PROBLEMELEL ENERGETICII REGIONALE 2(13) 2010
PROPERTIES AND PECULIARITIES OF SPACE-VECTOR-BASED
SYNCHRONIZED MODULATION FOR POWER ELECTRONIC
CONVERTERS
V. Oleschuk
Institute of Power Engineering of the Academy of Sciences of Moldova
Resume. This paper presents brief description of peculiarities of a novel method of
synchronized pulsewidth modulation (PWM) for power electronic converters. Comprehensive
comparison with standard PWM techniques has been done. Basic aspects of practical
relevance of new PWM method have been described.
Keywords: modulation strategy, voltage source inverter, electric drive.
PROPRIETĂŢILE ŞI PARTICULARITATILE METODEI MODULĂRII SINCRONE
VECTORIALE PENTRU CONVERTOARE ELECTRONICE DE PUTERE
V. Olesciuk
Institutul de Energetică al Academiei de Ştiinţe a Moldovei
Rezumat. Aceasta lucrare prezintă o scurtă descriere a unei noi metode de modulare sincronizate pentru
convertoare electronice de putere. Este efectuată comparaţia multilaterală cu tehnicile standarde ale modulaţiei a
impulsurilor în durată. Sunt descrise aspectele de bază de utilitate practică a noii metodei de modulare.
Cuvinte cheie: strategie de modulare, invertor de tensiune, actionări electrice.
СВОЙСТВА И ОСОБЕННОСТИ МЕТОДА СИНХРОННОЙ ВЕКТОРНОЙ МОДУЛЯЦИИ
ДЛЯ СИЛОВЫХ ПРЕОБРАЗОВАТЕЛЕЙ ЭЛЕКТРИЧЕСКОЙ ЭНЕРГИИ
В. Олещук
Институт энергетики Академии наук Молдовы
Аннотация. Описаны базовые особенности нового метода синхронной векторной широтно-импульсной
модуляции (ШИМ) для электронных преобразователей параметров электрической энергии. Выполнен
сопоставительный анализ предложенного метода со стандартными разновидностями ШИМ.
Продемонстрированы некоторые аспекты практической полезности нового метода синхронной ШИМ.
Ключевые слова: стратегия модуляции, автономный инвертор напряжения, электропривод.
I. INTRODUCTION
Energy is the life-blood for continual progress of civilization. Today more than a half
of the total electrical energy is transformed on the way from extraction to end-use. Power
electronic equipment is a key element in conversion of billions of kilowatts of electrical
energy.
Operation of power electronic converters is based on on switchings of semiconductor
devices (power transistors and thyristors), and principle of modulation of pulse signals is the
basic for their control. Characteristics of power conversion systems are in dependence of the
used methods of modulation. Two last decades have been marked by fast application of
methods of space-vector modulation, based on space vector representation of the set of output
signals of converters, which are ones of the most suitable for adjustable speed motor drives
[1]-[8].
Almost all versions of classical space-vector modulation are based on the
asynchronous principle, which results in sub-harmonics (of the fundamental frequency) in the
spectrum of the output voltage of converters, that are very undesirable in most applications
[3]. In order to avoid some disadvantages of standard space-vector PWM, novel methods of
synchronized PWM have been recently proposed for drive converters [9]-[11].
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II.
CONVENTIONAL SPACE-VECTOR MODULATION
Fig. 1 shows a simplified structure of three-phase voltage source inverter supplying the
induction motor IM as a load. The corresponding space vectors of the output voltage of the
inverter (six active vectors 1 – 6, and two zero vectors 0 and 7) are also presented here.
Fig. 1. Three-phase inverter with induction motor IM, and its output voltage vectors
Fig. 2 and Fig. 3 illustrate conventional (classical) approach for consideration of
different continuous and discontinuous versions of space vector PWM in the undermodulation
control mode [6]. In accordance with standard space-vector approach, which is possibly the
best among all the pulsewidth modulation techniques for variable-frequency drive
applications, the time domain modulation signals are translated to the complex reference
voltage vector which rotates in the complex coordinates [1]-[2],[4],[6]. So, consideration of
space-vector PWM methods and techniques is based in this case on the complicated nonlinear modulation functions (Fig. 2) together with such sophisticated parameter, as zerosequence signals (the bold lines in Fig. 2, carrier signals are not shown here).
Fig. 3 shows zero-state partitioning for these modern methods of pulsewidth modulation.
Mapping the zero-state partitioning of the time domain modulation waves of Fig. 2 onto the
vector space domain, the direct digital instrumentation equivalency can be easily obtained [6].
Determination of the duty-cycles for conventional space vector PWM for inverters is based on
the set of trigonometric control functions.
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Fig. 2. Modulation waveforms of modern PWM methods [6]
Fig. 3. Zero-state partitioning of modern PWM methods [6]
III. BASICS OF A NOVEL METHOD OF SZNCHRONIYED PWM FOR VOLTAGE
SOURS INVERTERS
In order to avoid some disadvantages of classical space-vector modulation, novel
method of synchronized PWM has been recently proposed [9]-[11]. Table I shows basic
peculiarities of the proposed method of modulation, and it is compared here with conventional
voltage space-vector modulation [9].
Table I. Basic Parameters of PWM Methods
Control
(modulation)
parameter
Conventional
schemes of
vector PWM
Proposed
method
of modulation
Operating and
maximum
parameter
Modulation
index m
Duration of subcycles
Centre
of the k-signal
Operating and
maximum
voltage V and Vm
Operating and maximum
fundamental frequency
F and Fm
V / Vm
F / Fm
T

 (k  1) (sec)
 k (angles/degr.)
Algebraic
PWM
Switch-on
durations
(active
switching
states)
Tak  1.1mT [sin(600   k  1.1m [1 
A(k  1)F ]
k )  sink ]
tak  1.1mT sin k
tbk  1.1mT sin(600 
 k   i  k 1[0.5
 6(i  k )F ]
k   k
Trigonometric
PWM
k  1.1m 
cos[(k  1) ]
 k  i  k 1[0.5 
0.87 tan(i  k ) ]
k   k
k )
Switch-off
states (zero
voltage)
k    k
t0k  T  tak  tbk
' (clock-point notches)
Special
parameters
providing synchronization
of the process
of PWM
 " (signals, the next to the ' )
Fi (boundary frequencies,
where
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'  0 and  "  0 )
PROBLEMELEL ENERGETICII REGIONALE 2(13) 2010
Fig. 4 and Fig. 5 illustrate the proposed method more in details. As it is shown in Fig.
4, the method is based on special simple representation of switching state sequences, which
are presented in Fig. 4 for typical schemes of continuous and discontinuous PWM. Also two
simple functions (Fig. 5) connecting relative width of active switching states with their
position
Fig. 4. Switching state sequences for typical PWM schemes:
a) CPWM; b) DPWM0; c) DPWM2; d) DPWM3; e) DPWM1 [9]
angle from the beginning of clock-intervals, degrees
a)
angle from the beginning of clock-intervals, degrees
b)
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Fig. 5. Variation of the functions for total switch-on durations (a), and of the minor part of the
total switch-on durations (b)
inside the 600-clock-intervals, are basic for determination of parameters of pulse signals.
These functions, as it is shown in Fig. 5, can be easily approximated by the corresponding
linear functions, which are good for fast on-line computation. during realization of real-time
control algorithms. It is used conventional designation of switching state sequences in Fig. 4
for the switches of the phases abc of standard three-phase voltage source inverter (see Fig. 1),
i.e., 1 – 100, 2 – 110, 3 – 010, 4 – 011, 5 – 001, 6 – 101, 7 – 111, 0 –000, where 1 corresponds
to switch-on state, 0 corresponds to switch-off state.
IV. PRACTICAL RELEVANCE OF THE PROPOSED PWM METHOD
Novel method of synchronized pulsewidth modulation is characterized by big facility
for analysis, synthesis, optimization and digitization of modulation processes in drive
systems. It has also a set of features which can be useful for practical utilization.
Synchronization of the Voltage Waveforms
Problem of synchronization of the output voltage of drive converters is one of the
most important problem for high-power drives, because standard asynchronous methods of
PWM result in sub-harmonics (of the fundamental frequency), that are undesirable in power
drive systems. If the converter is supplying an induction motor, the sub-harmonics at zero or
close to zero frequency, even though small in amplitude, will result in large currents that will
be highly undesirable [3].
Investigations of the drive systems on the base of standard three-phase inverters
proved the fact, that the proposed method allows providing of effective voltage
synchronization for modulated converters with low frequency ratio between the switching
frequency Fs and fundamental frequency F. In particular, Fig. 6 presents a comparison of
Weighted Total Harmonic Distortion factor (WTHD, averaged values of WTHD) of the line
output voltage of standard three-phase inverter between conventional continuous
asynchronous PWM (curve 1 in Fig. 6), and two versions of synchronized continuous PWM,
based on algebraic and trigonometric control func-tions (curves 2 and 3 in Fig. 6) [9]. The
presented results show advantage of trigonometric version of synchronous PWM in
comparison with asynchronous PWM until frequency ratio is equal to about 100, and also
advantage of algebraic synchronized PWM in comparison with the asynchronous one, until
frequency ratio is equal to 70.
WTHD (%)
2.5
2.0
1
2
1.5
3
1.0
0.5
FS /F
0
20
40
60
80
100
Fig. 6. WTHD of the line voltage of standard converter for asynchronous continuous PWM
(1), and for synchronized algebraic (2) and trigonometric (3) continuous PWM
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Computational Efficiency of Control Algorithms
Problem of computational effectiveness of control algorithms is between existing
control problems for power converters, because almost all versions of voltage space vector
modulation are based on continuous calculation of trigonometric functions, which need much
more time for computation comparing to algebraic correlations. And using of the lookup
tables tends to give reduced pulsewidth resolution unless it is very large.
Fig. 7 presents universal algorithm to calculate pulse patterns for conventional threephase inverter with synchronized PWM [10], based on either trigonometric or algebraic
control functions, presented in Table I. Table II presents the averaged results of the
comparison of computing time between algorithms of algebraic and trigonometric versions of
discontinuous PWM with the 300-non-switching intervals. Algebraic variant of PWM is based
here on the four-step piece-wise approximation of the basic quasi-sine function (curve 2 in
Fig. 5,a). Presented in Table II results show, that average computational time for algebraic
algorithms of modulation consists 0.33 in comparison with algorithms based on trigonometric
functions, and it is mainly due to the lack of such costly functions as tangents and cosines for
algebraic versions of synchronized PWM.
So, pure algebraic algorithms of synchronized PWM can provide increase of
computational speed in power electronic converters and drives with real-time control
algorithms.
F

i
Fi 1 and F i
1
k
"

k
1
k
Direct synthesis of the waveform
Fig. 7. General algorithm for calculation of voltage pulse patterns for converters with
synchronized PWM
Table II. Comparison of Computing Speed of PWM Algorithms
Computing time for the Trigonometric
basic functions, %
PWM
Algebraic
PWM
tangents
48.3
---
cosines
38.7
---
Total
100
33.4
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Cancellation of undesirable common-mode voltages
Bearing failures of adjustable speed motor drives fed by PWM converters are caused
mainly by bearing currents. They arise mainly to the large rate of change of the specific
common-mode voltages in three-phase loads, which is typical for conventional methods and
techniques of PWM. So, some specialized schemes of synchronized PWM have been
elaborated in order to eliminate the common-mode voltages and to prevent the systems from
bearing currents and bearing failures, with potential increase of its reliability and the life span
[11].
In particular, elimination of the common-mode voltages can be provided in dual
inverter-fed open-end winding motor drive (Fig. 8) with the specialized PWM schemes and
algorithms [12]-[14]. Fig. 9 shows the switching state vectors of two inverters of dual
inverter-fed drive system, which provide mutual compensation (Fig. 9,a) or full elimination
(Fig. 9,b) of the common-mode voltages in the load.
Fig. 8. Dual inverter-fed drive system with single dc-link [12]
a)
b)
Fig. 9. Voltage space-vector combinations, providing mutual compensation (a) and full
elimination (b) of the common-mode voltages
Application of algorithms of synchronized PWM for control of dual inverter-fed
drives without common-mode voltages provides effective synchronization of operation of two
inverters, with synchronization of the voltage waveforms of each inverter and of the resulting
motor phase voltage, the spectra of which do not contain even harmonics and sub-harmonics
during the whole control range [13]-[14]. Fig. 10 presents results of analysis of WTHD factor
for the drive system with continuous (CPWM) and discontinuous (DPWM) versions of
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synchronized PWM, for two basic control schemes, presented in Fig. 9 [14]. Average
switching frequency of each inverter is equal to 1 kHz.
Linear Output Voltage Control during Overmodulation
The proposed PWM methods provide high-quality linear control of the fundamental
voltage of converters in the zone of the highest fundamental frequencies [9]. In particular,
Fig. 11 presents results of comparison (for standard three-phase inverter) of the linearity of
the fundamental voltage in the overmodulation zone between conventional PWM (Fig. 11a)
and algebraic version of synchronized PWM (Fig. 11b) [9]. It shows that the fundamental
voltage has improved linearity during overmodulation in converters with synchronized PWM.
Fig. 10. WTHD factor versus modulation index
Fig. 11. Fundamental voltage versus frequency for converters with standard (a) and
synchronized (b) PWM
Educational Aspect
The proposed direct time-domain-based approach for analysis and synthesis of voltage
space-vector PWM allows avoiding the use of such complicated sophisticated functions and
parameters of conventional schemes of modulation, as non-linear modulation functions,
carrier and reference waveforms, zero sequence signals, etc. So, it can provide an
improvement of understanding of modern PWM methods and techniques, and may be used
widely in teaching [15].
V. CONCLUSION
The proposed novel method of synchronized PWM is characterised by the following practical
properties:
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it provides continuous synchronization of the voltage waveforms of converters, and its spectra do
not contain even harmonics and sub-harmonics, which is especially important for the systems with an
increased power rating;
pure algebraic versions of the proposed methods provide increased computing speed in comparison
with control algorithms on the base of trigonometric functions;
- it allows to realise high quality linear control of the fundamental voltage of converters during
overmodulation;
- simplicity and physical clearness of the proposed metho-dology of PWM may stimulate its using for
teaching.
REFERENCES
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2002).
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Sons, 1995).
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[6] A.M. Hava, R.J. Kerkman, and T. Lipo, “Simple analytical and graphical methods for
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[9] V. Oleschuk, and F. Blaabjerg, “Direct synchronized PWM techniques with linear control
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[10] V. Oleschuk, and F. Blaabjerg, “Synchronized scheme of continuous space-vector PWM
with the real-time control algorithms”, Proc. IEEE Power Electr. Specialists Conf., 2004,
pp. 1207-1213.
[11] V. Oleschuk, and F. Blaabjerg, “Synchronised PWM schemes for three-level inverters
with zero common-mode voltage”, International Journal of Electrical Engineering, 2(1),
2002, pp. 43-48.
[12] M.R. Baiju, K.K. Mohapatra, R.S. Kanchan, and K. Gopakumar, “A dual two-level
inverter scheme with common mode voltage elimination for an induction motor drive”,
IEEE Trans. Power Electr., 19(3), 2004, pp. 794-805.
[13] V. Oleschuk, F. Profumo, A. Tenconi, and R. Bojoi, “Synchronised pulsewidth
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Int’l Conf. on Power Electr. and Intelligent Control for Energy Conservation, 2005.
[14] V. Oleschuk, B.K. Bose, A.M. Stankovic, and A. Sizov, “Phase-shift-based synchronous
modulation for an open-end winding motor drive with elimi-nation of zero sequence
currents”, Proc. IEEE Power Electr. and Drive Systems Conf., 2005, pp. 325-330.
[15] V. Oleschuk, F. Blaabjerg, and A.M. Stankovic, “Direct time-domain-based approach for
study of space-vector pulsewidth modulation”, Proc. IEEE Power Electr. Education
Workshop, 2005, pp. 87-93.
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Valentin Oleschuk (oleschukv@hotmail.com), Dr.Sc., is Chief Scientist of the Power Engineering Institute of
the Academy of Sciences of Moldova. He is author and co-author of two books and more than 220 publications
in the area of power electronics and electric drives, including more than 60 IEEE publications. He is also the
author of 89 patents and authors certificates in this field. His research interests include control and modulation
strategies for power converters, electric drives and renewable energy systems.
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