Steady State Analysis oj PWM Inverter Fed Cage Induction Motor Drive
Steady state analysis ofPWM inverter fed cage
induction motor drive
Sharad.S.Patili
2
,
R.M.Holmukhe2
,
P.S.Chaudhari3
)Electrical Engineering Department, JSPM's Jaywantrao Sawant College of Engineering, Pune, India
Electrical Engineering Department, Bharati Vidyapeeth University,College of Engineering, Pune, India
3Scientist, DRDO, Pune, India
'rajeshmholmukhe@hotmail.com
Abstract: Cage induction motor is a popular choice for variable
speed operations, over a wide range, with variations in supply
frequency and voltage.
It is capable of giving long-term
stability, and good transient performance.
For Cage Induction motor drive ( CIMD ), variable voltage
and variable frequency supply can be obtained by one or more
power inverters, with suitable triggering and supporting control
circuits.
PWM inverter and cyclo -converter both are capable of
providing variable voltage supply and both have been used to
control the speed of induction motor. However a PWM inverter
offers several advantages over cyclo converter. PWM inverter
advantages are frequency can be varied over a wide range, good
power factor, good efficiency and free from voltage
regulation ,used in traction,
PS, and in emergency power
supplies.
In present investigation:
1) A mathematical model of Cage Induction motor drive has
been developed, which can reliably predict the steady state
performance of PWM inverter fed cage induction motor drive.
2) The system is simulated on Digital computer, based on coupled
circuit approach. The mathematical model has been developed in
terms of measurable parameters of the system. A computer
program has been developed in 'MATLAB' for the purpose of
digital simulation.
3) Steady state performance of the motor is evaluated for
sinusoidal supply and PWM inverter supply at nominal
frequency.
Based on the investigation, it is concluded that performance
of the motor is comparable in both the cases of supply. It is
observed that distortions are reduced as modulation index
decreases in the PWM inverter line voltage. As carrier ratio is
increased line current is nearly sinusoidal. Settling time is
reduced with PWM inverter supply.
Keywords: PWM inverter, Mathematical model
I.
I TRODUCTIO
Electrical drives play an important role as an
electromechanical
power converter. The fast growing
advancements in semiconductor technology have made a
revolution in the field of drives. The statically controlled de
drives have been widely used as variable speed drive due to
easy implementation of torque control loop because torque is
directly proportional to current when air gap flux is constant.
Thus a fast acting armature current loop gives effective torque
control. The speed can easily be controlled from rated speed
down to standstill by armature current through either phase
controlled converters or choppers. However D. C. Motors
suffer from certain drawbacks such as frequent maintenance
due to presence of mechanical commutator, no suitability for
use in Hazardous locations or dusty atmosphere, limited
overloading capacity accentuated sparking at high currents
and speed etc. Therefore, dc motor is not the best suite"
adjustable speed drive for all applications. The squirrel cage
induction motor has been the most widely used electric motor
since its inception at the end of 19th century. Over sixty
percent of the power flows through the windings of cage
motor.
The unique feature of cage motors is: the absence of sliding
electrical contacts, Poles and commutator resulting in an
extremely simple and rugged construction. They are available
in ratings over wide range and offer almost maintenance free
and efficient operation. Above all they can work in Hostile
environments where other type of motors cannot be used.
On account of its inherent advantages, frequency
controlled induction motors are better suited for adjustable
speed requirements compared to de or synchronous motors.
Apart from satisfying the requirements of variable speed
application, they help in saving energy losses in large fans,
pumps blowers, compressors etc.
PWM INVERTER
An inverter is a device that converts de power into ac power.
This can be broadly classified into two types:
Voltage Source Inverter (VSI) and Current Source Inverter
(CSI). A Voltage fed inverter (YFI) or Voltage source inverter
(VSI) is one in which the de source has small or negligible
impedance. In other words, a voltage source inverter has stiff
dc. Voltage source at its input terminals. Therefore it is an
adjustable frequency voltage source. A Current fed inverter
(CFI) or current source inverter (CSI) is fed with adjustable
current from dc source of high impedance i.e. form a stiff de
current source, output current waves are not affected by the
load.
For controlling the speed of an ac drive the flux should be
kept constant, i.e. the air gap voltage to frequency (Elf) ratio
should be kept constant. Since we vary the frequency to
control the speed, hence voltage should be varied accordingly
to keep ElF ratio constant. This voltage variation can be
achieved in three ways:
I. By variation of the alternating voltage output from the
inverter.
2. By variation of the direct voltage input to the inverter.
II.
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Proceedings of International Conference on Energy Optimization and Control (ICEOC-2010)
December 28 - 30.2010. Aurangabad, Maharashtra, India
3. By switching techniques within the inverter circuit.
Discussion on each of the methods is beyond the scope of this
text, but last one is important in context of this text as
It gives the idea of PWM techniques. The chopping
techniques which is used for controlling the dc input voltage
in accordance with frequency can also be applied within the
inverter circuitry. If we introduce pulses of variable duration
in the basic square wave output voltage then the magnitude of
the, fundamental can be varied. For this fast devices
controlled turn off is required. Therefore hy simple
introduction of pulses one can control the output voltage in
accordance with frequency. Switching control in PWM
inverters are
however complex, but by introduction of high switching
devices like MOSFET, this problem can be over come.
There exists a number of techniques for implementing pulse
width modulation in power inverters, some of popular
techniques are:
I. Single pulse modulation
2. Multiple pulse modulation
3. Square wave PWM
4. Sinusoidal PWM
III. MATHEMATICAL MODEL OF PWINVERTER
FED CAGE INDUCTION MOTOR DRIVE
This topic presents the generalized equations describing the
behaviour of pulse width modulated fed squirrel cage
induction motor drive based oil the coupled circuit approach.
The system has been analysed in a synchronously rotating
reference frame. With the help of d-q transformation of
variables basic equations for induction motor, are developed
in per unit system. The mathematical model so developed, has
been used for analysing the drive under sinusoidal as well as
PWMinput.
3.1 INTRODUCTION
The suitability of any drive to a given application is
characterized by its steady state and dynamic behavior. In
order to analytically predict the drives performance, it is
essential to develop a mathematical model of the drive under
required operating conditions, using reasonable assumptions.
Generalized equations describing, the behavior of three-phase
symmetrical induction motor is established by considering it
an elementary two pole idealized machine. A computer
program using 'MATLAB" software is developed here to
solve the state equations using Fourth Order Runge - Kutta
method to Simulate the performance of the drive.
The PWM output voltage waveforms of the three-phase
system are, generated based on sinusoidal pulse width
modulation technique. These voltages are then transformed
into d-q components and regarded as forcing functions in the
d-q model of an induction motor. The model has been
developed neglecting hysteresis and eddy current losses.
STATOR
WINDING
3.2 MATHEMA TICAL MODEL OF INDUCIION
MACHINE
The generalized equations describing the behaviour of an
induction motor under steady state and transient conditions are
established by considering it as an elementary two pole
idealized machine. The effect of number of poles is taken into
account by multiplying the expression for torque by number
of pole pairs.
An ideal three-phase induction motor, is regarded as a group
of linear coupled circuits. Concentrated coils have showed
distributed stator and rotor windings.
Organised by - Department of Electrical Engineering, Govt. College cf Engineering, Aurangabad - 431 005. Maharashtra, India
374
Steady State Analysis of PWM Inverter Fed Cage Induction Motor Drive
Mathematical Model of Induction Motor in matrix form
expressed as
Lss 0
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ics I 3.20
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=
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I.,
3.3 TRAMSFORMA TION TO SYNCHRONOUSLY
ROTA TING REFERENCE FRAME
Substitution of equation (3.20) in equation. (3.5) to (3.10)
gives a set of differential equations, which are non-linear due
to time varying nature of the coefficients. These equations can
however be converted to a set of linear equations by adopting
d-q trans formation. By doing so, the time varying coefficients
are eliminated, and variable and parameters are expressed in
mutually decoupled direct and quadrature axes. The d-q
equations of an induction motor can be expressed either in
stationary or in rotating reference frame. The use of a
reference frame that rotates at synchronous speed provides an
advantage that with sinusoidal excitation the variables appear
as de quantities in steady state condition. The transformation
to d-q axes reference frame rotating at synchronous speed. to
rad/sec is given by Fig 3.2,
A mathematical model has been developed from a three phase
PWM inverter. The model developed can be used to predict
the dominant feature of the drive under steady state and
transient conditions. The model neglects hystrresis and eddy
current losses. The turn ON and turn OFF periods are very
small, to treat the device as an ideal switch.
IV .STEADY-STATE ANALYSIS
This chapter deals with steady state analysis of PWM signal
fed, cage induction motor drive. Using mathematical model,
developed in chapter 3, performance characteristics Of the
drive under steady state are, Obtained For comparison,
corresponding performance. Characteristics of the motor when
fed from sinusoidal supply are also presented.
4.1 INTRODUCTION
The growing application of variable speed cage induction
motor fed from variable. voltage variable frequency source
has created the need for detailed analysis under steady state
operation for predetermination of the performance. The
knowledge of the steady state performance characteristics of
the drive is necessary to identify the application area of the
drive, for improvement in its performance for the optimization
of the system for meeting the desired specifications.
As the motor operates at variable speed, it is necessary that the
motor input. Parameters, voltage and frequency be adjusted
suitably to get the required speed and torque.
Equivalent circuit approach for predetermination of the steady
state performance of the induction motor is well suited, when
the. input voltage is sinusoidal. However, when the motor
voltage is non-sinusoidal, as in the case of present drive, it is
more convenient to Work out the performance in time domain
on instantaneous basis. The modulating wave and a carrier
wave voltage of a particular carrier ratio are generated and the
signals obtained by comparing them are used to trigger
various PWM inverter devices.
The PWM voltage is considered as forcing function to the
coupled circuit Model of induction motor and waveforms of
the motor currentSare obtWi'ed mtime domain. This requires
the mathematical model of the drive to be solved through
numerical techniques. From the initial standstill conditions the
motor is allowed to build up under a given load torque until
steady state is reached. The steady state is identified when the
motor current waveform successively exhibits identical cycles.
The voltage-current waveforms are then used to compute the
steady-state performance in time-domain. This analysis is
carried out at a selected frequency of 50 Hz and at no and full
load condition.
4.2 PERFORMANCE OF THE TEST MOTOR ON
SINUSOIDAL SUPPLY
In this section steady-state performance of the specific
induction motor, is presented with, the sinusoidal supply to
establish its behaviour. Performance curves are obtained under
nominal supply (rated voltage and rated frequency) shown in
fig 4.I.This curve is used to determine motor performance at a
given frequency for comparison when the motor is fed from
PWM inverter supply.
4.2.1 PERFORMANCE UNDER NOMINAL VOLTAGE
AND FREQUENCY
The steady state performance curves have been obtained using
equivalent circuit of the motor The equivalent circuit
parameters of the test motor, given in the Appendix, are
obtained through light running and blocked rotor tests. The
test motor's nameplate data are as shown in Table 4.1.
Table 4.1
TEST MOTOR NAME PLATE DATA
Connection
Delta
Nominal Line Voltage
415.0 volts
4.9 Amps
Nominal Line Current
Nominal Power Outout
2.2KW
1400 RPM
Nominal Sneed
Since the nameplate current refers to full load operation, it has
been used for identifying the full load operating point on the
performance curves.
Fig.4.1 shows the computed steady-state performance from
equivalent circuit approach with respect to speed in the entire
375
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Proceedings of International Conference on Energy Optimization and Control (IC£OC-2010)
December 28 - 30,2010, Aurangabad, Maharashtra, India
sub-synchronous region, from standstill to synchronous speed,
when the motor is operated from rated voltage and frequency
supply. The full load operating- points have also been
identified on theses characteristics and are reproduced in
Table 4.2. It may be noted that the calculated power output is
a little more than the nameplate value. This is due to
neglecting friction and windage losses and core losses in
calculations.
.15
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105
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15
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os,,~
IS
Table 4.2
TEST'MOTOR PERFORMANCE ON SINUSOIDAL SUPPLY UNDER
FULL LOAD
Supply Voltage
Supply frequency
Line current
Motor torque
Power output
Power input
Efficiency
Power factor
Speed
Air Gap voltage
In actual unit
415.-00 volts
50.00Hz
4.90 A.
16.56Nw-m
2.4IKW
2.81KW
-1440 RPM
367.00volts
In per unit
0.707
1.000
1.225
0.740
0.686
0.800
0.860
0.800
0.960
0.626
From Fig 4.1 (a) it is noted that motor's starting torque is 1.04
p.u. which is 1.4 times the full load torque. The full load slip
is 0.072 p.u. The starting current in Fig 4.1 (g) is 4.8 p.u.
which is 3.92 times the, full load current.Figs.4.1 (g) show
variation of power input and power output respectively with
respect to speed. Curves 4.1 (c and e) show variations of
power input and power output figures (b and d) shows power
factor and efficiency, the full load values of them being 0.796
pu. and 0.856 p.u. Fig 4.1 (f) shows air gap voltage. The air
gap voltage is seen to be 0.664p.u. (or 389.7 volts) under no
load which slightly drops to 0.626p.u. (367 volts) under full
load condition.
4.3 OPERATION ON PWM INVERTER SUPPLY
The output voltage of PWM inverter is non-sinusoidal. The
fundamental component of this voltage can be utilized to
select the value Of Supply voltage.
4.3.1 VOLTAGE TO FREQUENCY CONTROL IN PWM
INVERTER
In present work both voltage and frequency at the output of
inverter are varied to achieve speed control under v/f control
to maintain high torque capability at all frequencies. The ratio
v/f is Chosen corresponding to the rated voltage and
frequency.
In PWM inverters, amplitude of fundamental output voltage is
directly proportional to the modulation index 'm', which is
defined as.
M = VrNc = Amplitude of modulating wave/amplitude of
carrier wave .
The frequency ratio or carrier ratio is defined as
K = fc / f = Carrier frequency / Frequency of modulating wave
If the frequency ratio 'K' is chosen to be multiple of three
identical phase voltage waveforms at the inverter output are
produced, resulting in a balanced three phase system.
In sinusoidal PWM, three phase sinusoidal voltages are
compared with a carrier wave to obtain PWM pattern. This is
illustrated in Fig 4.2 (a) compares sinusoidal modulating wave
of phase 'a' with a triangular carrier waveform symmetrically
placed about zero reference axis. In this illustration the carrier
ratio is chosen to be 20 and the corresponding modulating
index selected is 1.0 This comparison is used to generate a
pole voltage (pva) waveform as shown in Fig 4.2 (b) which
swings between + (V d /2) to -(V d /2),where Vd is the de
link voltage at the input of inverter. In present case the value
of Vd 1.5 P.u. The logic employed in generating the pole
voltages is that pole voltage is + (Vdl2) at those instants when
amplitude of modulating wave is greater than that of the
carrier wave, otherwise it is -(Vd / 2). Thus the pole voltage
has only two levels (either positive or negative) and is called
two-level PWM waveform. The pole voltage waveform is
considered as the voltage of a phase with respect to mid point
of the de source Vd. A 3-level PWM pole voltage waveform
is also commonly employed.
Fig 4.2 (c) shows the comparison of sinusoidal modulating
waveform. Of phase 'B' with carrier wave. The modulating
waveforms of phase B is 1200 lagging in time phase with
respect to modulating wave of phase 'A'. This comparison
yields pole voltage waveform. 'pvb ' as shown in the Fig, 4.2
(d). The line voltage Vab is obtained as
Vab = pva - pvb
The waveform of other line voltages v be and v ca at the
output of inverter are obtained in a similar manner. Thus,
V be = pvb - pvc
V ca = pve - pva
Organised by - Department of Electrical Engineering, Govt. College of Engineering, Aurangabad - 43/ 005. Maharashtra, lndia
376
Steady State Analysis of PWM Inverter Fed Cage Induction Motor Drive
Where [V] is the voltage vector
[i) is the current vector
[R] is the impedance matrix free of p terms
-COLas
For wye-connected load at the output of inverter the phase
voltages may also be from pole voltages as
V as = ( 2 pva - pvb - pvc )/3
V bs = ( 2 pvb - pvc - pva)/3
Vcs = (2 pvc - pva - pvb)/3
COLas
[R]
4.4 SYSTEM EQUATIO
o
o
Rss
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o
·SCOLrr
Lss
o
l.ss
o
l.ss
o
o
(X]=
o
0
S UNDER STEADY STATE
In case of sinusoidal input to the motor, motor voltages and
currents attain steady ac values under steady state. When
referred to synchronously rotating d-q reference frame they
appear to be dc quantities and their time derivative become
zero. However in case of PWM inverter fed induction motor
drive the input voltage is non-sinusoidal and therefore for
steady state. The dynamic equations of the motor that are
nonlinear may be solved by numerical analysis method to get
steady state currents.
Rewriting equation 3.44
4.4.1 DIGITAL SIMULATIO
P(wr)=
The dynamic state of the induction motor can be represented
by the voltage-current relations in the motor and may be
expressed in the following form
[V] = [R] [i) + l/w[X] [pi]
Or
P[i] = w[-[X] -I [R] [i) + [xrl [V]
-COLIl
=
The phase voltages of phase 'A' ' Vas' and the line voltage V
ab' obtained in this manner are shown in fig 4.2 (e) and (f)
respectively.
The amplitude of fundamental line to neutral voltages for a
star connected load fed from a PWM inverter is found to be.
VI = m [Vd/2]
This equation points to two ways of achieving, control of
output fundamental voltage V 1 (i) Keeping the modulating
index m = 1.0 and varying (Vd ) supply voltage at the inverter
input which results in variation of output fundamental voltage
VI and (ii) for a given supply voltage, varying modulation
index 'm' between 1.0 and 0.0 In the present work,
performance of the drive under modulation index m 1.0 is
observed.
If V d is chosen 1.5 p.u. as in Fig 4.2, equation (4.1) becomes
VI =0.75
o
0
Lil
o
0.5(Te-TL)/H
Equations (4.5) and (4.6) constitute a set of five non-linear
differential equations. This set can be efficiently solved on a
digital computer using numerical integsatlon technique.
Fourth order Runge - Kutta method of Ffuinerical integration is
adopted here. The accuracy of integration depends on the
377
Proceedings of International Conference on Energy Optimization and Control (ICEOC-20 10)
December 28 - 30,2010, Aurangabad, Maharashtra, India
integration interval; smaller the interval, greater is the
accuracy. A step interval of 0.00002 second is selected in the
present work.
4.4.2 COMPUTATION
PROCESS IN PWM INVERTER
The computation process adopted in present work has been
illustrated through flow charts shown in present Fig 4.3 to 4.5
It begins by taking initial values of rotor speed and machine
phase currents and hence ids, iqs, idr, iqr as zero. The value of
step length, base, frequency, operating frequency, initial
values of applied load torque and modulation index m are also
provided as input. The phase voltages Vas, Vbs, and Vcs and
line voltages Vab, Vbc , and Vca at the output of PWM
inverter are computed using' PWM' given in flow chart of Fig
4.4 It generates three phase sine voltages and carrier wave of
given carrier ratio. The PWM waveform is generated by
comparing the amplitudes of three sinusoidal voltages and the
carrier wave amplitudes using the concept of two level
modulation.
...•.
St.,.
I
The test motor is delta connected, its line. and phase voltages
are to be obtained from the converter output. The line voltages
Vab, Vbc Vca and phase voltages Vas, Vbc, Vcs are
calculated from the inverter pole voltages. Using d-q
transformation, the line voltages are then transformed into
Vds and Vqs- Equation (4.4) are then used in the main
program of Fig 4.2 to calculate the currents ids, iqs idr, and iqr
The d-q transformation is used once again to obtain phase
currents ias, ibs, and ics as shown in the Fig 4.5 The next
cycle of calculation starts with the above-calculated values as
new initial values of variables, and 'PWM' calculation is done
once again. In this manner, using the chosen step length, the
voltages and currents are computed until the machine reaches
steady state. At the end of each cycle, the torque developed by
the motor (Te) and its speed ((0 r) is also computed for given
Load torque (TL)
I
Rewriting these relations for stator,
ids = 2/3 [ias cosfll +ibs cos(SI - 2m3) + ics cos(SI + 2m3)]
iqs = - 2/3 [ias sinSI +ibs sin(SI - 2m3) + ics sin(S1 + 2m3)]
Expression (4.8) and (4.9) can be written in inverse manners
as
ias = ids cosS I - iqs sinS I
ibs = ids cos (S I - 2m3) - iqs sin (8 I - 2m3)
ics = ids cos (8 I + 2m3) - iqs sin (S I + 2m3)
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4.4.3 VOLTAGE AND CURRENT EXPRESSIONS FOR
MOTOR
The phase currents are related to d-q current components in
accordance with transformation defined in equations (3.21) to
(3.24)
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and phase currents are not the same.
the line currents
Organised by - Department of Electrical Engineering, Govt. College of Engineering, Aurangabad - 43 J 005. Maharashtra, India
378
/
Steady State Analysis of PWM Inverter Fed Cage Induction Motor Drive
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4.4.4 EXPRESSIONS FOR INPUT POWER, OUTPUT
POWER AND EFFICIENCY
Power output can be determined from the electromagnetic
torque Te and angular shaft speed at every step by
Pout = Te * w r (mech)
02
i ~j
.TT..l·····'
!...•..~
;..•....
•...•.i-..~~
,
~
!
:
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01
= Pout I Pin
V. SIMULATION RESULTS
Performance of the drive has been obtained with rated
frequency using the computational results outlined in the
previous section. The results of full load operation of the
motor are presented here for operation on
(a) Sinusoidal supply
(b) PWM inverter supply
The waveforms of motor voltage, current, torque, input power
and output power are obtained in time domain and are
pres6nted for operation in time domain, and are presented for
operation -at typical frequency of 50 Hz. Full load operation is
considered by choosing a load torque TL = 0.74 p.u., inertia
constant H is taken as 0.1024sec. The computation is also
done considering saturation of the magnetic circuit. At the
given frequency, the selection of voltage to be applied to the
motor is done as below.
(a) Sinusoidal supply
For V/f control, the voltage to be applied for an operating
frequency of fl Hz is found in the following manner.
U.l
03
U ·u
••••
I4J.ls.l,s..._V_u..wPWloiS\fl>!y
{.)_()J!opcod«l
__
(I)u..c.m..
(<l_~(t}"""",,,,,,,."""""""!Odo~o,"lIII(t.f"'looI~
A
I
Chosen vlfratio = VL-L (RMS) I f= 400 V/50 Hz = 8
At frequency fl Hz
VL-L (rms) = 8 * f 1
Or V ph (rms) = VL-L (rms) 1"'3 = 8* fl 1"'3
Or V ph (peak) = ("'2 I "'3 )* 8 * fl 1("'2/"'3)*
Or V ph (peak) = f 1 ISO
Thus, Vph (peak) = 1.0 for f 50 Hz
I
!
.1
400
I
I
(b) PWM inverter supply
For a de link supply voltage Vd chosen equal to 1.5 P.u., per
unit fundamental phase voltage (peak value) is obtained from
equation (3.1) as
VI =0.75 m
The modulation index is selected as m = 0.8 for 50 Hz
Two level modulation is adopted with a carrier ratio of20
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Proceedings of International Conference on Energy Optimization and Control (ICEOC-20l0)
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The simulation results for f = 50 Hz operation, when the drive
fed from sinusoidal supply or PWM inverter supply are given
in the Figs. 4.6 and 4.7 respectively. Fig 4.6 (a) shows the
applied phase / line voltage to the delta connected stator of the
motor. As already mentioned the peak value of phase/line
voltage is has been set to base voltage 1.0 p.u. Fig. 4.6 (a and
b) show electromagnetic torque developed and speed. Their
steady state values being 0.74 p.u. and 1.0 p.u. respectively.
Figs 4.6 (c and d) show phase and line currents, they are
steady at 1.0 p.u and 1.74 p.u. Figs 4.6 (e and t) show input
and output power, they are steady at 0.741 and 0.68 p.u.
Figs 4.7 (a - t) present the waveforms under PWM operation.
For two level modulation, the peak value of pole voltage, line
voltage/phase voltage are respectively Vd / 2 and Vd. In
present case Vd is Chosen as 1.5 p.u. and therefore peak value
of line voltage is 1.5 p.u.
Figs.4.7 (a and b) show electromagnetic torque and speed.
Figs 4.7 (c and d) show phase and line current It is noticed
that although the distortion is more in voltage waveform, the
current waveform has less amount of distortion due to the fact
the motor winding has high reactance to the applied harmonic
voltage.
Fig 4.7 (e) shows the variation of input power to the motor. It
reveals that the effect of harmonics on motor voltages and
currents has an. effect of input power too. The input power is
obtained as the product of instantaneous voltages and currents.
Its average value is almost equal to that of sinusoidal supply.
In the Fig.4.7 (t), the output power is obtained as the
product of instantaneous torque and shaft speed .. Since the
oscillation in speed is very small, the output power follows the
nature of torque. As compared, with the input power,
oscillations in the output power have been reduced. Moreover
the average power seems to be very close to that of sinusoidal,
supply.
Resonant peak is reduced from 3.4 p.u. to 2.8 p.u. for torque
while is, almost same for other parameters, settling time is
reduced from 0.42 see to 0.18 sec. Steady state performance is
almost same for both the cases.
In this study, the performance of PWM inverter fed cage
induction motor drive under steady state condition has been
investigated. The performance has been digitally simulated
using, the dynamic mathematical model. A computer program
has been developed in 'MATLAB' for the purpose of digital
simulation.
The performance of test motor operated from sinusoidal
supply and PWM inverter supply is presented for transient
and- steady state period. Comparison has been made for
drive's simulated performance when fed from sinusoidal
supply or PWM inverter source of supply. Performance under
sinusoidal supply is the best the Motor can offer. Under PWM
supply, the performance further deteriorates. However the
deterioration is not significant as under PWM supply also the
motor current is nearly sinusoidal.
CONCLUSIONS
The aim of this study has been to devise a mathematical
model, which can reliably predict the steady state performance
of PWM inverter fed cage induction motor drive. The model
has been developed on coupled circuit approach of the motor.
The mathematical model has been developed in terms of
measurable parameters of the system.
The operating frequency has been selected as 50Hz. The
steady state performance is computed under full load. The
sources considered are sine wave supply and PWM supply.
The characteristics of the motor under sinusoidal supply
operation are obtained. For sinusoidal PWM inverter the
steady state performance is checked
SCOPE FOR FURTHER WORK
Drives performance can be calculated in following manners:
I. Variable frequency operation may be considered.
2. Switches are considered to be ideal, but at high switching
frequencies the switching losses will be very high reducing
efficiency. So efforts can be made to reduce switching losses
by (a) Resonant topology (b) Actively clamping concept (c)
Two amplitude oscillation theory
3. This study was done in open loop. A closed loop scheme
can be devised for better control.
4. Machine model may include core losses for better accuracy
of results
5. Different controllers may be used and performance- may be
calculated for each one.
6. Vector control method can be used.
ACKNOWLEDGMENT
Bharati Vidyapeeth University College of Engineering, Pune-
43
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Organised by - Department of Electrical Engineering, Govt. College of Engineering, Aurangabad - 431 005. Maharashtra, India
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