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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.
Key words: modulation strategy, voltage source inverter, electric drive.
PROPRIETÂJILE §I PARTICULARITÂJILE METODEI MODULÂRII SINCRONE VECTORIALE PENTRU CONVERTOARE ELECTRONICE DE PUTERE
V. Olesciuk
Institutul de Energetica al Academiei de §tiin^e a Moldovei Rezumat. Aceastâ lucrare prezintâ o scurtâ descriere a unei noi metode de modulare sincronizate pentru convertoare electronice de putere. Este efectuatâ comparai multilateralâ cu metodicele standarde ale modula^iei a impulsurilor în duratâ. Sunt descrise aspectele de bazâ de utilitate practicâ a noii metodei de modulare. Cuvinte-cheie: strategie de modulare, invertor de tensiune, actionâri 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].
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 zero-sequence 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.
PROBLEMELEL ENERGETICII REGIONALE 2(13) 2010 Fig. 2. Modulation waveforms of modern PWM methods [6]
SVPWM: ;0 = Ç, =0.5 DPWMMAX:ï0= 0 DPWMMIN:Ç,= 0
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 Operating and maximum voltage V and Vm Operating and maximum fundamental frequency F and Fm
Modulation index m v / F / Fm
Duration of subcycles T T
Centre of the ^-signal (angles/degr.) T(k -1) (sec)
Switch-on durations (active switching states) Trf = 1.1mT[sin(600 ak) + sin ak ] = l.lmT sin a sin(600 -ak) Algebraic PWM Trigonometric PWM
Pk = 1.1m r[1 -A(k- 1)F] 7k = pi-k+1[°.5 -6(i-k)rF] Pk - 7k Pk = l.lmrx cos[(k- 1)r] 7k = Pi-k+1[°.5-0.87tan(i - k)t] pk -7k
Switch-off states (zero voltage) t0k = T - tak - tbk Xk = T- Pk
Special parameters providing synchronization of the process of PWM X (clock-point notches) P (signals, the next to the X ) Fj (boundary frequencies, where X ^ 0 and P ^ 0 )
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]
5 10 15 20 25
angle from the beginning of clock-intervals, degrees
a)
0.5
0.4
0.3
0.2
0.1
r* -
linear _
~
O 5 10 15 20 25 30
angle from the beginning of clock-intervals, degrees
b)
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 (%)
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
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 three-phase 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.
fL
T
\ /
i
\ /
F-1 and Fi
\ /
\ 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 basic functions, % Trigonometric PWM Algebraic PWM
tangents 48.3 ---
cosines 38.7 ---
Total 100 33.4
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 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.
□ 018
□ .017
□ .016
□ .015
□ .014
□ .013 ’ 0.012
□ .011
7
/
- CPWMschemeFig12b ^
^ CPWMschemeFigl 2a
-
- X -
/
DPWMschemeFig12a -
y
' 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
modulation index m
Fig. 10. WTHD factor versus modulation index
1.1
1.05
1
0.95
0.9
0.65
Vi/V* ' ' 1.1 v,/v*
a> 1 b)
0.9
F F
40
42
44
46
48
50
40
42
44
46
48
50
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:
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
[1] B.K. Bose, Modern Power Electronics and AC Drives (Prentice Hall, Upper Saddle River, 2002).
[2] D.G. Holmes, and T. Lipo, Pulse Width Modulation for Power Converters. Principles and Practice (IEEE Press, 2003).
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[5] V.G. Agelidis, and M. Calais, “Application specific harmonic performance evaluation of multicarrier PWM techniques”, Proc. IEEE Power Electr. Specialists Conf., 1998, pp. 172-178.
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[7] I. Nagy, “Control of bidirectional power conversion”, Proc. IEEE Int’l Symp. Ind. Electr., 1993, pp. 176-182.
[8] S. Halasz, A.A.M. Hasan, and B.T. Huu, “Optimal control of three-level PWM inverters”, IEEE Trans. Ind. Electr., 44(1), 1997, pp. 96-106.
[9] V. Oleschuk, and F. Blaabjerg, “Direct synchronized PWM techniques with linear control functions for adjustable speed drives”, Proc. IEEE Applied Power Electr. Conf., 2002, pp. 76-82.
[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 modulation for control of inverter-fed open-end winding motor drives”, CD-ROM Proc. 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.
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.
