Estimating parameters of IM

< University Of Malaya Engineering Faculty (Ac Machine 2017) >
[ 1 ]
Khiri.A Elrmali khairi.elrmali@gmail.com
Abstract: The single phase equivalent circuit is largely used to model the three-phase induction motors in
steady-state operation and under sinusoidal balanced voltages. This present study discusses about the
development of a Simulink model of a three phase induction motor block which takes the inputs in form of the
test results obtained by the No-load , Blocked rotor & DC resistance tests and simulates to give the equivalent
circuit parameters as well as various operating characteristics . However, the determination of the circuit
parameters through standard method compared with alternative methods, i.e., non-standard tests.
Keywords-Induction motor, No-load test, Blocked rotor test, DC resistance test, MATLAB, Simulink
I-INTRODUCTION
Three-phase induction motors (TIM) operating
under steady-state regime are commonly modeled
using a per phase equivalent circuit, which enables
the calculation of quantities such as line current,
power factor, input and output power and
efficiency simply as a function of supply voltage,
frequency and slip. The circuit parameter values are
traditionally determined through tests described on
IEEE Standard 112 [1], such as no load and locked
rotor tests. Although such procedures provide
reliable results, their requisites may be impractical
in some places or situations. First, the necessary
instrumentation is not often available where the
motor is operating, thus demanding the
transference of the machine to a testing site or
laboratory. Second, the necessary interruption in
the operation of the motor is undesired in critical
industrial processes. Finally, the knowledge of the
circuit parameter values may be desired prior to
acquisition for simulation of even didactic purposes
Many methods and schemes are developed for
parameter estimation of large induction motors, but
these are generally not applied in smaller machines
due to limitations related to sensing device size and
economic considerations
There are various techniques to estimate the
induction motor parameters, such as:
1. Conventional techniques
2.Soft computing techniques
a)Fuzzy system
b) Artificial neural network
c) Genetic Algorithms
d) Particle swarm optimization(PSO)
e)Integration of above techniques
Some new methods are proposed in this study to
estimate motor parameters off-line from
manufacturer’s data
This paper presents a review on parameter
values estimation of the equivalent circuit of three
phase induction motors based on data provided by
manufacturers on catalogs, with special interest on
those dedicated to efficiency estimation result will
be compared to the simulation result. The dc test
no-load and blocked rotor tests simulation models
are developed by using MATLAB /Simulink and
Power System Block-set (PSB) The relevancy of
this study is by comparing the result obtained from
the laboratory with computer simulation will
facilitate in order to check the accuracy of virtual
induction motor's parameter
Estimating Parameters of a Three-Phase
induction motor using Matlab/Simulink

[ 2 ]
II-Model for the squirrel-cage induction motor
The steady-state operating characteristics of a
three-phase induction motor are often investigated
using a per-phase equivalent circuit as shown in
Figure 1
Fig(1). Per-phase equivalent circuit of an induction
motor
Where
R1- Stator Resistance
R2 - Rotor Resistance
X1 - Stator leakage reactance
X2 - Rotor leakage reactance
XM - Magnetizing reactance
S= slip
These all parameters of induction motor are
measured and given in Table III The values of
different parameters of 3-Ø squirrel cage induction
motor existing in Machine lab are tabulated below.
Table I: Input parameters for 3-phase squirrel cage
induction motor
INPUT QUANTITIES VALUES
Nominal power, L-L
voltage and frequency
4KW, 400V, 50Hz
Stator (Rs , Ls ) [1.405, 0.005839H]
Rotor (Rr, Lr) [1.395, 0.005839H]
Mutual inductance Lm 0.1722 H
Inertia, friction and
pairs of poles
0.0131 kg.m2
,
0.002985N.m.s 2

III-INDUCTION MOTOR TESTS
While selecting a proper motor it is necessary to
know the various operating characteristics as well
as the equivalent circuit parameters of the motor.
For this purpose following tests are conducted on a
three phase induction motor. No-Load Test
Balanced voltages are applied to the stator
terminals at the rated frequency with the rotor
uncoupled from any mechanical load.
Current, voltage and power are measured at the
motor input. The losses in the no-load test are
those due to core losses, winding losses, windage
and friction. Blocked Rotor Test The rotor is
blocked to prevent rotation and balanced voltages
are applied to the stator terminals at a frequency of
25 percent of the rated frequency at a voltage
where the rated current is achieved. Current,
voltage and power are measured at the motor
input.
In addition to these tests, the DC resistance of the
stator winding should be measured in order to
determine the complete equivalent circuit>
1) DC Test
The DC Test is performed to compute the stator
winding resistance RI. A dc voltage is applied to
the stator winding of an induction motor. The
resulting current flowing through the stator
winding is a dc current; thus there is no voltage
induced in the rotor circuit, and the motor
reactance is zero.
The stator resistance is the only circuit parameter
limiting current flow and can be computed as
ResistanceStator=R
ReadingAmmeter=I
ReadingVoltmeter=Vwhere
2
S
dc
dc
dc
dc
S
I
V
R 

[ 3 ]
Fig(2a)Set-up for measurement of stator resistance
Identify the way the motor block is connected.
• Star connected: Two links connect U
Remove the links and supply cables before
carrying out the test.
• Delta connected: Three links connect U
toW2, V1 to U2, W1 to V2. Remove the links
and supply cables before carrying out test.
Fig(2b)Experimental setup
The model shown in Figure (2b) is built to
represent then stator resistance measurements.
2) NO LOAD TEST
The no load test for an induction motor measures
the rotational losses of the motor and provides
information about its magnetization current. The
circuit diagram for the no load test is given below.
Fig(3a): Circuit Diagram for no load test
The equivalent input impedance is thus
approximately
ImpedanceloadNo=Z
phaseperPowerReactive=Qa
phaseperPowerReal=P
phaseperReadingAmmeter=Is
phaseperReadingVoltmeter=Vwhere
nl
2 ms
s
a
nl XX
I
Q
Z 
No-Load Test To perform the no-load test, the
model shown in Figure 4(b)
Fig(3b): No load test connection
3) locked-Rotor Test
The blocked-rotor test on an induction motor is
performed to determine some of its equivalent
circuit parameters . In this test, in order to prevent
rotation, the rotor is blocked.
The balanced voltages are then applied to the
stator terminals by using frequency which is 25
percent of the rated frequency and at a voltage
where the rated current is achieved.
Voltage, current, and power are measured at the
motor input.
The input power to the motor is given by
rs
s
locked
rs
s
lock
XX
I
Q
X
RR
I
P
R


2
4
1
2
The virtual blocked-rotor test can be carried out by
using the same Simulink model of no-load test.
However the only slightly difference is the inertia
and the friction parameters are reset to infinite
values (inertia=10000kg.m2
and friction=10000
N.m.s/rad)

[ 4 ]
Experimental setup
Calculate Machine Parameters
Rs can be obtained directly from DC-test
Then, Rr can be obtained from the locked-rotor
resistance
slockr RRR 
The leakage inductance can be obtained from the
locked-rotor inductance by assuming the ratio of
Xls to Xlr
If no information is given, it can be assumed that
Xls =Xlr
Hence
2
2
locked
ls
lslrlslocked
X
X
XXXX


Magnetizing inductance can then be obtained from
the no-load inductance
lsnlm XXX 
IV-SIMULINK IMPLEMENTATION
The parameters identified from experimental test
will then be validated by using virtual induction
motor from the MATLAB-Simulink. Table1 shows
the identified parameters used to dimension the
simulation machine
. 1) Virtual DC Test
The model shown in Figure 4(a) is built to
represent the stator resistance measurements.
Fig(4) :Simulink model of DC test
2) Virtual No-Load Test.
To perform the no-load test, the model shown in
Figure 4(b) is built.To simulate the model for no
load test, mechanical torque (Tm) is set to zero
Fig(5): Simulink model for no load test
Total 3ph real input power is measured, while
per-phase-based real and reactive power is
measured in simulation model
Fig(6): Measurement in simulation model

[ 5 ]
The simulation results for induction motor existing
in Electrical Machines lab are shown in fig
The stator and rotor current response of squirrel
cage induction motor is shown in Fig(7a). The
rotor current fluctuates between 0 and0.3 at 0.15
sec. the stator current is drawn about 4.5A at 0.2
sec
In Fig (7b) the time response of electromagnetic
torque and motor’s speed waveform.
Fig (7a) stator & rotor current of SCIM
Fig(7b):Simulation Results of Induction motor
3) Virtual Blocked-Rotor Test
The virtual blocked-rotor test can be carried out by
using the same Simulink model of no-load test.
However the only slightly difference is the inertia
and the friction parameters are reset to infinite
values (inertia=10000kg.m2
and friction=10000
N.m.s/rad) or To simulate the model for locked
load test, rotational speed (wm) is set to zero
Fig(8): Simulink model for locked load test
Total 3phase real input power is measured, while
per-phase-based real and reactive power is
measured in simulation model
Fig(9): Measurement in simulation model
V-RESULT AND DISCUSSION
In this section, the result of simulation tests are
presented in Table II where various quantities such
as voltage, current and power are required to
compute the equivalent motor parameters.
Table II: Results of simulation test of SCIM

[ 6 ]
for computing a particular electrical parameter
values of Rs, Rr, Xs, Xr and Xm. In simulating
models,it is necessary to have knowledge of the
methods which can be applied
Table III : Equivalent circuit parameter
determined by simulation and corresponding error
Based on the result obtained, the percentage error
from the result of SCIM simulation values are same
which means that it is accurate
circle diagram of induction motor
Electrical machines circle diagram is a graphical
representation of its equivalent circuit. This means
that whatever information can be obtained from the
equivalent circuit, the same can also be obtained
from the circle diagram. The advantages of a circle
diagram are its simplicity and quick estimation of
the machines operating characteristics.

VI-ESTIMATION OF PARAMETER
VALUES FROM CATALOG DATA
motor parameters are estimated from
manufacturer data with a numerical method. This
off-line parameter estimation method requires a
computer and necessary software to make these
calculations
To verify the proposed methods, no-load and
locked rotor tests are applied to SCM. parameters
are calculated from no-load and locked rotor tests
results and compared with estimated motor
parameters
In this method, approximate circuit model, is used.
Rated voltage, rated current, rated power factor,
output power, frequency, rotor speed and
measured stator resistance are used to estimate
motor parameters. Flow chart of this method is
seen in Fig
Fig(10): Flow chart of Method
Test Va(Volt) Ia(Amp) P(w) Q(AV)
DC 100 47.3 ---- ----
No load 233.8 4.086 152.3 948.4
Locked 231.7 51.45 7701 9418
Simulation
parameter
Estimation
parameter
Error %
Rs 1.405 1.409 0.28%
Rr 1.3195 1.395 5.7%
Ls 0.005839 H 0.005613H 3.87%
Lr 0.005839 H 0.005613H 3.87%
Lm 0.1722 H 0.16918 H 1.75%

[ 7 ]
Rotor copper losses can be calculated as in
equation
 
losscopperRotorP
losseswindageandfrictionp
:
1
3
.
.
2
RCL
wf
wfoutrr
where
s
s
PPRIPRCL








❶ Calculation of Rr
Referred rotor current can be written as
   22
rsrs
r
XXsRR
V
I



Assume that
  22
s 4RR& rrs XsXX 
If the assumptions seen above are valid, rotor
current and rotor copper losses formulas can be
rearranged as below
 
 2
2
2
2
2
3
sRR
RV
P
sRR
V
I
rs
r
RCL
rs
r







From above equation
a
acbb
RcbRaR
PRRV
s
PR
R
s
P
rrr
RCLsr
RCLs
r
RCL
2
4
0
03
2
2
2
222
2

















❷ Calculation of Rc
Core loss is calculated as in equation
 
fwRCLSCLloss
rs
s
SCL
outinloss
llin
PPPP
sRR
RV
P
PPP
IVP






con
SCL2
2
P
losscopperstatorPwhere
3
cos3


Rc is calculated as in equation
con
c
P
V
R
2
3 

❸ Calculation of Xm
It is assumed that imaginary part of the stator
current flows on magnetizing reactance.


sinI
V
Xm 
❹ Calculation of Xs
   
jBA
XXjsRRjXRZ rsrsmceq



1111
If tangent of load angle is written as in equation
 
 
  22
4
2tantan1
tan
srs
srs
cm XsRR
XsRR
RX
A
B








 



so stator leakage reactance can be calculated by
solving the roots of equation
 
  0tan
tan1
2
tan1
4 22




















sRR
sRR
RX
XX
RX
rs
rs
cm
ss
cm
The performance of the motors calculated from
estimated parameters and calculated parameters
from no-load and locked rotor tests results are
compared Name plate values of these motors
provided by the manufacturer and from the tests
results.
The 4kW, 50 Hz, 230/400 V power factor 0.9 and
efficiency=0.86, 4-pole star connected
three-phase squirrel-cage induction machine From
the name-plate values, the following nominal
quantities can be calculated
Efficiency
in
out
P
P

Active input power cos3 llin IVP 
slip
s
rs
N
NN
s



[ 8 ]
Torque at rated speed
r
m
e
w
P
T 
Rotor resistance
e
r
fT
spV
R


2
.2

Rotor time constant


tan2
1
fs
r 
Magnetizing inductance rrm RL 
 
 
 
  m
m
r
r
e
m
l
in
sin
LLs
RrRs
L
R
mNT
radw
A
kw
V
p
Ikwp
s
1.005.0
1671.0169.1143.0
sec143.0
84.25tan046.0502
1
169.1
71.26502
046.043400
.71.26
71.26
4000
sec/75.149
30
1430
54.7
39.0400
705.4
pf3
,,,,705.4
86.0
4000
deg84.259.0cos,,,046.0
1500
14301500
2
1



















 





The method only provides values for two
parameters.and values of errors was
m
r
L
R


%02.3100
1722.0
1670.01722.0
%2.16100
395.1
169.1395.1




VII. CONCLUSION
The objectives of this study have been met where
the induction motor model was successfully
developed using Matlab-Simulink and the accuracy
of the developed tests model's parameters can be
obtained from simulation. The result was good
correlation in term of relative percentage error
which indicates as the accuracy of virtual induction
motor's parameter.
We used three tests to determine the different
equivalent circuit parameters , which are the
resistance measurement to determine the windings
resistance Rs , the No load Test to determine Xm ,
and finally the Locked Rotor Test to Rr , Xs & Xr.
This concludes that the Matlab/Simulink is a
reliable and sophisticated way to analyze and
predict the behavior of induction motors
Second part non standard method is applied to
induction motor and estimation results are
compared with test results
The assessment is based on the closeness of the
resulting parameter values to reference values has
improved the accuracy of calculations for the
studied motor.

[ 9 ]
PARAMETER ESTIMATION CODES
References
[1] Munira Batool, 2Aftab Ahmad “ Mathematical modeling
and speed torque analysis of three phase squirrel cage
induction motor using Matlab /Simulink for electrical
machines laboratory” International Electrical Engineering
Journal (IEEJ) Vol. 4 (2013) No. 1, pp. 880-889
[2] Rahmatul Hidayah Salimin“ Parameter Identification of
Three-Phase Induction Motor using MATLAB-Simulink “
EEE 7th International Power Engineering and Optimization
Conference (PEOC02013). Langkawi. Malaysia. 3-4 June
2013
[3] Mayank pratap Singh“Parameter Estimation of Three
Phase Induction Motor: An Innovative Approach”
[4] K.K.Pandey*, P. H. Zope “ Estimating Parameters of a
Three-Phase induction motor using Matlab/Simulink “
International Journal of Scientific & Engineering Research,
Volume 4, Issue 12, December-2013
ISSN 2229-5518
[5] Çalar Hakki Özyurt“ Parameter and speed estimation of
induction motors from manufacturers data and
measurements” the Middle East Technical University
JANUARY 2005
[5] Juhamatti Nikander “ Induction Motor Parameter
Identification in Elevator Drive Modernization” helsinki
university of technology 7.1.2009
clear
clc
%========= input data
Rs=1.405;
V=326.6;
I=4;
f=50;
omga=2*pi*f;
pf=0.84;
p=4;
n=1430;
Pout=4000;
fi=acos(pf);
ns=120*f/p;
s=(ns-n)/ns;
Pfw=0.01*Pout;
Prcl=(Pout+Pfw)*s/(1-s);
%========= 1 calculation of Rr
a=Prcl/s^2;
b=(2*Rs*Prcl/s)-(3*V^2);
c=Prcl*Rs^2;
delta=b^2-4*a*c;
Rr=(-b-sqrt(delta))/(2*a)
%========= 2 calculation of Rc
Pscl=3*V^2*Rs/(Rs+Rr/s)^2;
Ploss=(3)*V*I*pf-Pout;
Pcore=Ploss-Pscl-Prcl-Pfw;
Rc=3*V^2/Pcore
%========= 3 calculation of Xm
Xm=V/(I*sin(fi))
Lm=Xm/omga
%========= 4 calculation of Xs
aa=4*(1/Xm-tan(fi)/Rc);
bb=2;
cc=((Rs+Rr/s)^2*(1/Xm-tan(fi)/Rc)-tan(fi)*(Rs+Rr/s));
delta=bb^2-4*aa*cc;
Xs1=(-bb+sqrt(delta))/(2*aa)
Ls=Xs1/omga

[ 10 ]

Estimating parameters of IM

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