DOI 10.4010/2016.1502
ISSN 2321 3361 © 2016 IJESC
Research Article
Volume 6 Issue No. 5
Simulation and Modeling of Sinusoidal Pulse Width Modulated
Inverter Fed Induction Motor Using PI Controller
Shreyash Vir1, Dr. Sarika Kalra2
Research scholar 1, Assistant Professor 2
Department of Electrical Engineering
Sam Higginbottom Institute of Agriculture, Technology & Sciences (Deemed-to-be University), Allahabad, India
Abstract:
This paper presents a v/f control of induction motor with different pulse width modulation ( PWM) techniques as sine triangle pulse
width modulation ( SPWM) by PI controller The Space vector pulse width modulation(SVPWM) using MATLAB SIMULINK is
simulated. Induction motor modelled in the synchronous q-d reference frame. The performance of IM with various supply voltage
and frequency are compared using these techniques for speed control, utilization of AC supply voltage, fundamental peak of the
output voltage and motor speed. The dynamic performance of IM using SVPWM under reference speed and load torque variations
is studied also. The results show that the SVPWM is the efficient one because it’s superior performance characteristics. The
operation of IM with v/f method using PI controller for closed loop system is enhancement when SVPWM technique is applied.
Keywords: Space vector modulation, SPWM, v/f control of Induction motor, PIC Controller, Induction Motor Drive.
I.
INTRODUCTION
Induction motors are the most widely used electrical motors
due to their reliability, low cost and robustness. However,
induction motors do not inherently have the capability of
variable speed operation. Due to this reason, earlier dc motors
were applied in most of the electrical drives. But the recent
developments in speed control methods of the induction motor
have led to their large scale use in almost all electrical drives.
Out of the several methods of speed control of an induction
such as pole changing, frequency variation, variable rotor
resistance, variable stator voltage, constant V/f control, slip
recovery method etc., the closed loop constant V/f speed
control method is most widely used. In this method, the V/f
ratio is kept constant which in turn maintains the magnetizing
flux constant so that the maximum torque remains unchanged.
Thus, the motor is completely utilized in this method. During
starting of an induction motor, the stator resistance and the
motor inductance (both rotor and stator) must be kept low to
reduce the steady state time and also to reduce the jerks during
starting. On the other hand, higher value of rotor resistance
leads to lesser jerks while having no effect on the steady state
time. The vector control analysis of an induction motor allows
the decoupled analysis where the torque and the flux
components can be independently controlled (just as in dc
motor). This makes the analysis easier than the per phase
equivalent circuit. Induction motors are widely used in many
industrial processes due to their rigid nature, reliability and
robustness. However, induction motors have fixed speed
limiting them from being used in other processes. Available
speed control techniques such as variation of supply voltage,
variation of number of poles, variation of motor resistance,
constant V/F ratio control and slip recovery method are some
of the methods of speed control characterized by low efficiency
and high maintenance cost. Improvement in power electronics
technology though advancements in semiconductor electronic
devices have led to development of variable frequency motor
drive, an electronic device used to control speed of an
induction motor with increased efficiency, reliability and low
cost. This paper seeks to carry out modeling, simulation and
International Journal of Engineering Science and Computing, May 2016
performance analysis of a variable frequency drive using
MATLAB/SIMULINK model. Control of speed of induction
motor was successfully achieved from zero to nominal speed
by varying frequency of applied AC voltage using pulse width
modulation method.
II SYSTEM DICRIPTION
1. Dynamic model of induction motor
The stator of induction motor consists of three phase balanced
distributed windings with each phase separated from other two
windings by 120 degrees in space. When current flows through
these windings, three phase rotating magnetic field is
produced. The dynamic behaviour of the induction machine is
taken into account in an adjustable speed drive system using a
power electronics converter. This machine constitutes an
element within a feedback loop. Study of the dynamic
performance of the machine is complex due to coupling effect
of the stator and rotor windings; also the coupling coefficient
varies with rotor position. So a set of differential equations
with time varying coefficients describe the machine model.
To derive the dynamic model of the machine, the following
assumptions are made:
1. No magnetic saturation;
2. No saliency effects i.e. machine inductance is independent
of rotor position;
3. Stator windings are so arranged as to produce sinusoidal
mmf distributions;
4. Effects of the stator slots may be neglected;
5. No fringing of the magnetic circuit
6. Constant magnetic field intensity, radially directed across
the air-gap;
7. Negligible eddy current and hysteresis effects;
A balanced three phase supply is given to the motor from the
power converter. For dynamic modeling of the motor two axes
theory is used [1]. According to this theory the time varying
parameters can be expressed in mutually perpendicular direct
(d) and quadrature (q) axis. For the representation of the d-q
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dynamic model of the machine a stationary or rotating
reference frame is assumed.
For convenient qs axis is aligned with the as-axis i.e. θ = 0 and
zero sequence component is neglected. So the transformation
relations are reduced to
(4)
(5)
Fig.2 (a) Coupling effect in stator and rotor winding of
motor (b) Equivalent two-phase machine
In stationary reference frame the ds and qs axes are fixed on the
stator, whereas these are rotating at an angle with respect to the
rotor in rotating reference frame. The rotating reference frame
may either be fixed on the rotor or it may be rotating at
synchronous speed. In synchronously rotating reference frame
with sinusoidal supply the machine variables appear as dc
quantities in steady state condition.
2. Axes transformation
(a) Three phase to two phase transformation
A symmetrical three phase machine is considered with
stationary as-bs-cs axes at 120 degree apart as shown in
fig.3.2.
(6)
(7)
(8)
(b) Two phase stationary to two phase synchronously
rotating frame transformation
The stationary ds-qs axes are transformed to synchronously
rotating de-qe reference fram
which is rotating at speed ωe with respect to ds-qs axes with the
help of fig.3.3. The angle between ds and de axes is θe = ωet.
The voltages vdss, vqss can be converted to voltages on de-qe
axis according to the following relation
(14)
(15)
Fig.1 as-bs-cs to ds-qs axis transformation (θ = 0)
The voltages vas, vbs, vcs are the voltages of as, bs, cs phases
respectively. Now assuming that the stationary ds-qs axes are
oriented at θ angle as shown and the voltages along ds -qs axes
to be vdss, vqss respectively, the stationary two phase voltages
can be transformed to three phase voltages according to the
following equations:
(1)
(2)
(3)
The phase voltages in matrix form can be written as;
Fig.3 Stationary d-q frame to synchronously rotating frame
transformation
The transformation of rotating frame parameters to stationary
frame is according to the following relations:
By inverse transformation, vdss and vqss can be written in terms
of three phase voltages in matrix form as follows:
Where v0s = zero sequence component which may or may not
present.
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(9)
(10)
Assuming that the three phase voltages are balanced and
sinusoidal given by following
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(11)
(12)
(13)
3.
Voltage source inverter
In VSIs the input voltage is maintained constant and the
amplitude of the output voltage is independent of the nature of
the load. But the output current waveform as well as magnitude
depends upon nature of load impedance. Three phase VSIs are
more common for providing adjustable frequency power to
industrial applications as compared to single phase inverters.
The VSIs take dc supply from a battery or more usually from a
3-ϕ bridge rectifier.
A basic three phase VSI is a six step bridge inverter, consisting
of minimum six power electronics switches (i.e. IGBTs,
Thyristors) and six feedback diodes. A step can be defined as
the change in firing from one switch to the next switch in
proper sequence. For a six step inverter each step is of 60º
interval for one cycle of 360º. That means the switches would
be gated at regular intervals of 60º in proper sequence to get a
three phase ac output voltage at the output terminal of VSI.
Fig.2.5 shows the power circuit diagram of three phase VSI
using six IGBTs and six diodes connected anti parallel to the
IGBTs. The capacitor connected in to the input terminals is to
maintain the input dc voltage constant and this also suppresses
the harmonics fed back to the dc source. Three phase load is
star connected.
4. PI Controller Structure
The use of PI controllers to command a
induction motor’s speed is often characterized by an overshoot
in tracking mode and a poor load disturbance rejection. This is
mainly caused by the fact that the gains of the controller cannot
be set to solve the overshoot and load disturbance rejection
problems simultaneously. Overshoot elimination setting will
cause a poor load disturbance rejection, and rapid load
disturbance rejection setting will cause important overshoot or
even instability in the system.
To overcome this problem, the use of VGPI controllers is
proposed. A PI controller is a generalization of the classical PI
controller where the proportional and integrator gains vary
along a tuning curve. Each gain of the proposed controller has
four tuning parameters.

Gain initial value or start up setting which permits
overshoot elimination.
 Gain final value or steady state mode
setting which
permits rapid load disturbance rejection.

Gain transient mode function which is a polynomial curve
that joints the gain initial value to the gain final value.

Saturation time which is the time at which the gain reaches
its final value.
The degree n of the gain transient mode polynomial function is
defined as the degree of the variable gain PI controller. If e(t) is
the signal input to the VGPI controller the output is given by :
(14)
With
(15)
(16)
Where pi K and K pf are the initial and final values of the
proportional gain Kp and Kif is the final value of the integrator
gain Ki. The initial value of i K is taken to be zero. It is noted
that a classic PI controller is a VGPI controller of degree zero.
The VGPI unit step response is given by:
Fig.4 Three phase VSI using IGBTs
3.4 Hysteresis controller
DTC of induction motor drives requires two hysteresis
controllers. The drive performance is influenced by the width
of the hysteresis bands in terms of flux and torque ripples,
current harmonics and switching frequency of power
electronics devices. Current distortion is reduced by small flux
hysteresis band and torque ripple is reduced by small torque
hysteresis bands. In each sampling time, the switching state of
the inverter is updated. The inverter state remains constant,
until the output states of the hysteresis controller change within
a sampling interval. If the hysteresis band is fixed, the
switching frequency totally depends on the rate of change of
torque and flux.
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(17)
If s t ≥ t , the unit step responses of a PI and VGPI controllers
are both linear with slope if K . From these results, one can say
that a PI controller has the same properties with a classical PI
controller in the permanent region with damped step response
in the transient region. A VGPI controller could then be used to
replace a PI controller when we need to solve the load
disturbance rejection and overshoot problems simultaneously.
The PI controller in vector control of IM is used as presented in
Figure 4.
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Fig 5 The Structure of VGPI controller in DFIM vector
control
The tuned VGPI controller is given by:
Fig 8 stator current ( at 400 v and 30.76Hz)
(18)
III SIMULATION RESULTS
The proposed method has been tested and simulation
results are shown Figures. This model has been implemented
using MATLAB/SIMULINK environment with SIMPOWER
system toolbox. Using V/F methods the corresponding
Simulation results are obtained. The simulation is carried out at
different voltages and frequency in such a manner that in each
case their ratio is same. In each, case we see that the voltage is
different but speed of induction motor remains nearly constant.
The stator current at different voltage level is not equal because
when the speed of induction motor changes stator withdraws
more current. The simulation model and results obtained iare
given below;
Fig 6 Simulation model
Case 1. When supply voltage is 400 v and frequency is 30.76
Hz so that their ratio is 13. In this case PI controller compares
the speed of Induction Motor with reference speed and send
error signal to invertor gate controller. The gate controller
circuit generate such a pulse so that their voltage is equal to
input voltage but in this case motor stator current is different
which is shown in fig.
Fig 9 Invertor output voltage ( at 400 Vand 30.76Hz)
Case 2. When supply voltage is 650 V and frequency is 50 Hz
so that their ratio is 13. In this case the inverter out voltage is
650 but stator withdraws more current from the supply to
maintain constant current. The waveform is stator current,
induction motor, electromagnetic torque and inverter output
voltage is shown below,
Fig 10 rotor speed and electromagnetic torque ( at 650 v
and 50 Hz)
Fig 7 rotor speed and electromagnetic torque ( at 400 v and
30.76Hz)
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Fig 11 stator current ( at 650 v and 50Hz)
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maintain constant c speed. The waveform is stator current,
induction motor, electromagnetic torque and inverter output
voltage is shown below,
Fig 12 Invertor output voltage ( at 650 v and 50Hz)
Case 3. When supply voltage is 800 Hz and frequency is 61.5
Hz so that their ratio is 13. In this case the inverter out voltage
is 800 but stator withdraws more current from the supply to
maintain constant current. The waveform is stator current,
induction motor, electromagnetic torque and inverter output
voltage is shown below,
Fig 16 Rotor speed and electromagnetic torque ( at 900 v
and 69.2 Hz)
Fig 13 Rotor speed and electromagnetic torque ( at 800 v
and 61.5 Hz)
Fig 14 Stator current ( at 800 v and 61.5Hz)
Fig.17 Stator current ( at 900 v and 69.5Hz)
Fig 18 Invertor output voltage ( at 900 v and 69.5Hz)
Finally, we can say that the induction motor speed remains
almost constant in each case, but the electromagnetic torque,
stator current and inverter voltage change.
IV CONCLUSION
Fig 15 Invertor output voltage ( at 800 v and 61.5Hz)
Case 4. When supply voltage is 900 V and frequency is 69.2
Hz so that their ratio is 13. In this case the inverter out voltage
is 900 V but stator withdraws more current from the supply to
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PWM Inverters for 3-Ф were modelled and studied.
The PWM signals were generated by comparing either a
triangular waveform with a sinusoidal waveform using
relational operators. These PWM signals were then applied to
the gates of forced-commutation devices like IGBT‟s so as
trigger them in a specific sequence to be able to convert the DC
supply voltage to an AC output voltage. The DC supply could
either be from a battery, a fuel cell, or from a rectifier which
receives AC supply from the mains. A 3-Ф PWM Inverter was
also fashioned using the Simulink Library blocks PWM
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Generator and Universal Bridge. In all cases, successful
Inverter action was obtained. An Induction Motor was run with
the help of a PWM Inverter without implementing any kind of
speed control mechanisms and the various characteristic curves
were obtained. It was observed that there were a lot of transient
currents in the stator and rotor at the time of starting and they
took some time to settle down to their steady-state values. The
lower the stator resistance, the quicker the transients died down
and hence, the stator resistance should be kept very low. In an
uncontrolled Induction Motor, torque was observed to rise to a
maximum value and then settle at the base value, while rotor
speed was observed to rise to its rated value and remain
constant there. Open-loop V/f Control was implemented using
MATLAB and it was observed that by varying the supply
frequency and terminal voltage such that the V/f ratio remains
the same, the flux produced by the stator remained constant. As
a result, the maximum torque of the motor remained constant
across the speed range. Closed-loop V/f Control used a
Proportional integral Controller to process the error between
the actual rotor speed and reference speed and used this to vary
the supply frequency. The Voltage Source Inverter varied the
magnitude of the Terminal Voltage accordingly so that the V/f
ratio remained the same. It was observed that again the
maximum torque remained constant across the speed range.
Hence, the motor was fully utilized and successful speed
control was achieved.
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[10] M.Vasudevan, R.Arumugam “New Direct Torque Control
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[11] M.Vasudevan, R.Arumugam, S.Paramasivam“ High
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Scheme for Induction Motors Fed with a Three-level Inverter”,
World Academy of Science, Engineering and Technology 2008
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