IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 50, NO. 6, DECEMBER 2003 1187
A Harmonic Elimination and Suppression Scheme for
an Open-End Winding Induction Motor Drive
Krushna K. Mohapatra, Student Member, IEEE, K. Gopakumar, Senior Member, IEEE,
V. T. Somasekhar, Student Member, IEEE, and L. Umanand
Abstract—In this paper, a harmonic elimination and suppres-
sion scheme for a dual-inverter-fed open-end winding induction
motor drive is presented. Two isolated dc-link sources with voltage
ratio of approximately 1:0.366 are required for the present drive.
These two isolated dc links feeding two inverters to drive the open-
end winding induction motor eliminate the triplen harmonic cur-
rents from the motor phase. The pulsewidth-modulation scheme
proposed enables the cancellation of all the 5th- and 7th-order
(
6 1
, where
=13 5 7
etc.) harmonic voltages and
suppresses the 11th- and 13th-order harmonic voltage amplitudes
in the motor phase voltage, in all modulation ranges. The next
higher order harmonics present in the motor phase voltages are
23rd, 25th, 35th, 37th etc. (
6
1
,
=46
, etc.). By using
triangular carrier wave and proper modulating waves for each
inverter, the open–end winding induction motor can be operated
in the entire modulation range, eliminating all the
6
1
harmonics (
=13 5 7
etc.) coupled with 11th and 13th
harmonic suppression. The proposed scheme also gives a smooth
transition to the overmodulation region.
Index Terms—Harmonic elimination, harmonic suppression,
open-end induction motor, pulsewidth-modulation (PWM) drive.
I. INTRODUCTION
I
N ORDER to reduce inverter switching losses and limit the
ripple currents in the motor phase multilevel inverters of the
type three-level, five-level, etc., [1]–[3] are preferred to the con-
ventionaltwo-levelinverter. However, thisincreasein number of
levelsenhances thepowercircuit complexitiesand inturn affects
the cost of the system dearly. Another interesting and suitable
topology called the open-end winding induction motor (IM)
drive are presently being studied for high-power applications
[4]–[7]. The neutral of the IM is disconnected in an open-end
winding drive and two separate three-phase inverters feed the
motor from bothends of the stator winding.The invertersare fed
from dc-link sources of half the magnitude, when compared to
thesame inconventionaltwo-levelinverters[4]. Inorder to avoid
the flowof triplen harmonic currents inthe motor phase,isolated
dc-link power sources or harmonic filters are required for these
drives[4]–[6].Similartoaconventionalmultilevelinverter,more
voltagespacephasor levelscanbe achievedby usingasymmetric
dc-link voltages for the two inverters [7]. In the present work,
a technique to eliminate and suppress certain harmonics in an
open-end winding induction motor drive is studied. There are
Manuscript received November 26, 2001; revised January 15, 2003. Abstract
published on the Internet September 17, 2003.
The authors are with the Centre for Electronics Design and Technology, In-
dian Institute of Science, Bangalore 560012, India (e-mail: kgopa@cedt.iisc.
ernet.in).
Digital Object Identifier 10.1109/TIE.2003.819670
well-established techniques to suppress and eliminate different
harmonics in normal IM drives [8]. By using notches at suitable
points in the square wave certain harmonics are eliminated from
the output [8]. Theseschemes requires extensive offline compu-
tations to determine the notches for different speed ranges. One
of the schemes uses staircase type modulating wave to suppress
the harmonics [9]. The disadvantages of all those schemes are
the need for lookup tables and large offline computation. This
paper presents a unique and simple scheme for an open-end
winding IM drive, where all the 5th- and 7th-order (
,
where
,etc.)harmonicsareeliminatedandthe11th-
and 13th-order harmonics are suppressed to a significant extent
for the entire modulation range. The other feature of the scheme
is that speed control using triangle carrier is possible with low
frequency harmonic elimination and suppression and with-
out resorting to very high-frequency pulsewidth-modulation
(PWM) switchings. A smooth transition to the overmodulation
region is also possible from the proposed drive scheme.
II. P
OWER CIRCUIT FOR THE DRIVE SCHEME
In an open-end IM drive the neutral point of the induction
motor is disconnected and two separate inverters feed the
three-phase windings of the motor from both ends [4]. Fig. 1(a)
shows the power circuit schematic of such a drive system. As
shown in Fig. 1(a), inverter-1 and inverter-2 feed the motor
from two isolated dc-link sources. The voltage ratio of the
two dc-link sources is 1 : 0.366. In the present case the dc-link
voltage of inverter-1 is V
and the dc-link voltage (Vdc) of
inverter-2 is 0.366 V
.
Fig. 1(b) shows the voltage space vector positions of the indi-
vidual inverters (inverter-1 and inverter-2). It can be noted that
the magnitude of voltage space vector of inverter-2 is 36.6% of
that of inverter-1 [Fig. 1(b)]. Fig. 2(a) shows the resultant space
vectors using only certain space vector combinations from in-
verter-1 and inverter-2. The voltage space vector amplitudes of
inverter-1 and inverter-2 depends on the inverters dc-link volt-
ages. To get a 12-sided voltage space vector combination, for
the vector combinations 13
,15,24,26,35,31,46,42,
51
,53,62,64[Fig. 2(a)], the switching vector magnitude
of inverter-2 should be 0.366 times that of inverter-1 [Fig. 2(b)].
This can be calculated from the geometry of Fig. 2(b). Since
the switching vector magnitude of a two-level inverter is pro-
portional to the value of its dc-link voltage, a dc-link voltage
ratio of 1 : 0.366 between inverter-1 and inverter-2 is needed
to realize a resultant 12-sided polygonal voltage space phasor
location of Fig. 2(a). The set of certain space vector combina-
tions of 13
,15,24,26,35,31,46,42,51,53,62,
0278-0046/03$17.00 © 2003 IEEE
1188 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 50, NO. 6, DECEMBER 2003
(a)
(b)
Fig. 1. (a) Schematic of power circuit for the proposed scheme. Vdc
=
0
:
366
V . (b) Vector diagrams of individual inverters.
(a)
(b)
Fig. 2. (a) Selected combinations of the vector positions from inverter-1 and
inverter-2. (b) Calculation of dc-link voltage ratio (k) for both inverters.
64 [Fig. 2(a)] makes a 12–sided polygon at their vertices with
a dc-link voltage ratio of 1 : 0.366 between the inverters. By
using vector positions at the vertices of the 12–sided polygon
(adjacent vectors are 30
separate), appropriately for PWM op-
eration, all the 5th- and 7th- (
, etc.)-order
harmonics can be cancelled from the motor phase voltage. This
set of 12 space vectors can be divided into two sets, one con-
sisting of vectors 13
,24,35,46,51,62and the other
(a)
(b)
Fig. 3. Individual voltage space-vector switching pattern and its duration
for inverter-1 and inverter-2 for a resultant 12–sided polygonal space vector
switching. (b) Pole voltage
(
V
;
V V
)
of inverter-1 and pole voltage
(
V
;
V V
)
of inverter-2.
consisting of vectors 15 ,26,31,42,53,64, separated by
30
. Therefore, if these two sets of vectors are switched (clock-
wise direction) with a 30
phase delay in time, the fundamental
component of both these sets add up because the fundamental of
the leading set of vectors move by 30
clockwise in space when
lagging set of vectors are switched. However, the 5th-order har-
monics (negative-sequence components
,
etc.) of the leading set of vectors move by 150 anticlockwise
in space when lagging set of vectors are switched, and comes
exactly in opposition to the 5th harmonics of the lagging set of
switching vectors and cancel each other. Hence, the 5th order
harmonics (
, etc.) of both sets of vectors
cancel each other. This is also true with the 7th-order harmonic
components (
, etc.) produced by the leading
set of vectors, which rotate by 210
clockwise and comes in
exact opposition to that of the lagging set and, hence, cancel
each other. Thus, a 30
vector disposition of switching vectors
[Fig. 2(a)], cancels all the 5th- and 7th-order (
, ,
etc.) voltage harmonics from the motor phase.
III. H
ARMONIC ANALYSIS FOR THE ( ,
ETC.)-ORDER HARMONIC ELIMINATION SCHEME
The individual inverter voltage space vector switching and its
duration for the two inverters are presented in Fig. 3(a). It can be
noted from Fig. 3(a) that for inverter-1 the 60
duration of indi-
vidual vectors from 1 to 6
are separated into 30 intervals as
MOHAPATRA et al.: HARMONIC ELIMINATION AND SUPPRESSION SCHEME FOR AN OPEN-END WINDING IM DRIVE 1189
(a) (b)
(c) (d)
(e) (f)
(g) (h)
(i)
Fig. 4. Relative position of different harmonics of the motor phase from both
inverter-1and inverter-2.(a)Fundamental. (b) 5th harmonics. (c) 7th harmonics.
(d) 11th harmonics. (e) 13th harmonics. (f) 17th harmonics. (g) 19th harmonics.
(h) 23rd harmonics. (i) 25th harmonics.
and . The corresponding space vector switching pattern for
inverter-2 (
of Fig. 3(a) is separated into 30 interval space
vector switching pattern and are shown in Fig. 3(a) as
and
. From Fig. 3(a) it can be seen that there is a 30 phase dif-
ference between the two sequences (i.e., between the switching
vector patterns
and of Fig. 3(a). Similarly the switching
vector pattern
leads by 120 from [Fig. 3(a)] and the
switching vector pattern
lags by 120 from [Fig. 3(a)].
The corresponding pole voltage waveforms for the two inverters
are presented in Fig. 3(b).
The phasor diagram of the fundamental and different har-
monic components of switching vector patterns
, , and
of Fig. 3(a) are shown in Fig. 4. There is a phase separa-
tion of 30
between the vectors and of Fig. 4(a). Fig. 4(a)
alsoshowsthat the fundamental component
of the switching
vector pattern
of Fig. 3(a) leads by 135 from the reference
point (i.e., vector
leads by 120 [Fig. 4(a)] and funda-
mental component
of the switching vector pattern of
Fig. 3(a) lags by 135
from the reference point (i.e., vector
lags by 120 [Fig. 4(a)]. Fig. 4(b) shows the phasor diagram
of the 5th harmonics. The 5th harmonic component
of the
switching vector pattern
of Fig. 3(a) leads by 75 (15 5)
from the reference point [Fig. 4(b)] and 5th harmonic compo-
nent
of the switching vectorpattern of Fig. 3(a)lags by 75
(15 5) from the reference point [Fig. 4(b)]. The 5th harmonic
component
of the switching vector pattern [Fig. 3(a)]
lags by 45
(135 5 lead) from the reference point [Fig. 4(b)]
and 5th harmonic component
of the switching vector pattern
of Fig. 3(a) leads by 45 (135 5 lag) from the reference
point [Fig. 4(b)], or, in other words,
leads by 240 (120 5
600) from and lags by 240 (120 5 600) from
[Fig. 4(b)]. Table I gives the relative angular positions (Fig. 4),
of the different harmonics phasors of the switching vector pat-
terns of
, , and of Fig. 3(a), with respect to the
reference point. Because inverter-1 and inverter-2 are feeding
from opposite ends, the space vectorof inverter-2 should be sub-
tracted from that of inverter-1 to get the resultant motor phase
voltage vector. As shown in Fig. 4 and Table I it can be noted
that all the
, etc.-order harmonics of the pole
voltage of inverter-1 and inverter-2 support each other, and all
the
, , etc.-order harmonics of the pole volt-
ages of both inverters (inverter-1 and inverter-2) oppose each
other. Hence, by selecting the dc-link voltages of both inverters
in proper ratio (i.e., the dc-link voltage of inverter-1
V to
the dc-link voltage of inverter-2 (Vdc) equal to 1 : 0.366) all the
, etc.-order harmonics can be cancelled from
the motor phase voltage. The calculation of amplitude of dif-
ferent harmonics are given below.
A. Amplitude of Fundamental and all the
,
etc., Harmonics (1st, 25th, 49th, etc.)
The dc-link voltage of inverter-2,
(1)
Now, the fundamental component [
and of Fig. 4(a)]
of sequence
and of Fig. 3(a), can be written in relation
to that of sequence [Fig. 3(a)]
and as
(2)
where
and [Fig. 4(a)] are the fundamental components of
pole voltage of inverter-1 for sequences
and [Fig. 3(a)].
The combination of vector patterns
and of Fig. 3(a) gener-
ates square-wave pole voltages [Fig. 3(b)] with the fundamental
component
(square wave) is [Fig. 4(a)]
V (3)
Hence, total fundamental voltage
for the motor phase
(resultant of both the inverters) voltage is
(4)
1190 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 50, NO. 6, DECEMBER 2003
TABLE I
P
HASOR POSITIONS OF DIFFERENT HARMONICS OF SWITCHING VECTOR PATTERNS OF THE TWO
INVERTERS
Substituting (2) and (3) in (4),
V
V (5)
Similarly, all the
, etc., harmonics amplitudes
in motor phase voltage can be calculated and is found tobe equal
to
V , etc.
B. Amplitude of all the
, etc., Harmonics
(5th, 29th, 53rd, etc.)
Total 5th harmonic amplitude of the motor phase voltage can
be calculated from Fig. 4(b) (Table I)
(6)
Similarly, using the phasor diagram of Fig. 4 all the
,
etc., harmonics amplitudes in motor phase voltage can
be calculated and are found to be equal to zero.
C. Amplitude of all the
, etc., Harmonics
(7th, 31st, 55th, etc.)
Total 7th harmonic amplitude (from both the inverters) can
be calculated from Fig. 4(c) (Table I)
(7)
and all the
, etc., harmonics amplitudes in
motor phase voltage can be calculated in a similar way and are
found to be equal to zero.
D. Amplitude of all the
, etc., Harmonics
(11th, 35th, 59th, etc.)
Total 11th harmonic amplitude (motor phase voltage) from
Fig. 4(d) and Table I is
(8)
The amplitude of the 11th harmonic component of the square
wave [combination of vector pattern
and of Fig. 3(a)] is
V (9)
From (8) and (9) the total 11th harmonic for the motor phase
voltage [for the switching pattern of Fig. 3(a)] is
V
V (10)
and all the
, etc., harmonics amplitudes
in motor phase voltage can be calculated to be equal to
V , etc. In a similar way ampli-
tudes of all the other harmonics in the motor phase voltage can
be calculated for the inverters switching pattern of Fig. 3(a)
(Fig. 4 and Table I), and the calculated values are given in
Table II.
It can be noted that all the
, etc.-order
harmonics in the motor phase voltage are totally absent and all
the
, etc.-order harmonic amplitudes are 1.267
MOHAPATRA et al.: HARMONIC ELIMINATION AND SUPPRESSION SCHEME FOR AN OPEN-END WINDING IM DRIVE 1191
TABLE II
H
ARMONIC AMPLITUDES OF MOTOR PHASE VOLTAGE
(a)
(b)
Fig. 5. (a) Inverter-1 vector switching patterns (
I
and
I
) and Inverter-2 vector switching patterns (
II
and
II
) for the scheme of 11th and 13th harmonic
suppression with 15
phase shift. (b) Pole voltage waveforms for Inverter-1 and Inverter-2 with the inverter switching patterns of (a) for the scheme of 11th and
13th harmonic suppression with 15
phase shift.
times (0.807/0.637) amplitude of the same order harmonic of a
conventional inverter with square-wave pole voltage waveform
with a dc-link voltage of V
IV. SUPPRESSION OF 11TH- AND 13TH-ORDER HARMONICS
For an open-end winding drive with two inverters of dc-link
voltage ratio of (1: 0.366) all the (
, etc.)
harmonics get cancelled for a switching pattern shown in
Fig. 3(a). In Fig. 3(a) the switching pattern of inverter-1 is
separated into
and (with an angular difference of 30 ),
and the switching pattern of inverter-2 is separated into
and
(with an angular difference of 90 between them). Keeping
the same symmetry in switching pattern [Fig. 3(a)], of both the
inverters, the 11th- and 13th-order harmonics can be suppressed
in the individual inverters by adding additional notches in the
individual inverter pole voltages. For the new pole voltage
waveforms [Fig. 5(b)] the individual inverter vector switching
pattern
and of inverter-1, and and of inverter-2
are presented in Fig. 5(a). The vector switching pattern
again consists of two similar patterns separated by 30 and the
pattern
of inverter-1 is similar to the switching pattern ,but
delayed by 15
. This 15 separation is responsible for suppres-
sion of 11th and 13th harmonics in the inverter-1 pole voltage
waveform. The corresponding vector switching pattern
and of inverter-2 are also shown in Fig. 5(a). The leading
