A. Ansari et. al. / International Journal of Engineering Science and Technology
Vol. 2(5), 2010, 1260-1267
Mathematical Model of Asynchronous
Machine in MATLAB Simulink
1
A A Ansari, 2 D M Deshpande
(1Research Scholar, 2Presently working in M.A.National Institute of Technology, Bhopal,India)
Abstract— Different mathematical models have been used over the years to examine different problems associated
with induction motors. These range from the simple equivalent circuit models to more complex d,q models and abc
models which allow the inclusion of various forms of impedance and/or voltage unbalance. Recently, hybrid models
have been developed which allow the inclusion of supply side unbalance but with the computational economy of the
d,q models. This paper presents these models with typical results and provides guidelines for their use The dynamic
simulation of small power induction motor based on mathematical modelling is proposed in this paper. The dynamic
simulation is one of the key steps in the validation of the design process of the motor drive systems and it is needed
for eliminating inadvertent design mistakes and the resulting error in the prototype construction and testing. This
paper demonstrates the simulation of steady-state performance of induction motor by MATLAB Program Three
phase induction motor is modeled and simulated with SIMULINK model.
Keywords—Squirrel cage induction motor, modeling and simulation, MATLAB software, torque, speed.
1. INTRODUCTION
In recent years the control of high-performance induction motor drives for general industry applications and
production automation has received widespread research interests. Induction machine modeling has continuously
attracted the attention of researchers not only because such machines are made and used in largest numbers but also
due to their varied modes of operation both under steady and dynamic states. In an electric drive system the machine
is a part of the control system elements. To be able to control the dynamics of the drive system, dynamic behavior of
the machine need to be considered. The dynamic behavior of IM can be described using dynamic model of IM. The
dynamic model considers the instantaneous effects of varying voltages/currents, stator frequency and torque
disturbance. In this paper the dynamic model of IM is derived by using d and q variables in a synchronously rotating
reference frame.
Induction motor is simply an electric transformer whose magnetic circuit is separated by an air gap into two
relatively movable portions, one carrying the primary and the other the secondary winding. Alternating current
supplied to the primary winding from an electric power system induces an opposing current in the secondary
winding, when the latter is short-circuited or closed through external impedance. Relative motion between the
primary and secondary structure is produced by the electromagnetic forces corresponding to the power thus
transferred across the air gap by induction. The essential features which distinguish the induction machine from
other type of electric motors is that the secondary currents are created solely by induction, as in a transformer
instead of being supplied by a dc exciter or other external power sources, as in synchronous and dc machines.
2. Equivalent circuit- The parameters of equivalent circuit of Induction Machines are crucial when considering
advanced control techniques (i.e.Vector Control). Accidentally these are also uncertain parameters when the
machine is released from production. The most common ways, to manually determine induction motor Parameters
are to test motor under no-load and locked rotor conditions.
2.1 NO-LOAD TEST
The no-load test, like the open circuit test on a transformer, gives information about exciting current and rotational
losses. The test is performed by applying balanced rated voltage on the stator windings at the rated frequency. The
small power provided to the machine is due to core losses, friction and winding loses. Machine will rotate at almost
a synchronous speed, which makes slip nearly zero. This test is represented with an equivalent circuit in Figure
shown.
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A. Ansari et. al. / International Journal of Engineering Science and Technology
Vol. 2(5), 2010, 1260-1267
Values measured during this test are current and it’s angle with respect to
Known voltage. From this we can calculate total power supplied to the machine.
2.2 LOCKED ROTOR TEST
The locked rotor test, like short circuit test on a transformer, provides the information about leakage impedances and
rotor resistance. Rotor is at the stand still, while low voltage is applied to stator windings to circulate rated current.
Measure the voltage and power to the phase. Since there is no rotation slip, s=1 which gives us following equivalent
circuit.
3 Dqo transformation
In electrical engineering, direct–quadrature–zero (or dq0) transformation or zero–direct–quadrature (or 0dq)
transformation is a mathematical transformation used to simplify the analysis of three-phase circuits. In the case of
balanced three-phase circuits, application of the dqo transform reduces the three AC quantities to two DC quantities.
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Simplified calculations can then be carried out on these imaginary DC quantities before performing the inverse
transform to recover the actual three-phase AC results. It is often used in order to simplify the analysis of threephase synchronous machines or to simplify calculations for the control of three-phase inverters. The dqo transform
presented here is exceedingly similar to the transform first proposed in 1929 by R.H. Park. In fact, the dqo transform
is often referred to as Park’s transformation.
The dqo transform applied to three-phase currents is shown below in matrix form:
The inverse transform is:
4. DESCRIPTION OF POWER SYSTEM BLOCKSET
Matlab/Simulink is a systems simulator and unable to direct simulate electrical circuits Therefore for simulation of
electrical circuits power system block sets are used which incorporates libraries of electrical blocks and analysis
tools which are used to convert electrical circuits into Simulink diagrams. The electrical blocks are electrical models
such as electrical machines, current and voltage sources, and different electric elements, power electronic switches,
connectors, and sensors for measurement purpose. When the simulation starts Simulink use the Pm Blockset and
transfers the electrical circuit into a state–space representation with the initial conditions of state variables. The
actual simulation starts after this initial conversion, this allows the use of a wide variety of fixed step and variable
step algorithms available in Simulink. As variable time step algorithms are faster than fixed time step method
because the number of steps are less so these algorithms are used for small- and medium-size systems, And for large
systems containing a more number of states and/or power switches, a fixed time step algorithm is used. A Simulink
scopes can be used to display the Simulation results or these results can be sent to workspace during the simulation.
The variety of MATLAB functions and toolboxes are present for processing and plotting of waveforms from stored
data.
5. INDUCTION MOTOR MODEL IN SIMULINK
A generalized dynamic model of the induction motor consists of an electrical sub-model to implement the threephase to two-axis (3/2) transformation of stator voltage and current calculation, a torque sub-model to calculate the
developed electromagnetic torque, and a mechanical sub-model to yield the rotor speed.
Electrical sub-model of the induction motor the three-phase to two-axis voltage transformation is achieved using the
following equation.
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Where Vas, Vbs, and Vcs are the three-phase stator
voltages, while Vds and Vqs are the two-axis
components of the stator voltage vector .Fig shows
torque sub-model of induction motor In the two-axis
stator reference frame, the electromagnetic T is
given
by
Mechanical sub-model of induction motor from the torque balance equations and neglecting viscous friction, the
rotor speed ωo may be obtained as follows
Where J is the moment of inertia of the rotor and load and TL is the load torque
Stator current output sub-model
The stator current output sub-model is used to calculate the stator current amplitude according to the following
equation
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6. SIMULATION RESULTS
The induction motor chosen for the simulation studies has the following parameters: Rs=1.5 ohm
L s=0.012 H
Lm=0.1118 H
L r=0.1122 H J=0.054 kg m2
P=2
Ts=0.0546 nm
Tr=0.160 nm
The simulation results for developed torque, speed,Vsd,Vrd, Ird, Irq are presented.
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Torque developed
Speed RPM
Vsd & Vsq
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Speed RPM
Ird
Irq
5. CONCLUSIONS
SIMULINK is a powerful software package for the study of dynamic and nonlinear systems. Using SIMULINK, the
simulation model can be built up systematically starting from simple sub-models. The induction motor model
developed may be used alone, as in the direct-on-line starting example presented, or it can be incorporated in an
advanced motor drive system, e.g. field oriented control. The authors believe that SIMULINK will soon become an
indispensable tool for the teaching and research of electrical machine drives.
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