Conventional space vector pulse width modulation based asymmetrical dual inverter configuration produces high common mode voltage (CMV) variations. This CMV causes the flow of common mode current, which adversely affects the motor bearings and electromagnetic interference of nearby electronic systems. In this study, a simple and generalized carrier based pulse width modulation (PWM) technique is proposed for dual inverter configuration. This simple approach generates various continuous and discontinuous modulating signals based PWM algorithms. With the application of the discontinuous modulating signal based PWM algorithm to the asymmetrical dual inverter configuration, the CMV can be reduced with a slightly improved quality of output voltage. The performance of the continuous and discontinuous modulating signals based PWM algorithms is explored through both theoretical and experimental studies. Results show that the discontinuous modulating signal based PWM algorithm efficiently reduces the CMV and switching losses.
I. INTRODUCTION
With the advancement in power semiconductor technology, induction motors receive considerable importance in variable speed drive applications. Threephase voltage source inverter (VSI) is widely used power electronic converter for induction motor drive applications. Various PWM techniques have been employed to control the output voltage and frequency of VSI
[1]

[7]
. Among these methods, the continuous PWM (CPWM) (e.g, space vector PWM) and discontinuous PWM (DPWM) techniques display satisfactory performance in terms of DC bus utilization, switching losses, and current ripple
[1]

[7]
. However, these techniques exhibit high common mode voltage (CMV), which is the potential difference between the neutral point of induction motor and ground.
Correspondingly, high switching frequency is employed in VSI to increase its efficiency and reduce its current ripple and filter size. Nonetheless, at high switching frequencies, the sharp edges of CMV cause common mode current, which adversely affects motor bearings
[8]
,
[9]
. This particular effect can be reduced actively and passively. Passive methods use passive components such as inductors, transformers, and other passive elements
[10]
,
[11]
. Nevertheless, these passive elements increase the cost, size, and weight of inverter. Active methods involve multilevel inverter topologies
[12]

[14]
and modified pulse patterns for VSI topologies
[15]

[17]
.
The modified pulse pattern methods for the conventional twolevel VSIs apply the active zero state PWM
[15]

[17]
and near state PWM
[16]
,
[17]
methods to reduce CMV without using any extra components. These methods reduce CMV with a slightly increased ripple in line current because of the opposite pulses in line voltage.
The multilevel inverter topologies, such as diode clamped inverter
[12]
and Hbride inverter topologies
[13]
,
[14]
, moderately reduce CMV with an output voltage of improved quality. However, the operation of these topologies requires clamping diodes, voltage balancing capacitors, and separate DC sources, which increase the cost and weight of the multilevel inverter with reduced efficiency. Moreover, these conventional multilevel inverter topologies have a few drawbacks, including neutral point fluctuations
[18]
and complex control algorithms. To overcome these drawbacks, the dual inverter topology, a new multilevel inverter topology, was introduced for induction motor drive applications
[19]

[26]
. In this inverter configuration, the neutral point of squirrelcage induction motor is removed, and a total of six stator terminals are available as shown in
Fig. 1
. Correspondingly, an open end winding induction motor is realized.
Open end winding induction motor.
The open end winding induction motor is fed by two 2level inverters from both ends as shown in
Fig. 2
. This setup is called a dual inverter configuration, which is popular in high power applications (e.g., submarine, electric vehicles, and electric locomotives). This particular configuration can be classified into symmetrical
[20]
and asymmetrical
[21]
configurations (
Fig. 2
) based on the application of input DC voltage. In these configurations, two 2level inverters feed the induction motor from both ends to generate 3 and 4level output voltages with the same number of switching devices
[21]
.
Dual inverter configurations.
The related literature has discussed various modulating strategies for controlling output voltage. However, these methods cannot reduce the CMV variations. Therefore,
[25]
presented a modified circuit topology for symmetrical dual inverter configuration. Nonetheless, this topology eliminates CMV with output voltage of poor quality. Consequently, many researchers
[26]
have tried to reduce CMV by improving the quality of output voltage with different converter topologies, which use several switching devices and complex control algorithms.
In this study, simple scalar based control algorithms are presented for fourlevel asymmetrical dual inverter configuration to reduce CMV with an output voltage of good quality. In particular, this study analyzes the conventional CPWM algorithm for asymmetrical dual inverter topology. A discontinuous modulating signal based PWM algorithm is then proposed to reduce the CMV. The proposed approach also reduces the switching losses of inverters. To validate the proposed method, experimental studies are performed, and the results are presented.
II. ASYMMETRICAL DUAL INVERTER CONFIGURATION
The asymmetrical dual inverter circuit configuration shown in
Fig. 2
(b) is a combination of two 2level inverter topologies. Input voltages 2V
_{dc}
/3 and V
_{dc}
/3 are applied to invertersI and II, respectively, to achieve the fourlevel output voltage. In this case,V
_{ao}
,V
_{bo}
, and V
_{co}
are the pole voltages of inverterI, V
_{a'o'}
, V
_{b'o'}
, and V
_{c'o'}
are the pole voltages of inverterII, V
_{aa'}
, V
_{bb'}
, and V
_{cc'}
are the effective phase voltages, and V
_{ab}
, V
_{bc}
, and V
_{ca}
are the line voltages. The potential V
_{oo'}
is the CMV. For an input DC voltage of 2V
_{dc}
/3, inverterI generates a pole voltage of 0 or 2V
_{dc}
/3. InverterII yields a pole voltage of 0 or V
_{dc}
/3for an input voltage of V
_{dc}
/3. Substituting these individual pole voltages in (1) yields the effective pole voltages. The switching pattern and effective pole voltages generated by the asymmetrical dual inverter configuration are given in
Table I
.
EFFECTIVE POLE VOLTAGE CALCULATION
EFFECTIVE POLE VOLTAGE CALCULATION
Table I
indicates that the dual inverter configuration can produce a fourlevel pole voltage, and it is therefore called as a fourlevel inverter topology. The expression of CMV (V
_{oo'}
) can be derived from the pole voltages as shown below.
To control the output voltage and frequency, PWM techniques are employed for the asymmetrical dual inverter configuration. In general, PWM techniques can be implemented based on scalar and space vector approaches
[6]
. This study mainly focuses on scalarbased PWM techniques.
III. CONVENTIONAL CONTINUOUS MODULATING SIGNAL BASED SCALAR PWM ALGORITHM
The control signals of the scalar PWM algorithm are generated by comparing the reference signals (modulating signals; V
_{r}
) with a high frequency carrier signal (triangular; V
_{t}
).
Fig. 3
illustrates that the intersection points define the switching instants. A scalar PWM technique generally provides freedom for the selection of reference
[7]
and carrier signals
[15]
. Therefore, for the threephase 2level inverter topology, three reference signals are compared with a common carrier signal to generate the control signals.
Realization of scalar PWM.
From the concept of scalar PWM techniques for multilevel inverters
[14]
, N1 level shifting carrier signals are required to generate the control signals for an Nlevel inverter topology. As the proposed asymmetrical dual inverter configuration is capable of generating fourlevel output voltage, threelevel shifting triangular signals are required (
Fig. 4
).
Realization of scalar PWM technique for the asymmetrical dual inverter configuration.
The comparison of reference signals with threelevel shifting triangular signals as given in
Table II
generates the control signals.
Table II
presents the switching logic for phasea of invertersI and II.
GENERATION OF SWITCHING LOGIC
GENERATION OF SWITCHING LOGIC
In the same manner of generating control signals for the threephase dual inverter configuration, three sinusoidal reference signals, each with a120°phase displacement, are compared with commonlevel shifting triangular signals. The mathematical expressions for the three reference signals are given in (3).
With the isolation of DC link voltages of each inverter (the isolation of terminals O and O' shown in
Fig. 2
(b)), the triplen harmonic current path does not exist in the threephase dual inverter configuration. In such condition, the potential V
_{OO'}
can be freely varied by injecting a zerosequence signal to the commended reference signals given in (3). The addition of zerosequence signal improves the DC bus utilization and influences the harmonic distortion. The zerosequence signal and resultant modulating signals can be obtained with the following equations
[7]
:
where V
_{max}
and V
_{min}
are the maximum and minimum of commended reference signals given in (3) at a given instant, respectively.
In (4), the zerosequence signal is generated based on the voltage magnitude test. Constant a
_{o}
lies between 0 and 1.
The block diagram shown in
Fig. 5
illustrates the scalar PWM algorithm for the dual inverter configuration. With proper selection of the zerosequence signal (for different values of a0 between 0 and 1) various continuous and discontinuous modulating signals are generated
[7]
. These modulating signals are compared with high frequency level shifting triangular signals to generate the pulses for invertersI and II. The most commonly used zerosequence signal (with a
_{o}
=0.5) and the resultant continuous modulating signals are shown
Fig. 6
.
Block diagram illustrating the scalar PWM technique for the dual inverter configuration.
Modulating and zerosequence signals.
The use of the continuous modulating signal with common level shifting carrier signals produces a conventional continuous modulating signal based PWM technique as discussed in
[21]
.
IV. PULSE PATTERN OF PWM TECHNIQUES
The threephase continuous modulating signals shown in
Fig. 6
demonstrate that within the modular range of 0°≤ωt≤60°, V
^{*}
_{a}
, V
^{*}
_{c}
, and V
^{*}
_{b}
have maximum , minimum, and intermediate values, respectively. For every 60°, these values vary. Therefore, the entire modular range is divided into six intervals. All these intervals are symmetrical; thus, the discussion is limited to the modular range of 0°≤ωt≤60°. To generate the pulse pattern, the modulating signals are compared with level shifting carrier signals (i.e., V
_{t1}
,V
_{t2}
,, and V
_{t3}
) as shown in
Fig. 4
. In the modular range 0°≤ωt≤60°, V
^{*}
_{a}
has a maximum instantaneous value and is compared with V
_{t3}
. Contrarily, V
^{*}
_{c}
has a minimum instantaneous value and therefore intersects with V
_{t1}
.V
^{*}
_{b}
has an intermediate value in the modular range 0°≤ωt≤60°, but its value is near to V
^{*}
_{c}
and V
^{*}
_{a}
at the start and end points, respectively. Hence, at the beginning of interval (0°≤ωt≤600) V
^{*}
_{b}
is compared with V
_{t1}
, at the ending of interval with V
_{t3}
and for a part of time with V
_{t2}
. Based on this modular range, 0≤ωt≤60° is again divided into three regions (i.e., A1,A2, and A3) as shown in
Fig. 6
. Because of this reason pulse pattern of the asymmetrical dual inverter configuration is analyzed at three different regions in the modular range of 0°≤ωt≤60°.
In all regions, a small time period (Ts=1/fs; carrier frequency) is considered for the analysis. Thus, the modulating signals appear as appear as straight lines as shown in
Fig. 6
. The discussion is conducted based on pole voltages because these voltages are replicas of the pulse pattern. In
Fig. 7
, three modulating signals (i.e., V
_{a}
^{*}
, V
_{b}
^{*}
,, and V
_{c}
^{*}
) intersect with three different level shifting carrier signals (i.e., V
_{t1}
, V
_{t2}
,,and V
_{t3}
). Based on switching logic given in
Table II
invertersI and II pole voltages are shown in
Fig. 7
. At any instant, inverterI generates a pole voltage of 2Vdc/3 or 0, and inverterII generates a pole voltage of V
_{dc}
/3 or 0.CMV can be calculated from the individual pole voltages with (2). The bottom traces in
Fig. 7
imply that the value of CMV generated by the conventional continuous modulating signal based PWM algorithm may vary between –V
_{dc}
/9 and 4V
_{dc}
/9.
Resulting output pole voltages of inverters and CMV with the continuous modulating signal based PWM algorithm in regions.
In
Fig. 7
(a), the CMV has a maximum value of 4V
_{dc}
/9 with a multilevel jump from V
_{dc}
/9 to V
_{dc}
/3. As previously mentioned, scalar PWM techniques generally provide freedom for the selection of reference and carrier signals. With this freedom, if the position of reference signal is changed the PWM technique gives significant advantages. With the change in position of reference signals V
^{*}
_{a}
or V
^{*}
_{c}
, the CMV is reduced. However, with the clamping of reference signal V
^{*}
_{a}
as shown in
Fig. 8
(a) along with CMV reduction phasea switching is reduced. In particular,
Fig. 8
(a) reveals that the peak value of CMV generated in region A1 is reduced to a magnitude of V
_{dc}
/3 from 4V
_{dc}
/9 with reduced phasea switching of inverterII. The pole voltages of the inverters and the generated CMV at instant A2 with continuous modulating signal based PWM technique are shown in
Fig. 7
(b). With the clamping of phasea as shown in
Fig. 8
(b),the CMV is decreased from V
_{dc}
/3 to 2V
_{dc}
/9. Similarly, when phasea is clamped in region A3, the CMV is reduced from 2V
_{dc}
/9 to V
_{dc}
/9. With the clamping of phasea in the entire modular range of 0°≤ωt≤60°, the CMV is decreased from –V
_{dc}
/9 and 4V
_{dc}
/9 to –V
_{dc}
/9 and V
_{dc}
/3, respectively. With the clamping of phasec in region A3 (
Fig. 8
(c)), the CMV in that region is reduced from –V
_{dc}
/9 and 2V
_{dc}
/9 to 0 and 2V
_{dc}
/9, respectively. Hence, the CMV in the modular range (0°≤ωt≤60°) is decreased from –V
_{dc}
/9 and 4V
_{dc}
/9 to 0 and V
_{dc}
/3, respectively. Therefore, to reduce the CMV and switching losses within the modular function range of 0°≤ωt≤60°, in region A1 phasea is clamped, in region A2 phasea clamped and in region A3 phasec is clamped. This type of symmetry is repeated in the entire modular range of (0°≤ωt≤360°) to reduce the CMV.
Pulse pattern of the discontinuous modulating signal based PWM algorithm in regions.
V. DISCONTINUOUS MODULATING SIGNAL BASED SCALAR PWM ALGORITHM
In the previous discussion and analysis, in the modular function range 0°≤ωt≤600, in region A1 phasea is clamped, in region A2 phasea is clamped and in region A3 phasec is clamped respectively. Based on observation, it can be generalized by using simple maximum and minimum magnitude test to the commended reference signals (i.e., V
_{a}
,V
_{b}
, and V
_{c}
). The magnitudes of these reference signals are calculated. If the signal has a maximum value and the intermediate signal is near to the minimum value signal, then the signal which is having maximum value is clamped to the positive DC bus. In the similar manner if the signal has a minimum value and the intermediate signal is near to the maximum value signal, then the signal which is having minimum value is clamped to the negative DC bus.
Based on observation of modulating signals in the entire modulation range, the modulating signals are almost similar to those (DPWM1) shown in
Fig. 9
as discussed in
[6]
. Each modulating signal is clamped to either a positive or negative DC bus for a period of 120°. As such, the switching of the corresponding device is ceased.
(a) Modulating signals and zerosequence signals. (b) threephase modulating signals.
Similar to the continuous modulation signal, the discontinuous modulating signals shown in
Fig. 9
can also be expressed mathematically. Three reference signals (V
_{i}
) are considered as depicted in (3), and zero sequence (V
_{zs}
) is added to the reference signals as in (4). Therefore, a new set of reference or modulating signals (V*
_{i}
) is obtained as in (5). The graphical representation of the reference signal, zerosequence signal, and obtained modulating signals are shown in
Fig. 9
(a).
Figs. 6
(a) and
9
(a) demonstrate that the commended reference signals are the same, but the zerosequence signal is changed. In (4), constant a
_{o}
is set as 0.5 in the entire modular range to obtain the continuous modulating signal. To generate the discontinuous modulating signal as in
Fig. 9
, constant a
_{o}
is set as 0 or 1 in the entire modular range. The value of a
_{o}
is chosen based on the following equations:
where V
_{max}
and V
_{min}
are the maximum and minimum values of the commended reference signals (i.e., V
_{a}
,V
_{b}
, and V
_{c}
), respectively.
Table III
lists the values of constant a
_{o}
.
aoVALUES FOR VARIOUS MODULATING
a_{o}VALUES FOR VARIOUS MODULATING
VI. RESULTS AND DISCUSSION
To validate the performance of the proposed PWM techniques, various numerical simulation studies are conducted on a v/f controlled induction motor drive. A prototype model of the asymmetrical dual inverter fed induction motor is developed, and control signals are generated based on the carrier comparison approach using a dSPACE 1104 control board. The carrier frequency is set as 1 kHz for the experimental studies.
The threephase induction motor (with 1Hp, 415V, 1.8A, and 50Hz) is fed from two 9.2 kVA PWM inverters with uncontrolled rectifiers at the front end. A DC bus voltage of 200V is employed to inverterI, and 100V is employed to inverterII. Therefore, an effective DC voltage of 300V is adopted. To observe the results in a digital storage oscilloscope 500V to 3.3V regulator (LV20P) is employed. As depicted in
Fig. 10
, the inverter with high input voltage is operated with low frequency ,whereas the inverter with low input DC voltage is operated with high frequency. With the continuous modulating signal, inverterII is continuously switched (
Fig. 10
(a)). However, this inverter is clamped for a time period of T
_{0}
/3(output frequency fo=1/T
_{0}
) with the discontinuous modulating signal (
Fig. 10
(b)).
Modulating signal, inverterI Aphase pulse pattern, inverterII Aphase pulse pattern.
With the discontinuous modulating signal, the switching of inverterII is reduced as well as its switching losses. The CMV, effective phase voltage, harmonic spectrum of effective phase voltage, and aphase stator currents with continuous and discontinuous modulating signal based PWM techniques are shown in
Figs.11
and
12
.
(a) CMV and effective phase voltage. (b) harmonic spectrum of effective phase voltage. (c) Aphase stator current with conventional continuous modulating signal based PWM technique at M=0.87 and fs=1000Hz.
(a) CMV and effective phase voltage. (b) Harmonic spectrum of effective phase voltage. (c) Aphase stator current with conventional discontinuous modulating signal based PWM technique at M=0.87 and fs=1000Hz.
With an effective DC input voltage of 300 V and continuous modulating signal based PWM technique, the CMV varies between –33.3V (–V
_{dc}
/9) and 133.3 V (4V
_{dc}
/9). The frequency of CMV is three times that of the output voltage frequency (f
_{o}
). With the application of the discontinuous modulating signal based PWM technique (by clamping any one phase at a time), the CMV is reduced from –33.3 V (–V
_{dc}
/9) and 133.3 V (4V
_{dc}
/9) to 0 V and 100 V (V
_{dc}
/3), respectively. Therefore, the CMV is reduced by 40% with the discontinuous modulating signal based PWM technique.
The phasea stator current under noload condition is shown in
Figs. 11
(c) and
12
(c). The switching frequency is maintained constant at 1 kHz for both the continuous and discontinuous modulating signal based PWM techniques. In this event, the harmonic spectrum exhibits a large amount of energy at the harmonics (multiples) of switching frequency (around 20 as shown in
Figs. 11
(b) and
12
(b)). Compared with the continuous modulating signal based PWM technique, the discontinuous modulating signal based PWM technique produces a high total harmonic distortion.
When the average switching frequency is maintained constant (1 and 1.5 kHz for the continuous and discontinuous modulating signal based PWM techniques, respectively), the discontinuous modulating signal based PWM techniques exhibit better performance in terms of the total harmonic distortion (
Fig. 13
) than the continuous modulating signal based PWM techniques.
Harmonic spectrum of effective phase voltage with discontinuous modulating signal based PWM technique at fs=1500Hz.
The preceding analysis verifies that at high modulation index the discontinuous modulating signal based PWM technique and at low modulation index continuous modulating signal based PWM technique show a satisfactory performance in reducing CMV. When the modulation index decreases, the discontinuous modulating signal based PWM techniques show high CMV. Therefore, the drives with discontinuous modulating signal based PWM technique should be operated at high modulation index to efficiently reduce the CMV and harmonics.
VII. CONCLUSION
Conventional control strategies for twolevel inverter topologies reduce the CMV by decreasing the quality of output voltage. In this study, continuous and discontinuous modulation signal based PWM techniques were discussed for the asymmetrical dual inverter configuration. In particular, the pulse pattern and implementation of these PWM techniques were analyzed. Theory of CMV reduction was verified by theory and laboratory experiments. The research results confirmed that the clamping of modulating signal to either a positive or negative DC bus reduces the CMV by maintaining the same quality of output voltage at high modulation index. Along with the CMV, the reduction switching losses of the inverters were reduced with the application of discontinuous modulating signal based PWM techniques.
BIO
M. Harsha Vardhan Reddy received his B.Tech degree from Rajeev Gandhi Memorial College of Engineering and Technology, Nandyal, Andhra Pradesh in 2009. In 2011, he obtained his M.Tech degree in power electronics and drives from Karunya University, Coimbatore. Currently, Harsha is affiliated with G. Pulla Reddy Engineering College (GPREC), Kurnool as an assistant professor. His areas of interests are power electronic control of drives.
T. Brahmananda Reddy graduated from Sri Krishna Devaraya University, Anantapur in 2001. He received his M.E degree from Osmania University, Hyderabad, India in 2003 and his Ph.D from Jawaharlal Nehru Technological University, Hyderabad (JNTUH) in 2009. Dr. Brahmanada is a professor at GPREC and is the head of the Electrical and Electronics Engineering Department of the same college. He has presented more than 100 research papers in various national and international conferences and journals. His research areas include PWM techniques, DC to AC converters, and control of electrical drives.
B. Ravindranath Reddy obtained his B.Tech degree in Electrical and Electronics Engineering from JNTU College of Engineering, Anantapur in 1991. He obtained his M.Tech degree in Energy Systems from the Institute of Post Graduate Studies and Research of JNTUH in 1997. Dr. Ravindranath completed his doctoral degree in Electrical Power Systems from JNTU, Anantapur . At present, Dr. Ravindranath works an executive engineer at JNTUH. He has published more than 15 research papers, and his areas of interests are power systems, high voltage engineering, and control systems. His research interests include Simulation studies on Transients of different power system equipment.
M. Suryakalavathi was born on 8thJuly 1966. She obtained her B.Tech degree from Sri Venkateswara University in 1988. She received her M.Tech degree from the same university in 1992. Consequently, Dr. Suryakalayathi obtained her doctoral degree from JNTUH and her post doctoral degree from Carnegie Mellon University, USA. She is presently professor at JNTUH College of Engineering. She has published 30 research papers. Her research of interests includes simulation studies on transients of different power system equipment.
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