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SYNCHRONOUS PWM CONTROL OF SYMMETRICAL DUAL THREE-PHASE DRIVE IN THE OVERMODULATION ZONE
V. Oleschuk, A. Sizov Institute of Power Engineering of the Academy of Sciences of Moldova
Abstract. The analysis of operation of symmetrical six-phase (dual three-phase) ac drive system (which is a promising solution for the medium-power and high-power applications) with synchronized pulse-width modulation (PWM) during overmodulation has been performed. The induction machine of this system topology has two sets of windings spatially shifted by 60 electrical degrees with isolated neutral points, which are connected with two standard three-phase inverters. Algorithms of synchronized PWM provide continuous synchronization of the phase voltage of the system in the zone of overmodulation. Simulation results are given for dual three-phase systems with two discontinuous versions of synchronized PWM and with combined synchronized scheme of pulsewidth modulation.
Key words: symmetric six-phase induction motor, converter control, modulation strategy, phase voltage synchronization.
REGLAREA SINCRONA A ACJIONARULII ELECRTIC SIMETRIC DUBLU TRIFAZAT
IN ZONA DE SUPRAMODULARE V. Olesciuk, A. Sizov Institutul de Energetica al Academiei de §tiin^e a Moldovei Rezumat. A fost efectuata analiza functionarii actionarului elecrtic simetric dublu trifazat (§ase faze) in zona de supramodulare (fiind de perspectiva pentru aplicare in sisteme de putere medie §i mare), reglate in baza algoritmilor modulatiei sincrone prin impulsuri de durata variabila. Motorul electric asincron al sistemului include in acest caz doua grupuri de infa§urari trifazate cu fir neutru izolat, cu decalaj de 60 grade electrice fata de celelalt, care sunt conectate prin doua invertoare trifazate standard. Algoritmi modulatiei sincrone asigura sincronizarea continua a curbelor tensiunii fazice ale sistemului in zona de supramodulare. Sunt prezentare rezultatele simularii proceselor in sisteme cu doua versiuni a modulatiei sincrone discontinue, precum §i intr-un sistem cu modulare sincrona combinata. Cuvinte-cheie: motor electric simetric cu §ase faze, controlul convertizoarelor, strategia modulatiei, sincronizarea curbei tensiunii fazice.
СИНХРОННОЕ РЕГУЛИРОВАНИЕ СИММЕТРИЧНОГО СДВОЕННОГО ТРЕХФАЗНОГО ЭЛЕКТРОПРИВОДА В ЗОНЕ СВЕРХМОДУЛЯЦИИ В. Олещук, А. Сизов Институт энергетики Академии наук Молдовы Аннотация. Выполнен анализ функционирования в зоне сверхмодуляции шестифазного (сдвоенного трехфазного) электропривода переменного тока (перспективного для использования в системах средней и большой мощности), регулируемого на базе алгоритмов синхронной широтно-импульсной модуляции (ШИМ). Асинхронный электродвигатель системы включает в этом случае две трехфазные группы обмоток с изолированными нейтралями, пространственно сдвинутых на 60 эл. градусов относительно друг друга, и соединенных с двумя стандартными инверторами напряжения. Алгоритмы синхронной ШИМ обеспечивают при этом непрерывную синхронизацию кривых фазных напряжений в системе в зоне сверхмодуляции. Приведены результаты моделирования процессов в системах с двумя разновидностями прерывистой синхронной ШИМ, а также в системе с комбинированной синхронной модуляцией.
Ключевые слова: симметричный шестифазный электродвигатель, управление преобразователями, стратегия модуляции, синхронизация фазного напряжения.
Introduction
Multiphase converters and adjustable speed drives have an increasing interest in the last years due to some advantages compared with standard three-phase systems. One of the perspective structures of multiphase systems is symmetrical six-phase (dual three-phase) induction motor drive
fed by two three-phase voltage source inverters [1]-[4]. The induction machine has in this case two sets of windings spatially shifted by 60 electrical degrees with isolated neutral points (Fig.1).
Fig.1. Dual three-phase (six-phase) motor drive with two neutral points
Dual three-phase motor drives have several advantages over their three-phase counterparts, such as: reduction of torque pulsations, of the rotor harmonic losses, and of the rated current of power switches; improved reliability at system level; the possibility to supply more than one machine from a single inverter to get a multi-motor, multi-phase drive [5].
High power/high current drives (ship propulsion, locomotive, electrical vehicles, etc.) are perspective area of application of six-phase drives. These power systems are characterized by low switching frequency of converters. It is known, that for high power drives it is necessary to synchronize the output voltage waveforms of modulated power converters for the minimization of undesirable sub-harmonics of voltage and current [6]-[7].
To provide continuous synchronization of the motor phase voltage of six-phase drives, novel method (methodology) of synchronized PWM has been disseminated for control of dual three-phase drives in the undermodulation region for both asymmetrical [8] and symmetrical [9] six-phase systems.
At the same time, control and modulation strategies for drive systems have specific peculiarities at the highest fundamental frequencies. So, this paper presents further development of a new method of PWM, applied for synchronous control of symmetrical six-phase converters in the zone of overmodulation.
Basic peculiarities of synchronized pulsewidth modulation
In order to avoid asynchronism of conventional versions of voltage space-vector modulation, novel method of synchronized PWM can be used for control of each inverter in a six-phase motor drive system [8]-[10].
Table I presents generalized properties and basic control correlations for the proposed method of synchronized PWM. Basic control functions are available for both undermodulation and overmodulation control zones in this case. It is also compared here with conventional asynchronous space- vector modulation. A more detailed description of laws and algorithms of synchronized PWM based on either algebraic or trigonometric control functions is in [10].
In the general case, control of symmetrical six-phase induction machine drive, at both undermodulation and overmodulation regions, is based on the 600-phase-shift of control and output signals of two inverters [1],[3],[9].
Table 1. Basic parameters of PWM methods
Control (modulation) parameter Conventional schcmes of vector PWM Proposed method of modulation
Operating and max parameter Operating & max voltage V and Vm Operating & maximum fundamental frequency F and Fm
Modulation index m V!Vm F/Fm
Duration of sub-cycles T X
Center of the A-signal ak (angles/degr.) r(_k -1) (sec)
Switch-on durations =l.lmr[sin(60° -at) + sin a»] =1.1 mT sina> tM =1.1 mTx sin(60° — a*) Algebraic PWM Trigonometric PWM
A=AP -Ax (*-1)tFK0,A У к ~ A-*»i[0-5 ■ <к« - ку&ус„г Рк-Гк A = Ax cos[(fc - l)i#C0rf] Yt=Pt- 0.9cn(l - kyr]Kov Pk ~Yk
Switch-off states (zero voltage) 'o* - t/,Jc II 1
Special parameters providing synchronization of the process of PWM P”~ АП - Ax сk-\yrFKml\K A’=(T-£")x КоЛК, P"= /3, x cos [(k-\yacoyt]K, A’=Cr-0")x ^ovl^s
Synchronous overmodulation control of dual three-phase converters
In accordance with the theory of vector space decomposition, the basic six-dimensional space (as, bs, cs, xs, ys, zs) of a dual three-phase induction machine with isolated neutral points can be transformed into two orthogonal two-dimensional subspaces (sa, sb) and (ml, m2) [1]. Voltage components Vsa and Vm1 in these subspaces, and also the phase voltage Vas = Vsa + Vm1, are calculated for symmetrical six-phase drive with two isolated neutrals as [4]:
VSa = 0.333(Va - 0.5Vb - 0.5Vc + 0.5Vx - Vy + 0.5Vz) (1)
Vm1 = 0.333(Va - 0.5Vb -0.5Vc - 0.5Vx + Vy - 0.5Vz) (2)
Vas = Vsa + Vm1 = Va - 0.333(Va + Vb + Vc) (3)
Vxs = Vsb + Vm2 = Vx - 0.333(Vx + Vy + Vz ), (4)
where Va, Vb, Vc, Vx, Vy, Vz are the corresponding pole voltages of each inverter (see Fig. 1).
In this case, the Vsa component, which produces useful rotating MMF k-th order voltage harmonics (k = 12m ± 1, m=1,2,3,..), is the useful component. But the Vm1 component, which generates loss-producing harmonics (k = 6m ± 1, m=1,3,5,..), is the undesirable voltage component.
Method of synchronized modulation, applied for control of symmetrical six-phase drives, is well suited for high quality linear control of the motor phase voltage of the drive system in the zone of overmodulation. Basic control correlations of this method (see Table I) include two special linear
functions (coefficients) of overmodulation Kov1 (5) and Kov2 (6), providing smooth pulses dropping process in this zone:
Kov1 = 1- (F - Fov1)/(Fov2 - Fov1)
(5)
Kov2 = 1- (F - Fov2)l(Fm - Fov2)
(6)
Typical control scheme for each inverter for standard V/F control of six-phase drive system during overmodulation is based on two-stage strategy with two threshold frequencies Fov1= 45.35 Hz (modulation index m=0.907 in this case) and Fov2 = 47.6 Hz (m=0.952) for the drive systems
with the maximum fundamental frequency equal to 50 Hz [6],[10]. So, control process consists from two basic parts in the overmodulation zone.
During the first control stage of the overmodulation zone, between the fundamental frequencies Fov1 and Fov 2, a smooth linear increase of total active signals (the ( -parameters in Table I) until the width of ( = t ( t - switching cycle) is observed for each inverter, with simultaneous smooth reduction of all notches X until zero at the Fov2 frequency.
It is known, that discontinuous schemes of space-vector PWM are the most preferable for drive control in the overmodulation zone. Fig. 2 - Fig. 3 present basic voltage waveforms (with spectra of the Vsa voltage) for period of the fundamental frequency of the symmetrical six-phase converter controlled in the mentioned above first part of the zone of overmodulation (F< Fov2: F=46.5Hz) in accordance with discontinuous synchronized PWM with the 300-non-switching intervals (DPWM30, Fig. 2), and with discontinuous synchronized PWM with the 600-nonswitching intervals (DPWM60, Fig. 3). Fig. 4 shows basic voltages and spectra of the Vsa voltage for symmetrical six-phase converter controlled by the combined scheme of synchronized PWM, where the first three-phase inverter is controlled in accordance with the DPWM30 algorithm, and the second inverter is controlled in accordance with the DPWM60 scheme. The average switching frequency is 900 Hz.
Fig. 2. Pole voltages Va and Vx, useful Vsa component of the phase voltage, and its spectrum, of the system with synchronized DPWM30 (F=46.5Hz)
Fig. 3. Pole voltages Va and Vx, useful Vsa component of the phase voltage, and its spectrum, of the system with synchronized DPWM60 (F=46.5Hz)
Fig. 4. Pole voltages Va and Vx, useful VSa component of the phase voltage, and its spectrum, of the system with combined DPWM30+DPWM60 control (F=46.5Hz)
Spectra of the useful component of the motor phase voltage (Figs. 2 - 4), and also spectra of the phase voltages of the symmetrical six-phase drives with algorithms of synchronized space-vector modulation include only odd (non-triplen) harmonics, and do not contain even harmonics and sub-harmonics.
In the second sub-zone of the drive control during overmodulation, between the FoV2 frequency and the maximum fundamental frequency Fm, there is a smooth decrease until close to zero value of the widths of all minor parts of active signals (of the y -signals in accordance with definitions of Table I).
Fig. 5 - Fig. 10 present basic voltage waveforms and spectrum of the VSa voltage of symmetrical six-phase system with three basic versions of synchronized PWM at the fundamental frequencies F=48.5Hz (Figs. 5 - 7), and F=49.5Hz (Figs. 8 - 10), which correspond to the control sub-zone of the highest fundamental frequencies, where modulation index m>0.952. The average switching frequency is equal to 900 Hz.
Fig. 11 presents basic voltage waveforms and spectrum of the VSa voltage of symmetrical six-phase system at the maximum fundamental frequency Fm = 50 Hz.
The motor phase voltage Vas (and its useful VSa component) of symmetrical dual three-phase (six-phase) drives have symmetry during overmodulation, and its spectra do not include even harmonics and sub-harmonics, which is especially important for high power/high current drives.
Fig. 5. Pole voltages Va and Vx, useful Vsa component of the phase voltage, and its spectrum, of the system with synchronized DPWM30 (F=48.5Hz)
Fig. 6. Pole voltages Va and Vx, useful Vsa component of the phase voltage, and its spectrum, of the system with synchronized DPWM60 (F=48.5Hz)
Fig. 7. Pole voltages Va and Vx, useful Vsa component of the phase voltage, and its spectrum, of the system with combined DPWM30+DPWM60 control (F=48.5Hz)
Fig. 8. Pole voltages Va and Vx, useful Vsa component of the phase voltage, and its spectrum, of the system with synchronized DPWM30 (F=49.5Hz)
Fig. 9. Pole voltages Va and Vx, useful Vsa component of the phase voltage, and its spectrum, of the system with synchronized DPWM60 (F=49.5Hz)
Fig. 10. Pole voltages Va and Vx, useful Vsa component of the phase voltage, and its spectrum, of the system with combined DPWM30+DPWM60 control (F=49.5Hz)
Fig. 11. Pole voltages Va and Vx, useful Vs component of the phase voltage, and its spectrum, of the system at the maximum fundamental frequency F=50Hz
Fig. 12 presents calculation results of Weighted Total Harmonic Distortion factor (WTHD) of the useful component of the phase voltage (of the Vsa voltage: averaged values of
/1000
WTHD = (1/ Vsai) ^ (Vsa / k)2 ) of symmetrical dual three-phase system with both identical and
V k=2
combined schemes of synchronized PWM in the overmodulation zone. The average switching frequency of each three-phase inverter is equal to 900 Hz during standard V/F control. The spectral characteristics, shown in Fig. 12, recommend combined DPWM30+DPWM60 scheme of synchronized PWM as the best choice to get reduced distortion of the useful component of the phase voltage of symmetrical six-phase system in the first half of the overmodulation zone.
Both in the first and the second parts of the overmodulation control zone of symmetrical dual three-phase system with synchronized PWM the spectra of the phase voltage of the induction motor contain only odd harmonics (without triplen harmonics), for any ratios between the switching and fundamental frequencies. These algorithms provide also smooth shock-less pulses-ratio changing during the whole control range.
WTHD of Vsa during over'modulation 0.05 1--------------------------------■-----------—
a>
9.9 0.92 0.94 0.96 0.98 1
modulation index m
Fig. 12. Averaged WTHD factor of the Vsa voltage versus modulation index
Conclusion
1. It has been shown, that combined scheme of synchronized PWM provides better spectral composition of the useful component of the phase voltage of dual three-phase drive in the first half of the overmodulation zone, in comparison with two identical schemes of modulation, used for control of the two inverters of six-phase system.
2. Both identical and combined schemes of synchronized space-vector-based PWM, applied for control of six-phase converters and drives, provide minimum number of switchings and minimal switching losses in power conversion systems.
3. Both identical and combined schemes of synchronized PWM allow continuous synchronization of the motor phase voltage during the whole overmodulation zone. The spectra of the phase voltage of symmetrical six-phase drives do not include even harmonics and sub-harmonics, which is especially important for high power/high current applications.
References
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About authors:
Valentin Oleschuk ([email protected]), Dr. (Habilitat) of Sc., is Chief Scientist of the Institute of Power Engineering of the Academy of Sciences of Moldova. His research interests include control and modulation strategies for power electronic converters, electric drives, and renewable energy systems.
Alexandr Sizov ([email protected]) is Researcher of the Institute of Power Engineering of the Academy of Sciences of Moldova. His research interests include modeling and simulation of
