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DUAL INVERTER-FED DRIVES WITH THE SYNCHRONISED MULTILEVEL
VOLTAGE WAVEFORMS
ACTIONARI ELECTRICE PE BAZA INVERTOARELE DUBLATE CU TENSIUNE
9
DE IE§IRE SINCRONIZATA §I MAI MULTE TREPTE.
ЭЛЕКТРОПРИВОДЫ СО СДВОЕННЫМИ ИНВЕРТОРАМИ И СИНХРОНИЗИРОВАННЫМ МНОГОУРОВНЕВЫМ ВЫХОДНЫМ
НАПРЯЖЕНИЕМ
V. Oleschuk, A. Sizov, A.M. Stankovic, E. Yaroshenko
RESUME
This paper presents results of investigation of dual inverter-fed open-end winding induction motor electric drive systems, controlled in accordance with the algorithms of novel methodology of synchronized vector modulation. Simulations give the behavior of the proposed techniques of synchronized modulation.
Keywords: open-end winding induction motor electric drives; dual voltage source inverters; synchronized vector modulation.
RESUMAT
Au fost cercetate sisteme de actionari electrice reglate in baza motorului electric asincron cu infa§urari disjunctionate, ce se alimenteaza de la doua invertoare cuplate, reglate in corespundere cu algoritmii modulatiei vectoriale sincrone. Sunt prezentate rezultatele modelarii sistemelor cu deferite tipuri de modulari vectoriale.
Cuvinte cheie: actionari electrice in baza motoarelor asincrone cu infa§urari disjunctionate; invertoare dublate de tensiune; modulare vectoriala sincrona.
АННОТАЦИЯ
Исследованы системы регулируемого электропривода на базе асинхронного электродвигателя с разомкнутыми обмотками, питающиеся от двух спаренных инверторов, регулируемых в соответствии с алгоритмами синхронной векторной модуляцией. Приведены результаты моделирования систем с различными видами векторной модуляции.
Ключевые слова: электроприводы на базе двигателей с разомкнутыми обмотками, сдвоенные инверторы напряжения, синхронная векторная модуляция.
1. INTRODUCTION
Power electronic converters are now basic workhorses in various power generation and power conversion systems including very wide-spread adjustable speed electric drives. Adjustable speed motor drives are used widely for effective control of pumps, compressors, fans, etc.
During the last years, different non-standard structures of adjustable speed electric drives attract more and more attention of researchers. In particular, multiphase motor drives have been analyzed and investigated, which were based on dual induction machine having two sets of three-phase windings, allowing to smooth the electromagnetic torque pulsations and to improve the overall system reliability [1]-[3].
Other perspective topologies of drives are based on the open-end winding induction
motor, fed by two standard three-phase inverters from both sides [4]-[6]. This topology with two cascaded two-level converters is capable of producing voltages which are identical to those of three-level and four-level converters. The cascaded converters are simpler to construct and offer more non-redundant switching states per number of active semiconductor than standard multilevel converters [5].
At the same time novel methodology of synchronised pulsewidth modulation (PWM) for three-phase voltage source inverters has been recently proposed, allowing avoiding asynchronous character of standard schemes of voltage space-vector modulation [7]-[8]. Taking into account an importance of mutual synchronization of the operating of dual inverter-fed drive systems, the proposed methodology of synchronised PWM can be successfully disseminated to new topologies of cascaded converters. So, this paper presents results of analysis and comparison of different versions of synchronised pulsewidth modulation, applied to one of perspective structure of open-end winding motor drives.
2. BASIC STRUCTURE OF DUAL INVERTER-FED DRIVE
Fig. 1 shows one of the basic structures of the drive system with an open-end winding induction motor [6]. Inverter 1 and Inverter 2 are standard three-phase voltage source inverters here. Auxiliary switches Sw} to Sw4 are bidirectional, inserted to block the triplen harmonic currents by creating an isolated switched neutral, and algorithm of control of auxiliary switches is described in [6].
Fig. 1.
Different PWM techniques have been elaborated for control of drive systems with an open-end winding motor [5],[6]. In order to avoid asynchronism of conventional versions of voltage space-vector modulation, novel method (methodology) of direct synchronised PWM can be used for control of each inverter [7],[8].
3. PECULIARITIES OF THE METHODOLOGY OF SYNCHRONISED PWM
Table I presents basic properties of a new methodology of PWM, and it is also compared here with standard voltage space-vector modulation. Fig. 2 shows the typical switching state sequences of three-phase inverter inside a diapason 0°-120°. It illustrates schematically some basic continuous (CPWM, Fig. 2,a) and discontinuous (DPWM, Figs. 2,b - 2,d) versions of PWM, which are used typically in adjustable speed drive systems. In Fig. 2, the conventional designation for state sequences for the switches of the phases abc of the inverter is used: 1 -100; 2 -110; 3- 010; 4- 011; 5 - 001; 6 - 101; 7 - 111; 0 - 000 (‘1’-switch-on state, ‘0’-switch-off state) [7].
Table I. Basic Parameters of PWM Methods
Control (modulation) parameter Conventional schemes of vector PWM Proposed method of modulation
Operating and max parameter Operating & max voltage V and Vm Operating & maximum fundamental frequency F and F„
Modulation index m V/Vm F!F„
Duration of sub-cycles T T
Center of the ¿-signal ak (angles/degr.) z(k — 1) (sec)
Switch-on durations =l.lm7’[sin(60° -at) + sinat] laJ = 1 1 mT sin ak t№ =l.lmrx sin(60° — uk) Algebraic PWM Trigonometric PWM
Д,=Д[1 -Ax (k iyrFK„rl] Yi =A-t*,[0.5- 6{i-kyvFW^ Pk Yk A = A>t cos[(t-l)rifDVl] Kt=A-t+lE 0.5- 0.9<n(i - kyt)K„v Pk-Yk
Switch-off states (zero voltage) ^Ok —T — — tbi II •1 і 1 : !
Special parameters providing synchronization of the process of PWM (k-\ytFKmi]K А’=(т-0")х KmlK, f}"~ \0, xcos A'=(r — /ї")х KortK,
Fig. 2a shows the switching state sequences for the most popular continuous version of voltage space-vector modulation (CPWM), and modulation principle is based here on continuous operation of all switches of the inverter during every switching period (sub-cycle).
The sequence of switchings is here: -0-1-2-7-2-1-0-. Fig. 3 shows more in details synchronous CPWM scheme for a quarter-period of the output voltage of inverter. The upper curve is here
Fig. 2. Switching state sequences for typical PWM schemes: a) CPWM; b) DPWM0; c) DPWM2; d) DPWM3; e) DPWM1 [7].
phase a
phase b
phase c Vab —
Fig. 3. Control and output signals for quarter-period of three-phase mnverter with continuous PWM (CPWM).
the switching state sequence, then - control signals for the cathode switches of the phases a, b and c. The lower curve in Fig. 3 shows the corresponding quarter-wave of the line output
voltage of the inverter. Signals {$ represent the total switch-on durations during the switching period t , signals yk are generated on the boundaries of the corresponding p. Widths of notches Ak represent the duration of zero sequences.
Special signals X (As in Fig. 3) with the neighboring ff ( /?5 in Fig. 3) are formed in the clock-points (00, 600, 1200..) of the output curve of inverters with synchronised PWM. They are reduced simultaneously till close to zero value at the boundary frequencies Fi, providing a continuous adjustment of voltage with smooth pulses-ratio changing.
4. SIMULATION OF PROCESSES IN DUAL INVERTER-FED DRIVES WITH SYNCHRONISED PWM
4.1. Drive Systems with Continuous Synchronised PWM
Synchronous symmetrical control of the output voltage waveforms of each inverter in accordance with basic PWM algorithm provides synchronous symmetrical regulation of voltage in the induction machine phase windings. Rational phase shifting between output voltage waveforms of the inverters is equal in this case to one half of the switching interval (sub-cycle) t (is equal to 0.5 r) [4].
Fig. 4 presents pole voltages of two inverters Vaio and Va20 , zero sequence (triplen harmonic components) voltage Vo, motor phase voltage Vaia2, and motor phase voltage without triplen harmonic components (actual motor phase voltage) Vaia2 - Vo. Both inverters are here under control in accordance with the scheme of continuous synchronised pulsewidth modulation (see Figs. 2a and 3, [7]). Switching frequency Fs of each inverter is equal to 1 kHz. Curves in Fig. 4 correspond to the fundamental frequency F equal to 20 Hz (modulation index m=0.4).
Fig. 5 shows spectral composition of the voltage waveforms presented in Fig. 4. It presents normalized harmonic spectrum (relative (Vk/Vdc) magnitudes of the k-harmonics of the presented voltages). The undesirable triplen harmonics are in the spectra of pole voltages of inverters and of motor phase voltage Va1a2, but actual motor phase voltage Va1a2 - V0 does not contain it due to special algorithm of operation of auxiliary switches Sw1 - Sw4 of the system, creating an isolated switched neutral [6]. Actual motor phase voltage of the drive system with synchronised PWM has quarter-wave symmetry, and its spectrum does not include even harmonics and combined harmonics (sub-harmonics).
Fig. 4. Voltage waveforms of drive system with continuous synchronised PWM (F=20Hz).
b)
c)
Spectral composition of Va1a2-Vo
o_______i_=__i______i____i____—l_____l=___i=___rw Wv
□ 1 □ 20 30 40 50 0Q 70 80 90 1 QQ
Order of voltage harmonies
d)
Fig. 5. Spectral composition of voltage waveforms for the drive system with continuous synchronised PWM at F = 20 Hz:
a) Va10; b) Va1a2; c) Vo'; d) Va1a2 - Vo.
Fig. 6 presents basic voltage waveforms (period of the basic waveforms) of the dual inverter-fed drive system with continuous synchronized PWM operating at the fundamental frequency equal to 40 Hz (modulation index m=0.8).
Fig. 6. Voltage waveforms of drive system with
continuous synchronised PWM (F = 40 Hz).
Fig. 7 shows the corresponding spectra of the presented voltage waveforms. In particular, curves in Fig. 7,d prove the fact that the spectrum of the actual motor phase voltage Vaia2 - V0 of the drive system with synchronised PWM contains only odd harmonics (without triplen order harmonics) at any ratios (round or not round) between the switching frequency and fundamental frequency.
b)
d)
Fig. 7. Spectral composition of voltage waveforms for the drive system with continuous synchronised PWM at F = 40 Hz: a) Va10; b) Va1a2i c) V0; d) Va1a2 - V0.
4.2. Drive Systems with Discontinuous Synchronized PWM
Fig.8 presents basic voltages waveforms for the drive system with discontinuous synchronous PWM (DPWM3 scheme of discontinuous PWM in accordance with Fig. 2,d [7]). It includes pole voltages of two inverters Va10 and Va20 , zero sequence (triplen harmonic components) voltage V0, motor phase voltage Va1a2, and motor phase voltage without triplen
harmonic components (actual motor phase voltage) Va1a2 - V0. The fundamental frequency is equal to 20 Hz in this case, and switching frequency is equal to 1 kHz.
Fig. 9 shows spectral composition of the voltage waveforms presented in Fig. 8.
d)
Fig. 9. Spectral composition of voltage waveforms for the drive system with discontinuous synchronised PWM at F = 20 Hz: a) Va10; b) Va1a2; c) V0; d) Va1a2 - V0.
Fig. 10 presents basic voltage waveforms (period of the basic waveforms) of the dual inverter-fed drive system with discontinuous synchronized PWM operating at the fundamental frequency equal to 40 Hz modulation index m=0.8).
Fig. 11 shows the corresponding spectra of the presented voltage waveforms.
Fig. 10. Voltage waveforms of drive system with
discontinuous synchronised PWM (F=40Hz).
d)
Fig. 11. Spectral composition of voltage waveforms for the drive system with discontinuous synchronised PWM at F = 40 Hz:
a) Va10; b) Va1a2; c) V0'; d) Va1a2 - V0.
The presented in Fig, 9,d and Fig. 11,d results of analysis of voltage spectral composition show, that actual motor phase voltage of the drive system with synchronised discontinuous
PWM has quarter-wave symmetry, and its spectrum does not include even harmonics and
combined harmonics (sub-harmonics).
4.3. Spectral Assessment of the Voltage Waveforms
In order to compare the modulation schemes proposed for control of dual inverter-fed drive systems, a comparative analysis of the spectra of the actual motor phase voltage has been executed based on computer simulation. Weighted Total Harmonic Distortion factor
(WTHD)(1), reflecting the actual level of a harmonic distortion for a first order ac filter, is well suited for using in adjustable speed drive and is used for determination of its quality [7]:
WTHD = (1 / V1 )
(1)
Fig. 12 presents averaged results of calculation of WTHD for actual motor phase voltage (Va1a2 -Vo) of the drive system for the analyzed continuous (CPWM) and discontinuous (DPWM) versions of synchronised modulation during standard scalar V/F control until the zone of overmodulation (modulation index m = 0.3-0.9). Average switching frequency of each inverter is equal to 700 Hz for both versions of PWM. Dotted lines in Fig. 12 show results of calculation of WTHD factor for the line-to-line output voltage of each inverter (Va1b1 = Va2b2) for both mentioned above schemes of synchronised PWM.
Fig. 13 shows WTHD versus modulation index for actual motor phase voltage of the drive system with average switching frequency of each inverter is equal to 1 kHz.
Fig. 12. WTHD of actual motor phase voltage (—), and of the line-to-line output voltage of each inverter (--------------------) (Fs = 700 Hz).
Fig. 13. WTHD of actual motor phase voltage (—), and of the line-to-line output voltage of each inverter (--------------------) (Fs = 1 kHz).
1= 1
Presented in Fig. 12 and Fig. 13 results of analysis of spectral composition of actual motor phase voltage for dual inverter-fed open-end winding motor drive show that Weighted Total Harmonic Distortion factor is much better for drive system with discontinuous (DPWM) version of synchronised PWM during all undermodulation control region.
CONCLUSION
Dissemination of the methodology of synchronised pulsewidth modulation to dual inverter-fed drive systems with open-end winding induction motors allows to provide quarter-wave symmetry of actual motor phase voltage during the whole control range including the zone of overmodulation.
The spectra of actual motor phase voltage do not include even harmonics and combined harmonics (sub-harmonics), which is especially important for the systems with low switching frequencies and increased power rate.
In dual inverter-fed drive systems algorithms of discontinuous synchronised PWM provide better spectral composition of actual motor phase voltage in comparison with continuous PWM schemes during the whole control range.
ACKNOWLEDGMENT
The presented research has been supported in part by the Award MOE2-2612-CH-04 of the US Civilian Research and Development Foundation for the Independent States of the Former Soviet Union (CRDF).
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Valentin Oleschuk, D.Sc., is Director of the Laboratory of Automated Electric Drives of Power Engineering Institute of the Academy of Sciences of Moldova. He is author and co-author of two books and more than 150 publications in the field of Power Electronics and Electric Drives, including 30 publications in the IEEE transactions and proceedings. He holds also 89 patents and authors certificates in this area. His research interests include control and modulation strategies for perspective topologies of power converters and drives.
Alexandr Sizov is Scientific Collaborator of the Laboratory of Automated Electric Drives of Power Engineering Institute of the Academy of Sciences of Moldova. He is author and co-author of about 40 publications and 10 authors certificates in the field of Power Electronics and Electric Drives. His research interests include elaboration, modelling and simulation of control algorithms and control systems for power electronic converters and drive systems.
Alexandar M. Stankovic (Fellow, IEEE), is Professor of the Electrical and Computer Department of Northeastern University (Boston, USA). He is author and co-author of more than 140 prestigious publications (mainly in the IEEE transactions and proceedings) on Energy Systems, Power Electronics and Electric Drives. His research interests include different aspects of control theory with its applications for energy processing systems, including generation, transmission and energy conversion.
Evgeni Yaroshenko holds position of Scientific Secretary of Power Engineering Institute of the Academy of Sciences of Moldova, and also works partly as Scientific Collaborator of the Laboratory of the Automated Electric Drives of the Institute He is author and co-author of more than 40 publications and of 9 patents and authors certificates. His research interests are connected with elaboration, modelling, simulation and implementation of modern topologies of adjustable speed drive systems.
