotor rectified current -Speed characteristics for different frequencies at
D=0.9
Figure 4.6 Ripple in rotor rectified current -Speed characteristics for different frequencies at
D=0.5
The low value of smoothing inductor was used. Though, as in other similar
applications, the presence of inductance will have reduced the fluctuations in current.
Figure 4.5 (a) & 4.6 (b) show the rotor rectified current against speed for 0.9 and 0.5
duty cycle at different values of chopper frequency. The variation in rotor rectified
current from minimum to maximum current level is larger in 50Hz chopper
frequency. From these characteristics we observe that increasing the chopper
frequency, the ripple in rotor rectifier current decreases.
24
4.4 Closed loop characteristics
4.4.1 Torque response
Figure.4.7 (a) and 4.7(b) show the electromagnetic torque response for duty cycle 0.5
and 0.9 respectively.
Fig.4.7 (a) Fig.4.7 (b)
Figure 4.7 Electromagnetic torque at (a) D= 0.5, (b) D=0.9.
4.4.2 Speed response
The rotor speed of WRIM drive with a RLC is affected by a duty cycle and reference
speed. Increasing the reference speed, rotor speed will be increases due to decreases
in rotor resistance. The rotor resistance decreases due to increases in turn “ON” period
25
of chopper. Figure 4.8 (a) and 4.8 (b) show the steady state speed response for duty
cycle 0.9 and 0.5 respectively. For different duty cycles d =0.9 and d = 0.5 the rotor
speed 152(rad/sec) and 148(rad/sec) respectively.
Fig.4.8 (a) Fig.4.8 (b)
Figure 4.8 Rotor Speed response (ωm in rad /sec) at (a) D= 0.5, (b) D=0.9.
4.4.3 Rotor rectified current response
The low value of smoothing inductor was used. Though, as in other similar
applications, the presence of inductance will have reduced the fluctuations in current.
Figure.4.9 (a) and 4.9 (b) show the rotor rectified current for duty cycle 0.5 and 0.9
respectively. Increasing the duty cycle, the ripple in rotor rectified current decreases.
26
Fig.4.9 (a) Fig.4.9 (b)
Figure 4.9 Rotor rectified current response at (a) D= 0.5, (b) D=0.9.
4.4.4 Speed response in rpm
The rotor speed of WRIM drive with a RLC is affected by duty cycle and reference
speed. Increasing the reference speed, rotor speed will be increases due to decreases
in rotor resistance. The rotor resistance decreases due to increases in turn “ON” period
of chopper. Figure 4.9 (a) and 4.9 (b) show the steady state speed response for duty
cycle 0.9 and 0.5 respectively. For different duty cycles d =0.5 and d = 0.9 the rotor
speed 1410rpm and 1458rpm.
27
Fig.4.17 (a) Fig.4.10 (b)
Figure 4.10 Rotor Speed (N in rpm) response at (a) D= 0.5, N=1410 rpm
(b) D=0.9, N=1458 rpm.
4.4.5 Rotor phase current response
The rotor current is approximately composed of alternating square pulse of (2π/3)
duration. Due to the leakage reactance of rotor and stator windings, the commutation
of current between diodes in the rectifier bridge is no longer instantaneous. There is a
period of current overlap where by two phase carry current simultaneously. Figure
4.11 (a) and 4.11 (b) show the rotor phase current response at normal operation at 0.5
and 0.9 respectively.
28
Fig.4.11 (a) Fig.4.11 (b)
Figure 4.18 Rotor rectified current at response (a) D= 0.5, (b) D=0.9.
4.5 Torque- Speed characteristics at D = 0.5 & D = 0.9
The computed torque -speed curve for different duty cycles at 0.5 and 0.9 are shown
in figure (4.19 and 4.20) respectively.
29
Figure (4.12) Torque -Speed characteristics at D = 0.5.
Figure (4.13) Torque -Speed characteristics at D = 0.9.
4.6 Rotor rectified current - Speed characteristics at D=0.9 & D=0.5
Figure 4.13 (a) and 4.14 (b) show the rotor rectified current against speed for 0.9 and
0.5 duty cycles respectively.
30
Figure (4.14) Rotor rectified current -Speed characteristics at D=0.9
Figure (4.15) Rotor rectified current -Speed characteristics at D=0.5
4.7 Comparison of open loop and closed loop characteristics
From the below figures 4.22 to 4.26 it is observed that the performance of WRIM
drive with a RLC is better in closed loop control compared to open loop control.
31
Figure (4.23) Rotor rectified current -Speed characteristics at D=0.9
Figure (4.24) Rotor rectified current -Speed characteristics at D=0.5
32
Figure (4.25) Torque -Speed characteristics at D = 0.9.
Figure (4.26) Torque -Speed characteristics at D = 0.5.
4.8 Conclusion
The wound rotor induction motor (WRIM) offers a lot of flexibility for wide range of
speed control compared to squirrel cage motor. With high switching ability of power
electronic devices, the effect of chopper frequency at different duty cycles of WRIM
drive with a RLC performance is studied. The results shown that with low value of
chopper frequency may cause fluctuations in motor speed and torque pulsation.
33
Increasing the chopper frequency, decrease the ripple in rotor rectified current, rotor
current, speed variation and improvement in the electromagnetic torque characteristics
of WRIM drive with a RLC is studied. And also the performance of WRIM drive with
a RLC is better in closed loop control compared than the open loop control.
CHAPTER 5
34
CONCLUSION
The wound rotor induction motor (WRIM) offers a lot of flexibility for wide range of
speed control compared to squirrel cage motor. The Simplest speed control scheme
for wound-rotor induction motors is achieved by changing the rotor resistance. It has
been established that this rotor resistance control method can provide high starting
torque and low starting current and variation of speed over a wide range below the
synchronous speed of the motor. The rotor resistance is altered manually and discreet
steps this mechanical operation is undesirable the response is slow and speed variation
is not smooth. These undesirable features of the resistance control can be eliminated
by using a chopper controlled external resistance. With high switching ability of
power electronic devices, the effect of chopper frequency at different duty cycles of
WRIM drive with a RLC performance is studied. The results shown that with low
value of chopper frequency may cause motor speed fluctuations and torque pulsation.
Increasing the chopper frequency, ripple in rotor rectified current, rotor current and
speed variations are decreased and electromagnetic torque characteristics are
improved. The performance of wound rotor induction motor drive with a resistively
loaded chopper is better in closed loop control compared to open loop control. In
closed loop control, speed regulation is better than the open loop control.
5.1 Major contributions
The major contributions of in this work are listed below
The dynamic modeling of wound rotor induction motor has been studied and
developed using MATLAB/SIMULINK toolbox.
The open loop control of wound rotor induction motor drive with resistively
loaded chopper was designed, developed using Matlab/Simulink toolbox. The
simulation results are obtained and the performance of drive was studied.
The analysis of high chopper frequency, duty cycle on the rotor current, rotor
rectifier current, rotor speed, ripple in rotor rectifier current and torque
pulsation for open loop control of wound rotor induction motor drive with
RLC have been studied.
The closed loop control scheme of wound rotor induction motor drive with
resistively loaded chopper was designed, developed using Matlab/Simulink
toolbox. The simulation results are obtained and the performance of drive
was studied.
35
The analysis of high chopper frequency, duty cycle on the rotor current, rotor
rectifier current, rotor speed, ripple in rotor rectifier current and torque
pulsation for closed loop control of wound rotor induction motor drive with
RLC have been studied.
The wound rotor induction motor drive with resistively loaded chopper provides
continuous and contact less adjustment of rotor resistance by electronic means. The
simulation results shown that the low value of chopper frequency may cause
fluctuations in motor speed and torque pulsation. Increase in the chopper frequency,
decrease the ripple in rotor rectified current, harmonic rotor current, speed variation
and improvement the electromagnetic torque waveforms.
36
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38
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