Simulink Representation of Induction motor
Reference Frames
Khalaf Salloum Gaeid, Hew Wooi Ping
Haider A.F.Mohamed
Dept. of Electrical Engineering
University of Malaya
Lembah Pantai, 50603 Kuala Lumpur
salim_hazim2000@perdana.um.edu.my
Department of Electrical & Electronic Engineering.
The University of Nottingham Malaysia Campus
Jalan Broga, 43500 Semenyih, Selangor Darul Ehsan,
Malaysia.
Abstract-The simulation of induction motor frames are
presented in this paper. The voltage, torque and current
waveforms are included in the comparison of the induction
motor frames. The main objective of the paper is to propose a
Simulink building block model. Students will be able to resolve
problems relating to mathematical reference frame
transformations will be able to apply reference-frame theory to
the analysis of induction motors, will be able to predict motor
drive performance using simulation software (Matlab
Simulink).
I.
INTRODUCTION
Induction motors are so common in industry that in many
plants no other type of electric machine can be found. A
dynamic model of the machine subjected to control must be
known in order to understand and design vector controlled
drives [1]. Space vectors of three-phase variables, such as
the voltage, current, or flux, are very convenient for the
analysis and control of induction motors [2]. Various types
of AC induction motors are available in the market;
different motors are suitable for different applications.
Although AC induction motors are easier to design than DC
motors, the speed and the torque control in various types of
AC induction motors require a greater understanding of the
design and the characteristics of these motors [3].
Simulink is selected since the simulation power system
module is useful for simulating drive systems. Depending
on in which coordinate system the current control task is
performed; the classical systems can be grouped in three
categories.
Stator Reference Frame
It is called stator reference frame because the d-q axis do
not rotate [4]. Stationary frame current control, when the
current command is transformed from the rotor flux
reference frame into stationary coordinates, and the current
control task is performed in stationary coordinates. In this
paper stator reference frame are obtained when wk =0 and
θk=0 as it can be seen in the Fig. 7.
Rotor Reference Frames
The induction motor model in the rotor flux reference
frame when d-q axis rotate at rotor speed w =wk and θk=wo
(where wo
is integration of wm and wo is the base
frequency).
Synchronous Reference Frame
Synchronous reference frame occur when the d-q axis
rotate at synchronous speed and when the measured stator
current is transformed into the rotor flux reference frame
and the current control task is performed by virtually
rotating controllers in the rotor flux aligned coordinate
system. Synchronous frame obtained when wm=ws and θk
= wo where θk is integration of (ws) [5],[6].The reliability
and cost are always an important issue in the market,
therefore the Simulink implementation of the induction
motor is very important to study the performance without
real implementation of the motors. It is well known that the
behavior and operation of electric machines and drives are
often difficult topics for students to comprehend and
instructors to teach. Classical methods of teaching machines
often focus on steady-state machine performance or
reduced-order models, such as the classical voltage-behindreactance models of synchronous machines, for describing
dynamic performance [6]. It should be noted that the model
neglects core loss as well as friction and windage loss [8].
G. Skibinski R et al. proposed a reflected wave building
block model that uses existing software on the market, is
simple, computationally fast, easily configurable, and
reasonably accurate and allows investigation with wide
variation of system parameters [8].The performance of the
direct torque control (DTC) method has been demonstrated
by simulations performed using a versatile simulation
package, Matlab/ Simulink. Several numerical simulations
have been carried out in a steady state and transient
operation on a speed control mode was proposed by H.F.
Abdul Wahab et al [10]. The rotor magnetic field vector is
not tied to the rotating mechanical rotor, but slips with
respect to it. Reference frames can help in understanding
motor reference-frame theory [11]. The computer program
has been designed as a complementary tool for the teaching
of the induction motor dynamics and it is now used for
student laboratory. It is supposed to work both as a teaching
aid and a learning tool [12]. A modular Simulink
implementation of an induction machine model is described
in a step-by-step approach [13]. Matlab simulation and
comparison between FOC (Field Orientation Control) and
DTC control schemes are presented by J.C Trounce. [14].
An artificial neural network is used to predict the operating
voltage and frequency when the load torque and speed are
changed. Simulation and experimental results are shown to
validate the scheme [15].
II.
SYSTEM MODELING
fr=(Lm+Lr1)Ir+LmIs
(16)
The basic mathematical relationships of this paper are
derived from the induction motor equivalent circuit shown
in Fig.1:
K1, K2, k3, k4 are gains
Vs=RsIs+dλs/dt+wkM..λs
(1)
ieDS=cos(wt)ias+cos(wt-2π/3)ibs +cos(wt-4π/3)ics
(17)
Vr=Rr Ir +dλr /dt +(wk –wm) M..λr
(2)
ieQS=-sin(wt)ias-sin(wt-2π/3)ibs -sin(wt-4π/3)ics
(18)
Where
wm and wk are the rotor speed and d-q reference frame
speed respectively
Ias=Icos(wt+θ)
(3)
Ibs=Icos(wt-2π/3+θ)
(4)
Ics=Icos(wt+2π/3+θ)
(5)
λs =LsIs +Lm Ir
(6)
λr =LmIs +Lr Ir
(7)
Where
Ls=Ls1+Lm
(8)
Lr =Lr1 +Lm
(9)
The torque of the induction motor can be represented as
in the next formula
Te = (3/4) p (λdsIqs-λqsI ds)/wm
(10)
Equations (1-18) are used to implement the induction
motor, which is composed of the (stator, rotor, current flux
transformation and the mechanical relationship).
Fig.2.
shows the general blocks of induction motor separately.
The flux current transformation block is shown in the Fig. 4,
which can be implemented by using. (6),(7),(8),(9),(13) and
(14). Fig.4 represents the mechanical relationships of the
induction motor based on (11). Fig.5. represents the stator of
the induction motor based on (1). Fig.6. represents the rotor
of induction motor according to the (2). Fig.7 can be
obtained by collecting all these blocks.
.
Fig. 2. General blocks of the induction motor
Taking note of Newton's second law of motion, one obtains
dwm/dt=(p/2j)Te-(f/j)wm-(p/2j)Tl
(11)
wm=dθm/dt
(12)
This can useful to implement the mechanical relationship
of the induction motor as shown in Fig.4
Fig. 3. Flux to current transformation block
Fig. 1. Induction motor equivalent circuit
The stator and rotor currents can be written as follows
Is=k1 fs-k 2fr
(13)
Ir=k3 fr-k4 fs
(14)
Where
fs=(Lm+Ls1)Is+LmIr
(15)
Fig. 4. Mechanical relationships block
algorithms applicable for similar systems of different size
[18]. The three-phase sinusoidal excitation can be adjusted
in both amplitude and frequency. The Simulink
implementation of the I.M can be seen in the Fig.7
The results obtained from the simulation are shown in
Figs. (8, 9 and 10) for the currents, voltages and torques
Fig. 4. Induction motor block (stator and rotor)
Fig. 5. Stator block implementation
Fig. 7. Implementation of the I.M [4]
Fig. 6. Rotor block implementation
cu rre n t
10
III.
SIMULATION AND EXPERIMENTAL RESULTS
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Fig. 9. Stator reference frame
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torque
The induction motor is, of course, an electromechanical
device so the model also requires expressions for the
electromagnetic torque and the speed of the machine.
Equation (10) expresses the electromagnetic torque in terms
of the flux linkages, and (11) determines the rotational
speed from the machine torque, load torque, and moment of
inertia. In both of the following equations, P is the number
of poles. To eliminate the time-varying inductances, the
equations are frequently transformed to q-d-0 variables in
the arbitrary reference frame. For this simulation, we used a
stationary reference frame, which has the advantage of
eliminating some terms from the voltage equations.
Induction motor d-q model in the arbitrary reference frame.
This subsystem must be masked and the motor parameters
must be specified in its dialog box. The inputs of the
subsystem are d-q axis voltages (vqs, vds), load torque (Tl)
and the speed of the arbitrary reference frame (ω) while the
outputs are d-q axis current (iqs, ids), electromagnetic
torque (Te) and the rotor mechanical speed ωm. Build the
induction motor d-q model using the equivalent circuit
given in Fig. 1. The zero-axis equivalent circuit can be
neglected since this is a 3-phase balance system. The
torque-speed relationship is described by (11) and the
electromagnetic torque generated by the motor can be
calculated according to (10) [17]
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voltage
Simulations have been performed in Matlab/Simulink to
verify the feasibility of voltages, torque and current of
induction motor. The induction machine is modeled in
vectorized form in conformity with state vector formulation.
All quantities in the simulation are given in normalized or
per unit (p.u.) values, which is common practice in electrical
engineering. p.u. notation makes design and control
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Fig. 10. Synchronous reference frame
According to the Figures above it must be pointed out that,
in the steady state, induction motors operate only on the
negative-slope part of the torque curve, that is, below the
critical slip. When the load increases, the resultant
imbalance of the motor and load torques causes deceleration
of the drive system. This results in an increased motor
torque that matches that of the load, ensuring stability of the
operation. Conversely, when the load decreases, the motor
accelerates until the load torque is matched again. Fig. 6.
Shows the stator phase currents as a function of time during
the free acceleration of the three-horsepower motor. Their
frequency is essentially constant at 50 Hz, but the amplitude
is much larger than rated current until the machine reaches
breakdown torque. At start, the rotor currents have a 50 Hz
frequency, but the frequency drops as the motor accelerates,
reaching very low frequencies as the motor nears
synchronous speed. Of course, once the motor reaches
synchronous speed there is no relative motion between the
rotor squirrel-cage bars and the rotating magnetic field.
Figures 8, 9 and 10 show the torque, current and voltage
responses obtained from the simulation of the induction
motor Fig.7. It must be said that all three different
references (stator, rotor and synchronous) gave the same
simulated results in the steady state. The validity of the
motor model is corroborated.
IV.
CONCLUSION
In this simulation, the system is assumed to be initially inert
so that all the initial conditions are zero. The motor is
started at no load at rated voltage and frequency. After
reaching steady-state conditions, the input voltage is
suddenly reduced in amplitude and frequency and soon after
full load is applied as a step function. The voltages and
currents can be observed on the scopes in both stator and
rotating frames. Note that, in steady-state, the stator currents
show up at stator frequency in the stator frame, as dc
quantities in the synchronous frame, and at slip frequency in
the rotor frame. The torque and speed time evolutions do not
depend on the choice of reference frame. This approach
provides a powerful design tool because of the ease of
observing the effects of parameter modifications and of
changes in system configurations and control strategies.
Using SIMULINK software, each block of the model may
be connected and modified easily
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
.[18]
[19]
Antoni Arias Pujol" Improvements Indirect Torque Control of
Induction Motors “November 2000.
Andrzej M. Trzynadlowski "Control of Induction Motor"Academic
Press 2000.
Rakesh Parekh" AC Induction Motor Fundamentals"2003 Microchip
Technology Inc.
R.J. Lee, P. Pillay and R.G Harley" D,Q Reference Frames for the
Simulation of Induction Motor "Electric power system research
8(1984/85) pp15-26.
M. Riaz" Simulation of electric Machine and Drive Systems"
University of Minnesota, 2001.
Zsolt Beres and Peter Vranka" Sensorless IFOC of Induction Motor
with Current Regulators in Current Reference Frame" IEEE
Transactions on Industry Applications, vol. 37, no. 4, July/August
2001.
Steven Pekarek and Timothy Skvarenina" ACSL / Graphic Modeler
Component Models for Electric Power Education" IEEE 1998.
P. Krause, O. Wasynczuk, and S. Sudhoff, "Analysis of Electric
Machinery," IEEE Press, Piscataway, NJ, 1995.
G. Skibinski R, Kerkman D, Leggate J, Pankau D. Schlegel"
Reflected Wave Modeling Techniques for PWM AC Motor Drives"
IEEE 1998.
H.F. Abdul Wahab and H. Sanusi" Simulink Model of Direct Torque
Control of Induction Machine" American Journal of Applied Sciences
5 (8): 1083-1090, 2008.
Dennis L. Feucht “Magnetic Reference-Frames" 2001.
G. D. Marques" A Computer Application For Teaching and Learning
On The Induction Motor Dynamics “1999.
Ozpineci, B. Oak Ridge “Simulink implementation of induction
machine model - a modular approach" IEEE Volume: 2, on pp 728734 2003.
J.C Trounce, S.D. Round and R.M Duke "Comparison by Simulation
of Three Level induction Motor Torque Control Schemes for Electric
Vehicle Applications" powerelectronics/documents/IPEC2001.
A. K. Sharma, R. A. Gupta, Laxmi Srivastava" Performance of ANN
Based of Indirect Vector Control Induction Motor Drive" JATIT,
2007.
www.mathwork.com
Bin Wu" Advanced Electromechanical Systems “ELE847 Course
Notes 2007
Ratna Chitroju, Teknikringen" Vector Control of Induction Motor"
Electrical Machines and Drives (EJ2200) Project Work.
K. L. Shi, T. F. Chan and Y. K. Wong" Modeling of the threephase Induction Motor using SIMULINK" IEEE 0-7803-3946-07