IEEE Transactions on Power Electronics Volume 14 issue 1 1999 [doi 10.1109 63.737589] Suresh, G.; Toliyat, H.A.; Rendusara, D.A.; Enjeti, P.N. -- Predicting the transient effects of PWM voltage wave

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 14, NO. 1, JANUARY 1999 23
Predicting the Transient Effects of PWM Voltage
Waveform on the Stator Windings of
Random Wound Induction Motors
G. Suresh, Student Member, IEEE, Hamid A. Toliyat, Senior Member, IEEE,
Dudi A. Rendusara, Student Member, IEEE, and Prasad N. Enjeti, Senior Member, IEEE
Abstract—In this paper, the effect of pulsewidth modulation
(PWM) voltage waveform on the voltage distribution among
the stator windings of random wound cage induction motors
is studied. First, a method of estimating the high-frequency
distributed-circuit parameters of the motor using finite-element
analysis is described. From these parameters, an equivalent
circuit is formed with the windings represented by partially dis-
tributed and partially lumped parameters. Using this equivalent
circuit, the voltage distribution among the turns and coils of
the motor are simulated using the SABER simulation package.
Through simulation, the effect of rise time of the PWM wavefront
on the voltage distribution is studied, and it is shown that the
rise time of the wavefront has influence on the additional voltage
stress on the line-end coil. In order to validate the simulation
procedure adapted, the simulation results are compared with
experimental results.
Index Terms— , induction motor, PWM drives, transient
effects, voltage stress.
I. INTRODUCTION
WHEN INDUCTION motors are fed from pulsewidth
modulation (PWM) inverter power supplies, the stator
winding is subjected to high-voltage stresses caused by the
train of wavefronts in the PWM voltage waveform. The volt-
age distribution among the turns and coils is highly nonlinear
because of the high of the wavefront, and this often
results in higher voltage stresses in the first few turns of the
line-end coil. These voltage stresses are several times higher
compared to stresses caused by sinusoidal waveforms. The
voltage withstanding capability of the commonly used magnet
wire is worsened when waveforms with high ’s and
fast switchings are imposed on the windings. This causes
premature failure of insulation and, hence, results in forced
outage of the drive system.
Most of the low- and medium-size induction motors are
fed from PWM voltage source inverters employing insulated
gate bipolar transistor (IGBT) switches because of several
advantages. With the advancement in power semiconductor
technology, it has been possible to keep the switching times
as low as 0.1 s. Although the inverter switching losses are
Manuscript received March 18, 1997; revised May 14, 1998. Recommended
by Associate Editor, A. Goodarzi.
The authors are with the Department of Electrical Engineering, Texas A&M
University, College Station, TX 77843-3128 USA.
Publisher Item Identifier S 0885-8993(99)00284-7.
reduced by keeping the switching time low, the insulation
integrity is affected because of the detrimental effects of the
sharp wavefronts on the motor windings. This problem is
worsened when the motor is connected to the inverter through
feeder cables. Depending on the surge impedances of the cable
and motor, the motor terminal voltage can be much higher than
the dc bus value and sometimes can even double because of
voltage reflections.
Many papers discuss the impact of PWM waveforms on
the motor windings [1]–[8]. In [1] and [2], the impact of
PWM waveforms on the random wound induction motors is
analyzed. References [3] and [4] give methods of simulating
the voltage distribution among the turns of random wound
machines using equivalent circuits. The parameters used in
the equivalent circuits are based on terminal measurements.
Reference [6] considers the effect of feeder cable and presents
a simulation procedure to compute machine terminal voltage
transients. References [3]–[5] and [7]–[12] explain the voltage
reflections caused at the motor terminals due to long feeder
cables and a few practical ways of suppressing the terminal
voltage transients. However, the distributed-circuit parameters
of the individual turns would be needed if the voltage dis-
tribution among the turns and coils needs to be estimated.
In the past, field analysis results have been reported for
studying high-frequency field effects in form wound induction
motor parameters for surge studies [13]–[16]. In this paper,
a method of deriving these parameters for a random wound
induction motor using finite-element analysis is presented.
Random wound motors differ significantly from form wound
motors because of their constructional differences. In form
wound motors, each turn in a coil occupies the same relative
position within the slot unlike random wound motors. Using
the method described, it is possible to compute the parameters
corresponding to different rise times of the PWM wavefront.
With the partially distributed surge equivalent circuit, SABER
[23] simulation is performed in order to estimate the voltage
distribution among the turns and coils of the motor. In order
to validate the method proposed, the simulation results are
compared with experimental results.
The organization of the paper is as follows. Section II
describes the problem under consideration in detail. Section III
details the method of estimating the high-frequency param-
eters of the motor winding. In Section IV, the details of
the partially distributed equivalent circuit model used for
0885–8993/99$10.00 1999 IEEE

24 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 14, NO. 1, JANUARY 1999
simulation are presented. Simulation and experimental results
are presented and discussed in Section V. A brief review
of recently published literature on the practical remedies is
given in Section VI. Section VII presents the summary and
conclusions.
II. DESCRIPTION OF THE PROBLEM
In order to estimate the voltage distribution among the coils
of the stator during a typical PWM wavefront, it is necessary
to use a high-frequency distributed-circuit model for the stator
winding [15]. This is mainly because of the high-frequency
content of the wavefront with sharp rise time. The machine
behavior at such high frequencies (which are in the order of
megahertz) corresponding to fast switching transients is totally
different than at power frequency, and, hence, calculating
the distributed parameters is very difficult. For example, at
megahertz-range frequencies corresponding to switching times
in the order of fractions of microseconds, the steel laminations
act like flux barriers, and, hence, most of the flux produced
by the windings will be leakage fluxes. The high-frequency
eddy currents induced in the rotor confine the flux to the
air gap itself, and, hence, there will be no flux penetration
across the air gap. Since the magnetic steel laminations act
as flux barriers, the flux lines are confined to the stator slot
portion itself, as will be shown later. It is also essential to
represent the winding by its distributed equivalent circuit since
the wavelength of the high-frequency traveling wave is very
small compared to that of the power frequency.
The distributed-circuit parameters to be calculated for the
individual turns are the self-inductance and resistance of each
turn, mutual inductances between turns within the same slot,
turn-to-ground capacitances, and turn-to-turn capacitances [3],
[4], [7], [8], [15], [16]. The distributed parameters of the
individual turns depend on the slot geometry and also on
their relative position within the slot. For example, a turn
located near the slot wall will have a higher turn-to-ground
capacitance compared to a turn located in the middle of
the slot. A turn which is located in the middle of the slot
will have a lesser turn-to-ground capacitance because of the
larger separation between the turn conductor and ground.
Furthermore, the conductors around the turn located in the
middle of the slot act as a shield between the turn and ground.
These factors complicate the computation of the parameters.
Another difficulty with random wound machines is that the
relative positioning of the individual turns in different slots
may not be the same.
In order to overcome these difficulties, finite-element anal-
ysis techniques are used to compute the circuit parameters of
the coils even at high frequencies. A single-slot model of the
machine will be enough to calculate all the parameters required
for simulation if it is assumed that the relative positioning of
the individual turns within the slots remains the same in a
given phase which is a reasonably good assumption.
The following are the advantages of using finite-element
analysis.
• Actual material properties can be defined for computing
the parameters.
• High-frequency field effects on the parameters can be
considered.
• The exact geometry of the slot can be modeled for
computing the parameters.
The details of the finite-element model along with the
procedure of computing the various parameters are presented
in the following section.
III. FINITE-ELEMENT ANALYSIS OF THE SINGLE-SLOT MODEL
For computing the equivalent circuit parameters of the coils,
a single-slot model of the cage induction motor was used. The
motor used for analysis in the present work has the following
specifications: 3 HP, 3 phase, 4 pole, 60 Hz, and 230/460 V.
The stator has 36 slots and has a single-layer random winding
with 6 coils per phase, each coil having 54 turns.
The Ansoft [24] package is used for performing finite-
element analysis of the single-slot model which basically
consists of one stator slot pitch with all the turns placed
randomly to simulate random winding. The slot wall insulation
and individual turn insulation are also modeled in order to
compute the capacitance values accurately. Although the flux
lines do not penetrate the air gap, the rotor slot portion is also
modeled. The package computes the field quantities per unit
length of the single-slot model assuming symmetry in the axial
direction. There are different solvers available in the package
for performing electric and magnetic field analysis. From the
finite-element analysis results, the impedance and capacitance
matrices are obtained which are then used for forming the
equivalent circuit. The details of the finite-element analysis
are explained in the following sections.
A. Computation of the Inductance and Resistance Matrices
For computing the inductance and resistance matrices, an
eddy-current analysis option available in the Ansoft package
is used. Once the geometry of the single-slot model is created,
an eddy-current analysis solver is used. The setting up of
the eddy-current analysis includes setting up the excitation,
defining boundary conditions, etc. When eddy-current analysis
is used, the package automatically defines each conductor as
a current source. The only boundary condition used is balloon
boundary condition in which a surface far away from the slot
model is set to zero magnetic vector potential. The frequency
for which the eddy-current analysis has to be computed is
also defined in the analysis.
The main advantage of using an eddy-current solver is
that the effects of time-varying currents in parallel conductors
are considered in the analysis. Furthermore, the eddy-current
effects caused in the conductors at high frequencies are taken
care of. Time-varying currents flowing in a conductor produce
a time-varying magnetic field in planes perpendicular to the
conductor. In turn, this magnetic field induces eddy currents
in the source conductor and in any other conductor parallel to
it. The eddy-current field solver calculates the eddy currents
by solving for and in the field equation
(1)

SURESH et al.: PREDICTING THE TRANSIENT EFFECTS OF PWM VOLTAGE WAVEFORM 25
where is the magnetic vector potential Wb/m, is the elec-
tric scalar potential, is the relative magnetic permeability,
is the angular velocity at which all quantities are oscillating,
is the conductivity, and is the relative permittivity.
The simulator computes the impedance matrix in two steps.
First, it solves for the inductance matrix associated with the
model. Then it solves for the resistance matrix and then
computes them to form the impedance matrix using the
relationship
(2)
The individual elements in the impedance matrix are com-
puted as follows. The simulator generates an eddy-current field
solution for each conductor in the model. The first turn is set
to 1-A current in the first solution with all the other turns set
to zero current. In the second solution, only the second turn is
set to 1-A current with all the other turns set to zero current.
After each field solution, the inductance and resistance are
computed using the following relations:
(3)
(4)
where is the energy stored in the magnetic field (J), is
the ohmic loss (W), and is the peak value of the current
(amp) (in this case, the peak value of the current is 1 A).
After each field solution, the solver calculates the self-
inductance of the conductor which was assigned 1-A current
during the analysis. Also, the mutual inductances of the
conductor with all the other conductors are computed. Sim-
ilarly, the resistance terms are also computed after each field
solution. The final output of the eddy-current analysis is a
54 54 impedance matrix. Thus, the complete impedance
matrix required for the circuit simulation is obtained in one
eddy-current analysis.
The flux plot obtained from the eddy-current analysis shows
some interesting results of the high-frequency behavior of the
machine. The flux plot obtained from the eddy-current analysis
is shown in Fig. 1. The flux plot shows that the flux lines
are confined to the slot portion itself, and the flux lines do
not penetrate the steel laminations because of high-frequency
effects. Also, there is no flux passing through the air gap to
the rotor. The impedance matrix also shows that the different
turns have different impedances depending on their relative
positioning within the slot.
B. Computation of the Capacitance Matrix
The capacitance matrix is also computed in a similar way.
For computing the capacitance matrix, the Ansoft electrostatic
analysis package is used. During the electrostatic analysis,
each conductor is defined as a voltage source and assigned
1 V with all the other conductors set to 0 V. A boundary
value condition is used for electrostatic analysis in which the
stator laminations are defined to be at zero electric potential.
The electrostatic field simulator computes the static electric
fields arising from potential differences and charge distri-
Fig. 1. Flux distribution in the slot during eddy-current analysis.
butions. The field simulator solves for the electric potential
in the field equation derived from Gauss’ law and is
given by
(5)
where is the charge density.
After each field simulation, the capacitance values as-
sociated with the conductor which was assigned 1 V are
computed, which includes the turn-to-ground and turn-to-turn
capacitances between the turn being excited and all the other
turns. Thus, 54 different solutions are required to obtain
the capacitance matrix. However, one electrostatic analysis
performs all the simulations required automatically. After the
electrostatic analysis is complete, a capacitance matrix of order
54 54 is obtained. The capacitance between conductors “ ”
and “ ” is calculated as follows:
(6)
where is the energy in the electric field associated with
flux lines that connect charges on conductor “ ” to those on
conductor “ ” From the analysis results, it was found that the
turn-to-ground capacitance values in the capacitance matrix
are all not equal because of their relative positioning.
For computing the capacitance matrix, electrostatic analysis
is performed because of the fact that the variation of the
capacitance terms with frequency is negligible unlike the
inductance and resistance values [4], [15].
This completes the computation of the equivalent circuit
parameters of the stator winding which are used for simulating
the voltage distribution. In the present work, it is aimed at ex-
plaining a method of using finite-element analysis techniques
to estimate the high-frequency circuit parameters of the turns
in the stator winding. Using this method, the circuit parameters
are computed at two different frequencies and later used

26 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 14, NO. 1, JANUARY 1999
Fig. 2. Partially distributed equivalent circuit of the line-end coil.
for circuit simulation. The parameters of the winding which
correspond to the rise time of the wavefront for which analysis
has to be done were used for simulating the circuit. For
example, when it is desired to simulate the voltage distribution
with a 0.2- s wavefront, the surge equivalent circuit is formed
with parameters corresponding to 5-MHz frequency and so on.
The details of circuit simulation performed to determine the
nonlinear voltage distribution are explained in the next section.
IV. SIMULATION OF SURGE EQUIVALENT CIRCUIT
In the previous section, the methods of estimating the high-
frequency parameters of the turns and coils were explained.
The procedure adopted to form a partially distributed equiv-
alent circuit from these parameters in order to estimate the
voltage distribution among the turns and coils is presented in
this section.
The motor used for analysis has 36 stator slots with 6 coils
per phase, each coil having 54 turns, two groups of 3 coils each
connected in parallel. Although it is desired to represent all the
turns in the stator phases with distributed parameters, it is not
practical to implement it, and, hence, a simplified equivalent
circuit as suggested in [4] is used for simulation. It is well
known that during the PWM wavefront, the first few turns
in the line-end coil will have higher voltage stress compared
to the other turns. Hence, for circuit simulation, the first five
turns of the line-end coil are modeled with their distributed
parameters. The other turns in the first coil as well as the other
coils in the phase are represented by their lumped parameters.
For obtaining the lumped parameters, the diagonal terms in
the impedance matrix and capacitance matrix are considered,
and the nondiagonal terms are ignored.
Fig. 2 shows the distributed-circuit model of the line-end
coil. The other coils in the phase are modeled with their
lumped parameters. The parameters used in the circuit are
turn resistances, turn self-inductances (mainly leakage), turn-
to-turn mutual inductances, turn-to-ground capacitances, and
turn-to-turn capacitances. In order to simulate a typical PWM
wavefront, a step voltage source is used as input to the
equivalent circuit, and the circuit is simulated using SABER
package on a SUN platform. The rise time of the step voltage
source can be changed to any desired value depending on the
rise time of the actual wavefront in the inverter output.
A. Voltage Distribution Among the Machine
Winding with 0.2- s Rise Time
For simulating the voltage distribution among the turns of
the winding corresponding to 0.2- s rise time, the circuit
described earlier was used. A rise time of 0.2 s is chosen
since the switches in the inverter used to perform experiments
have a turn-on time of 0.2 s. The first few turns of the phase
A windings are represented by their distributed parameters
with the remaining turns in phase A modeled by lumped
parameters. The phase B winding is modeled wholly by its
lumped parameters. It is assumed that only phases A and
B are conducting, and, hence, phase C is not modeled. All
the parameters are obtained from the finite-element analysis
results which were performed at 5-MHz frequency. In SABER,
the rise time of the step voltage source is set at 0.2 s and
its amplitude at 295 V which is the dc bus voltage, and
the transient analysis option is used to obtain the voltage
distribution. The transient analysis results include the voltage
distribution among all the turns and coils modeled.
B. Voltage Distribution Among the Machine
Winding with 0.1- and 1- s Rise Time
Simulations of the transient voltage distribution which cor-
respond to a rise time of 0.1 and 1 s were also carried

SURESH et al.: PREDICTING THE TRANSIENT EFFECTS OF PWM VOLTAGE WAVEFORM 27
Fig. 3. PWM wavefront model used for simulation (rise time of the wave-
front s).
out in the same way as that of the previous case mainly to
study the effect of rise time of the wavefront on the voltage
distribution. The same equivalent circuit is used for this
case also. The parameters used in the simulation are derived
from the finite-element analysis results performed at 1-MHz
frequency corresponding to 1- s rise time. While performing
analysis for 0.1 s, the parameters obtained at 5 MHz are
used assuming these parameters to be almost equal to 10
MHz. Detailed discussion on the simulation results and the
comparison with the experimental results are presented in the
next section.
V. DISCUSSION AND COMPARISON OF
SIMULATION AND EXPERIMENTAL RESULTS
In this section, the results obtained through simulation are
discussed and compared with the experimental results. The
details of the induction motor used to obtain the experimental
results are given in the Appendix. The IGBT switches used in
the inverter have a typical rise time of 0.2 s. As described in
the previous section, the first set of simulations is carried out
with rise time equal to 0.2 s in order to make comparison
with experimental results.
A. Comparison of Simulation and Experimental
Results with 0.2- s Rise Time
Fig. 3 shows the PWM wavefront used for simulation. The
dc bus voltage for this operating condition is 295 V. Fig. 4
shows the simulated voltage drop across the line-end coil. It
should be noted that the voltage reaches a peak value of 105
V and oscillates before settling down at around 50 V. Fig. 5
shows the corresponding experimental results. The upper trace
in Fig. 5 shows the inverter output voltage which is applied
to the motor through a short cable. Trace 2 shows the motor
terminal voltage, and trace 3 shows the line-end coil voltage
which corresponds to the result shown in Fig. 4. Comparing
these two results, it should be noted that the oscillations seen
in the simulation results are not so much pronounced in the
experimental results. A close agreement between simulation
Fig. 4. Simulated voltage drop across the line-end coil (rise time of the
wavefront s).
Fig. 5. Experimental results of a PWM induction motor drive with a short
cable between the inverter and motor. Trace 1: inverter output voltage. Trace
2: motor terminal voltage. Trace 3: line-end coil voltage. Trace 4: Turn 1
voltage in the line-end coil.
and experimental results cannot be expected anyway because
of the complex nature of the problem and also the assumptions
made in simulation and in the formation of the equivalent
circuit. Interestingly, the peak values of the two voltages,
viz., simulated and experimental line-end coil voltages, match
reasonably well which is important from the motor design
point of view. Also, the two waveforms take around the same
time to settle down to the final steady-state value.
Fig. 6 shows the simulated voltage wave form across Turn
1 of the line-end coil with 0.2- s rise time. In Fig. 5, Trace 4
shows experimentally recorded voltage drop across Turn 1 of
the line-end coil which corresponds to Fig. 6.
B. Simulation Results with 0.1- and 1.0- s Rise Time
As described in the previous section, the circuit simulations
were carried out with 0.1- and 1- s rise time for the step