Circuits and Systems, 2013, 4, 16-19 Published Online January 2013 (
EMTP Induction Motor Model from Modal Measurements
for Inverter Surge Analysis
Asha Shendge, Naoto Nagaoka
Department of Electrical and Electronics Engineering, Doshisha University, Kyoto, Japan
Received September 14, 2012; revised December 4, 2012; accepted December 11, 2012
The over-voltage phenomenon is usually described using the traveling wave and reflection phenomena in variable speed
drive system. A voltage pulse, initiated at the inverter, being reflected at the motor terminals due to a mismatch between
the surge impedance of the motor and the cable. In this paper, resistance, inductance and capacitance of the cable and
the motor windings are obtained experimentally by modal measurements and suitable models are developed to match
the experimental results by considering resonance in the motor winding. This paper emphasize on Induction motor
model using the theory of natural modes of propagation. The developed model validity is investigated for inverter surge
Keywords: Induction Motor; Modal Measurements; Inverter Surge; EMTP
1. Introduction
An induction motor (IM) is an asynchronous AC ma-
chine that consists of a stator and a rotor. An induction
motor is widely used because of the rugged construction
and moderate cost. Recently, the variable speed drives
produced mostly consist of brushless motors and power
converters. In many cases the squirrel cage induction
motor is used and it is controlled by a voltage fed PWM
inverter. The motor is controlled via the PWM inverter
by keeping the amplitude and frequency of the reference
(sinusoidal) signals constant according to the desired
output speed. Thus, maintaining constant magnetic flux
in the motor. For micro-surge due to reflection and re-
fraction at motor terminal voltage peaks are developed. It
is necessary to have accurate induction motor model in
consideration of frequency dependent effect as motor
resistance, inductance and capacitance are frequency
dependent due to transient phenomena.
There are several studies carried out by different au-
thors to simulate peak voltages at motor terminals due to
inverter surge [1-5]. In this paper three phase induction
motor model is developed based on natural mode meas-
urements in steady state. The analytical calculations are
carried out using theory of resonance in motor winding.
The modal to phase transformation are implemented us-
ing a computational tool such as Maple, which provides
template, a convenient method to analyze matrix calcula-
tions. Thus suitable induction motor model is developed
for Electro-Magnetic Transient Program (EMTP). Motor
peak voltage that is surge voltage is proposed as input
step waveform. The validity of model is checked by ac-
tual transient measurement of inverter surge phenomena.
It is observed the model gives good agreement results for
inverter surge application.
2. Experimental Set Up
A 3 phase, 2.2 Kw, 50 Hz, 200 Volts, 9.2 Amp, 1430
RPM squirrel cage induction motor is used for analysis.
Motor stator is connected in Delta connection. Motor is
squirrel cage means rotor winding is shorted. Steady state
measurements are carried out on de-energized condition
for mode-0, mode-1 and mode-2. The current distribution
for all propagation modes is as shown in Figure 1. An
impedance analyzer is used as input source (Agilent
model 4294A 40 Hz - 110 MHz). Before measurements
calibration is done according to the manufacture’s manual.
2.1. Measured Results
Figures 2(a)-(c) are represents mode-0, mode-1 and
(a) mode-0 (b) mode-1 (c) mode-2
Figure 1. Current distribution of three propagation modes.
opyright © 2013 SciRes. CS
mode-2 measured impedances, respectively.
From measured waveform for mode-1 and mode-2 it is
observed, the response is same as RLC parallel resonance
and mode-0 response is same as discharging of capacitor.
2.2. Analytical Calculation
The analytical calculations are carried out based on well
known theory of resonance. For RLC parallel circuits at t
resonant condition, impedance is purely resistive i.e.
RZ (1)
Resonant frequency
in rad/sec is given by Equa-
tion (2)
(a) mode-0
(b) mode-1
(c) mode-2
Figure 2. Measured impedance of motor.
Quality factor Q is given by Equation (4)
QRCL (3)
Solving Equations (2) and (3), we obtained capaci-
tance as below
Once capacitance is calculated inductance can be ob-
tained by Equation (3) as R and Q are known from
measured waveform. Similarly, resonant frequency, and
bandwidth B in rad/m can be calculated easily from
and 2
B (5)
and 22
Also quality factor is given by
Using Equations (5) and (6) inductance and capaci-
tance are calculated from measured data at resonant fre-
quency. Tables 1 and 2 represent the respective parame-
From measurement of mode-0 capacitance is 3.5 nF.
The capacitance and inductance obtained in Tables 1
and 2 and mode-0 capacitance are used to plot against
total frequency range. The Figure 3 shows the reason-
able agreement some error observed due to approxima-
tion error.
2.3. Equivalent Motor Model
Figure 4 illustrates a model circuit of an induction motor
obtained from modal measurements. Resistance of in-
ductor is very small. It is approximately equal to Rdc
therefore it is neglected. From Figure 4 circuit it can be
observed three motor winding resistance Rm, inductance
Table 1. Mode-1.
ω0 (rad/m) ω1 (rad/m) ω2 (rad/m) R ()
509471.7 358686.8613 701894.9448 4617.94
B (rad/m) Q L (Henry) C (Farad)
343208.1 1.48444 0.006106124 6.30949E10
Table 2. Mode-2.
ω0 (rad/m) ω1 (rad/m) ω2 (rad/m) R ()
509471.7 358686.8613 701894.9448 4617.94
B (rad/m) Q L (Henry) C (Farad)
343208.1 1.48444 0.006106124 6.30949E10
Copyright © 2013 SciRes. CS
Figure 3. Comparison of measured and analytical value.
Figure 4. Simple model circuit for an induction motor.
Lm, capacitance Cm are in parallel and three motor body
to ground capacitance Cg.
3. Electro Magnetic Transient Program
(EMTP) Simulation [6]
Modal decomposition is given by the following matrices
 
 
 (9)
 (10)
A wave propagation characteristic of multi-phase sys-
tem is determined using the theory of natural modes of
propagation. Generally, a symmetrical three-phase im-
pedance and admittance matrices are transformed using
the current transformation matrix
T and voltage
transformation matrix
131 121
1301 ,1
131 121
12 13
0 23
12 13
 
 
 
 
 
From impedance, winding resistance and inductance
can be calculated while from admittance capacitances
can be calculated. R, L and C are incorporated in EMTP
line constant routine. No load, resistance is converted to
load condition by taking into account 6% core and me-
chanical loss. Table 3 represents the R, L and C obtained
in phase domain calculated using above transformation.
3.2. Motor Model Validity for Inverter Surge
Figure 5 illustrates an experimental circuit of measuring
a surge in an inverter circuit connected by a cabtyre cable
to a 3-phase squirrel cage induction motor (2.2 kW, 50
Hz, 200 V, 9.2 A, 1430 RPM). A 7.5 A/3.0 kVA PWM
inverter (Type VFS7-2015P, Toshiba Corporation) is
used as a 200 V, 60 Hz source. Terminal R, S and T
represents three phase supply voltage. Converter is rep-
resented by D1 - D6 diodes, capacitor C is DC link and
inverter transistors are represented by Sw1 - Sw6 switches.
Measurements are carried out for investigation of peak
voltage between motor phases Figure 6 illustrates a
model circuit for an EMTP simulation of an inverter
surge represented in Figure 5. The model developed in
this paper is used for inverter surge analysis. For the in-
verter surge simulation; the inverter is modeled by two
current sources with 0.1 internal resistance. A three
core cabtyre cable is represented by EMTP Semlyen’s
distributed parameter line model [9]. The peak voltages
between phases are measured.
3.3. Simulated Result
Figure 7 shows a comparison of a measured result and a
simulation result by EMTP Semlyen’s distributed line
model including the frequency-dependent effect of the
cabtyre cable. It is observed in the figure that the simula-
tion results agree rather well with the measured result.
Table 3. Phase domain parameters.
Rm L
m C
m C
600 9.22 mH 76.40 µF 1.04 nF
Figure 5. Experimental circuit.
Figure 6. EMTP representation.
Copyright © 2013 SciRes. CS
Copyright © 2013 SciRes. CS
Figure 7. Surge voltage at motor terminal.
Thus, it should be clear that a transient associated with a
cabtyre cable can be simulated well by proposed method
in co-operation with Semlyen’s line model of the EMTP.
4. Conclusion
In this paper, based on natural theory of modes meas-
urements are carried out on induction motor in steady
state condition. Based on modal measurements induction
motor model is developed for it’s used in Electro Mag-
netic Transient Program. The validity of model is invest-
tigated by practical inverter surge measurements. It is
observed using developed model the surge voltages at
motor terminals can be represented accurately. This model
can be used for different switching surge simulations.
5. Acknowledgements
The financial support provided by Japanese Government
(MONBUKAGAKUSHO: Ministry of Education, Cul-
ture, Sports, Science and Technology—MEXT) Scholar-
ship has made this research possible and it is greatly ap-
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