International Conference on Innovative Applications of Computational Intelligence on Power, Energy and Controls with their

Impact on Humanity (CIPECH14) 28 & 29 November 2014

Obtaining Maximum Torque Operation of Single Phase Induction

Motor Using Simulation Technique of MATLAB
Swati Singla Jyoti Srivastava D.Blandina Miracle
Assistant Professor Associate Professor Assistant Professor
KIET, Ghaziabad KIET, Ghaziabad KIET, Ghaziabad
swati.singla@kiet.edu jyoti.srivastava@kiet.edu blandina.miracle@kiet.edu

Abstract- Fractional KW electrical machines In most of the applications the motor usually runs
used in domestic and industrial applications are at a fixed speed. At most two or three speeds can
mostly asymmetrical two phase induction motor be obtained by manual operation. But in this
supplied by single phase supply. Though many manner, motor operates at low power factor and at
techniques are available for control of three less efficiency. Traditionally variable speed
phase induction machine for extracting its best operation of SPIM is obtained by the use of voltage
performance, but no such generalized technique control method using Triacs or Thyristors. But
is available for controlling Single Phase these techniques suffer from low power factor,
Induction Motor (SPIM). In this paper, a SPIM limited speed range and large harmonic injection
is studied, where a dynamic capacitor is used for into the supply
obtaining maximum torque operation. The
SPIM makes use of indirect current control of Most single phase motors are constructed with two
Voltage Source Inverter (VSI) with a capacitor asymmetrical windings, main and auxiliary
on its DC bus , so that it can work as a variable winding which are displaced 90 electrical degrees
capacitor. Then a maximum torque operation is around motor stator. The main winding carries a
obtained, by connecting this dynamic capacitor higher current rating and the auxiliary winding is
in series with the auxiliary winding, and is connected to the ac supply through a series
controlled in such a way to keep the main and capacitor, to make its current lead the main
auxiliary winding currents in phase quadrature winding current by approximately 90° in phase [9].
to each other. And along with dynamic
There are various control techniques available for
capacitor a dynamic model is developed in
the speed control of induction motor, like voltage
stator reference frame (d-q). For proposed
frequency i.e V/f control technique, vector control,
configuration, performance of the SPIM is
torque control and several other [7].
studied using MATLAB, to demonstrate the
effectiveness of the dynamic capacitor. In this paper we will use a current control
technique for the control of single phase induction
Keywords: SPIM, Maximum Torque Operation,
motor. For this, the condition for maximum torque
Indirect Current Control.
of induction machine is applied. The condition is
that the current in main winding and that in
I. INTRODUCTION auxiliary winding should always be 900 apart. And
A single phase induction motor can be seen as two this we obtain by controlling the firing angle of
phase induction motor as it has main and auxiliary voltage source inverter [10].
winding which are in phase quadrature with each
other. The only difference between supply of a two II. SYSTEM DESCRIPTION
phase induction motor and single phase induction
The VSI is controlled to imitate a dynamic
motor is that, the input voltage applied to the stator
capacitor which is used for low cost open loop
winding of two phase induction motor is
control of SPIM through an indirect current control
independently controlled to obtain a two-phase
scheme. The maximum torque that is available
voltage supply.
from the machine is being extracted by the
Lately, there have been various techniques, to dynamic capacitor that is used in this system. There
develop model of a two phase induction motor. The is no necessity of much modification in the already
dynamics of SPIM have been studied and existing equipment for the indirect current control
developed with MATLAB software. scheme as it can be easily attached to the existing
system.
2014
c CIPECH14. 304
 III. MATHEMATICAL
MODELING OF SPIM
As mentioned earlier, most single phase induction
motors are constructed with two asymmetrical
windings, main and auxiliary winding which are
displaced 90 electrical degrees around motor stator.
The main winding carries a higher current rating,
and therefore auxiliary winding has fewer turns [5].
Fig. 2 shows the schematic view of a two phase
induction motor, illustrating that the auxiliary (q)
windings and main (d) windings are not identical
sinusoidal distributed windings, but are arranged in
space quadrature[6].
Fig 1: Schematic of a SPIM with a dynamic capacitor dr-axis

The phase quadrature in between the main field

winding and auxiliary field winding is maintained qr- axis qs-axis
by an indirect current control of VSI so as to obtain
the maximum torque from the motor. A d-q
stationary reference frame model of the drive with
the proposed control scheme is developed. A Aux
demonstration of the system’s improved Winding ds-axis
performance has been shown through Matlab’s Main
Simulation results.
Windin
αβ
The SPIM system uses an indirect current control
scheme to control VSI with a capacitor on dc bus to
emulate a dynamic capacitor [1]. A schematic Fig 2 : Asymmetrical two-phase induction motor.
diagram of a SPIM along with a dynamic capacitor .
is shown in the Fig 1. The DC capacitor is charged
initially and the voltage across it is maintained by Fig 3. and Fig 4 shows the equivalent circuits of
controlling the switching of VSI. Switching of VSI asymmetrical two-phase induction motor in
is also governed by magnitude and phase of stationary (d-q) reference frame.
auxiliary winding current. The value of capacitor is For the asymmetrical two phase induction motor
large enough to suppress the ac ripples on the dc- the dynamic model equation can be written as d-q
bus of VSI. The dynamic capacitor is connected in reference frame variables. The two phase Induction
series with an auxiliary winding of SPIM as shown Motor’s stator and rotor voltage can be expressed
in Fig. 1.The auxiliary winding current is in phase as follows [4]:
quadrature with the main winding current by an
indirect current control of VSI. The phase
quadrature is maintained irrespective to the load
torque and the machine speed, such that it always
generates the maximum electromagnetic torque
from the machine. The changes in the load torque
or the rotor speed of the machine vary the main
winding current; correspondingly control circuit
changes the switching pattern of VSI to control
auxiliary current in order to maintain the phase
quadrature in two winding currents. The indirect
current controlled VSI controls the auxiliary
winding current, which under any start or run
condition of SPIM yield the highest available Fig 3: Main winding in d-axis
output torque.

2014 Innovative Applications of Computational Intelligence on Power, Energy and Controls with their impact on Humanity (CIPECH) 305
 And the mechanical dynamics is modeled by the
equation

J d/dt (ωr) = Te - TL (14)

IV. CONTROL & SIMULATION

SCHEME
The main winding of SPIM is directly
Fig 4: Auxiliary Winding in q-axis connected to ac supply, whereas auxiliary winding
in series with the dynamic capacitor is connected
across ac supply [1]. The motor is connected to a
Figures 3 and 4.[8] Shows the equivalent circuit of fan load, where the load torque is proportional to
an asymmetrical two-phase induction motor in the the speed. In order to extract the maximum torque,
stationary (dq) reference frame the phase angle adjustment of the auxiliary winding
current is controlled through the VSI with a
Vsd = R sd. Isd + d/dt (ψsd) (1) capacitor on DC bus for the control of auxiliary
current, such that the two currents always remain in
phase quadrature. The main winding current is
Vsq= Rsq. Isq + d/dt( ψsq) (2) chosen as a reference. The VSI is controlled to
emulate a dynamic capacitor. The computation of
Vrd = 0= Rrd. Ird + d/dt (ψrd)+ aωrψrq (3) reference auxiliary winding current is based on the
fact that a dynamic capacitor is acting as an ideal
Vrq = 0= Rrq. Irq + d/dt (ψrq)-1/ aωrψrd (4) capacitor modifying only the reactive power
burden in terms of leading current. The real
component of current consists of the part
previously being computed in an auxiliary winding
The components of stator and rotor flux linkages
along with the component of the current required to
equations can also be expressed as:
maintain the DC bus of VSI. The main winding
current is transformed in real and reactive
ψsd = Lsd I sd + LmdIrd (5) components using abc-dq transformation. The
implementation of the scheme in MATLAB
ψsq = Lsq I sq + LmqIrq (6) environment is shown in Fig.5. The in-phase sine
and cosine components for phase voltage are
ψrd = Lmd I sd + LrdIrd (7) computed through the single-phase PLL. To obtain
the real and reactive components of the single-
phase main and auxiliary currents, each current is
ψrq = Lmq I sq + LrqIrq (8) phase displaced by 900 to emulate the stationary
reference frame. These components of currents in
Using equation (5)-(8), as for the stator and rotor stationary reference frame are transformed with
currents equations are given by: Park's transformation in dq-reference frame. The
real component of the auxiliary current is modified
Isd = (Lrdψsd- Lmdψrd) / (LsdLrd – L2md) (9) to accommodate the inverter losses by maintaining
the dc-bus constant. Further the magnitude of the
Isq =( Lrqψsq- Lmqψrq) / (LsqLrq – L2mq) (10) auxiliary current is computed by the
implementation of equations in dq frame as shown
in Fig.5. Knowing the magnitude of real and
Ird = (Lsdψrd- Lmdψsd) / (LsdLrd – L2md) (11) reactive components of the auxiliary current, the
magnitude of reference auxiliary current is
Irq = (Lsqψrq- Lmqψrq) / (LsqLrq – L2mq) (12) computed as per eq.(1) as depicted in Fig.5. This is
then multiplied by unit vector in quadrature with
The equation of electromagnetic torque produced the main winding current to get the reference
by the machine is then given by the equation: auxiliary winding current. The leading quadrature
component is obtained by inverse Park's
transformation of the main winding components,
Te= pp (LmqIsqIrd- LmdIsdIrq) (13) selecting the second output, which is lagging
behind the main winding current by 900 and

306 2014 Innovative Applications of Computational Intelligence on Power, Energy and Controls with their impact on Humanity (CIPECH)
inverting the waveform, thus the leading quadrature V. STARTING CHARACTERISTEICS
current unit template is obtained. OF SPIM WITH DYNAMIC
CAPACITOR UNDER LOAD
TORQUE=0.25 p.u

Fig 6: Main & Auxiliary Winding Currents

Fig 7: Electromagnetic Torque

Fig 8: Rotor Speed (rpm)

Fig 5: Simulink Model

The implemented scheme is shown in Fig.5. The

auxiliary winding current control loop is
implemented using standard hysteresis current
controller to switch the VSI to act as a dynamic
capacitor with indirect current control. The
dynamic capacitor thus operates the machine to run
for maximum available torque condition Fig 9: Main Winding Currents with Simulation time =0.1
irrespective to the nature of the load torque and the Sec
motor speed. Thus, an optimal torque may be
extracted from the motor.

2014 Innovative Applications of Computational Intelligence on Power, Energy and Controls with their impact on Humanity (CIPECH) 307
 REFERENCES
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