induction machine with two sets of windings, spatially shifted by 30 el. degrees, can be based on four inverters, supplying open-end windings of ac motor (Fig.
2015 International Conference on Electrical Drives and Power Electronics (EDPE)
The High Tatras, 21-23 Sept. 2015
Six-Phase Motor Drive with Variable Switching Frequencies and Voltage Synchronization of Inverters Valentin Oleschuk, Vladimir Ermuratskii
Federico Barrero
Institute of Power Engineering Academy of Sciences of Moldova Kishinau, Moldova
Department of Electronic Engineering University of Seville Seville, Spain
Abstract—In this paper, modulation processes have been analyzed in six-phase asymmetrical motor drive on the base of four inverters with discontinuous synchronous modulation. It has been shown, that flexible PWM strategy based on control of switching frequencies of inverters as function of dc voltages allows to improve system performance and to insure voltage waveform symmetries during adjustment range. Simulations validate operation of systems with basic control modes.
II. SWITCHING STRATEGY PROVIDING CONTINUOUS VOLTAGE SYNCHRONIZATION OF DRIVE INVERTERS In order to assure voltage waveform symmetries of modulated inverters, method of synchronized modulation [7]-[8] can be used for PWM control of each inverter of sixphase system, and Table I presents its basic features and peculiarities, compared also with convention scheme of space-vector modulation [7]. Fig. 2 presents generalized flow-chart for determination of pulse patterns of inverter with synchronized space-vector PWM. Basic concept of the proposed PWM method is in continuous synchronization of positions of all central active signals in the centers of the 600-clock-intervals, with further symmetrical generation of other active signals, together with the corresponding notches, around the central signals. Boundary frequencies Fi and Fi −1 between control subzones of this method of modulation are calculated in a general form as functions of duration of sub-cycles τ in accordance with (1)-(2). Index i is equal to number of notches inside a half of the 600-clock-intervals, and is determined from (3), where fraction is rounded off to the nearest higher integer [7].
Keywords—converter control, modulation strategy, simulation
I. INTRODUCTION Multiphase converters and drives are perspective alternative of existing three-phase solutions for the mediumpower and high-power adjustable speed drive systems [1]-[3]. Topology of six-phase drive systems with asymmetrical induction machine with two sets of windings, spatially shifted by 30 el. degrees, can be based on four inverters, supplying open-end windings of ac motor (Fig. 1 [4]-[6]). These structures have additional degrees of freedom for organization of control strategies. So, this paper presents analysis of operation of six-phase system with flexible PWM control based on adjustment of switching frequency of each inerter (with separate dc-source) as a function of dc voltage.
Fig. 1. Six-phase drive on the basis of four inverters (INV1+INV2, supplied by Vdc1 and Vdc2 dc sources, as the first group, and INV3+INV4, supplied by Vdc3 and Vdc4 dc sources, as the second group) and with open-end winding asymmetrical six-phase induction motor.
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2015 International Conference on Electrical Drives and Power Electronics (EDPE) TABLE I.
BASIC FEATURES OF METHODS OF PWM
Control (modulation) parameter
Conventional schemes of space-vector PWM
Operating and max parameter
Operating & max voltage V and Vm
Modulation index m Duration of subcycles Center of the k-signal
Proposed method of synchronized modulation Operating & maximum fundamental frequency F and Fm
V / Vm
F / Fm
τ
T
Trigonometric PWM
Algebraic PWM Switch-on durations
Tak = 1.1mT [sin(60 0
β k = β1[1 − A ×
−α k ) + sin α k ]
(k − 1)τFKov1 ]
tbk = 1.1mT × Switch-off states (zero voltage)
cos[(k − 1)τK ov1 ]
βk − γ k
βk − γ k
sin( 60 0 − α k )
λk = τ − β k
t0k = T − tak − tbk
β " = β 1[1 − A ×
Special parameters providing synchronization of the process of PWM
β " = β1 × cos
(k − 1)τFKov1 ]K s [(k − 1)τK ov1 ]K s
λ ' = (τ − β " ) ×
λ ' = (τ − β ") ×
K ov1 K s
Kov1Ks
F
τ i Fi −1 and F i
β1 βk
β" λ′
λk
γ1
γk
Direct synthesis of the waveform Fig. 2. Diagram of determination of pulse patterns of inverter with synchronous pulsewidth modulation.
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III. OPERATION OF SIX-PHASE SYSTEM WITH VARIABLE SWITCHING FREQUENCIES OF MODULATED INVERTERS Phase voltages Vas and Vxs of the first and the second groups of dual inverters with four insulated dc-sources (Fig. 1) are calculated in accordance with (4)-(7) [6],[9]:
Vas = Va1 + Va2 - V01 V02 = 1/3(Vx1 + Vy1 + Vz1 + Vx2 + Vy2 + Vz2)
β k = β1 ×
γ k = β i − k +1[0.5 − γ k = β i − k +1[0.5 − 6(i − k )τF ]K ov 2 0.9tn(i − k )τ ]K ov 2
tak = 1.1mT sin α k
where K1=1, K2=3 for continuous versions of PWM, K1=1.5, K2=3.5 for discontinuous versions of PWM.
V01 = 1/3(Va1 + Vb1 + Vc1 + Va2 + Vb2 + Vc2)
τ (k − 1) (sec)
α k (angles/degr.)
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Fi = 1/[6(2i − K1 )τ ]
(1)
Fi −1 = 1/[6(2i − K 2 )τ ]
(2)
i = (1 / 6 F + K 1τ ) / 2τ ,
(3)
Vxs = Vx1 + Vx2 - V02,
(4) (5) (6) (7)
where Va1, Vb1, Vc1, Va2, Vb2, Vc2 and Vx1, Vy1, Vz1, Vx2, Vy2, Vz2 are the corresponding pole voltages of each group of threephase inverters, V01 and V02 are the corresponding zero sequence voltages of the first and the second inverter sections. To assure approximate equivalence of the phase fundamental voltages (and also power balancing) of two groups of inverters during scalar V/F control, it is necessary to provide linear correlations between modulation indices of four inverters and magnitudes of the corresponding dc voltages: m1 Vdc1 + m2 Vdc2 = m3 Vdc3 + m4 Vdc4
(8)
Also, switching frequencies Fs1 – Fs4 of four inverters can be used as additional control parameters for organization of rational control of the presented six-phase system. It is known, that basic losses of power switches of inverters are approximately proportional to the corresponding switching frequency. In particular, if inverters of equal rated power and power losses are used in this system topology, it is possible to correct proportionally relative switching frequency of individual inverter as a function of dc voltage of the corresponding dc-source. To analyze operation of six-phase system with controlled switching frequencies of inverters, several modes of operation of the system based on four inverters with discontinuous synchronized PWM (discontinuous pulsewidth modulation with the 300-non-switching intervals [6],[8],[10]) have been chosen for simulation of modulation processes in quadinverter system (Table II, Modes 1-6). It has been chosen, that INV4 has been supplied by the maximum relative dc voltage Vdc4=1, and dc voltages of other modulated inverters were equal or less of this value. Correspondingly, switching frequency of INV4 has been chosen equal to Fs4=1kHz, and switching frequencies of other inverters have been equal or bigger of this frequency. Fig. 3 – Fig. 20 present results of simulation of the system operated under Modes 1-6, it show basic voltage waveforms (normalized voltages) of six-phase four-inverter-based ac drive, together with spectral composition of the line-to-line and phase voltages of the system.
2015 International Conference on Electrical Drives and Power Electronics (EDPE) TABLE II.
Mode
F, Hz
1
32
2
38
3
36
4
37
5
33
6
45
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MODES OF OPERATION OF SIX-PHASE SYSTEM
Parameter Vdc m Fs Vdc m Fs Vdc m Fs Vdc m Fs Vdc m Fs Vdc m Fs
INV1
INV2
INV3
INV4
1 0.64 1kHz 0.5 0.76 2kHz 0.8 0.9 1.25kHz 0.75 0.98 1.33kHz 0.75 0.88 1.33kHz 0.95 0.947 1.05kHz
1 0.64 1kHz 1 0.76 1kHz 0.8 0.9 1.25kHz 1 0.74 1kHz 0.9 0.73 1.11kHz 0.98 0.918 1.02kHz
1 0.64 1kHz 0.5 0.76 2kHz 1 0.72 1kHz 1 0.74 1kHz 0.8 0.825 1.25kHz 0.96 0.937 1.04kHz
1 0.64 1kHz 1 0.76 1kHz 1 0.72 1kHz 1 0.74 1kHz 1 0.66 1kHz 1 0.9 1kHz
Fig. 5. Spectrum of the phase voltages (Mode 1).
Fig. 6. Basic voltage waveforms of six-phase system (Mode 2, F=38Hz, Vdc1=0.5Vdc4, Vdc2=Vdc4, Vdc3=0.5Vdc4, m1=m2=m3=m4=0.76, Fs1=Fs3=2kHz, Fs2=Fs4=1kHz).
Fig. 3. Basic voltage waveforms of six-phase system with equal dc-voltages (Mode 1, F=32Hz, Vdc1=Vdc2=Vdc3=Vdc4, m1=m2=m3=m4=0.64, Fs=1kHz).
Fig. 4. Spectrum of the line-to-line voltages (Mode 1).
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Fig. 7. Spectra of the line-to-line voltages (Mode 2).
2015 International Conference on Electrical Drives and Power Electronics (EDPE)
The High Tatras, 21-23 Sept. 2015
Fig. 8. Spectrum of the phase voltages (Mode 2).
Fig. 11. Spectra of the phase voltages (Mode 3).
Fig. 9. Basic voltage waveforms of six-phase system (Mode 3, F=36Hz, Vdc1=Vdc2=0.8Vdc3=0.8Vdc4, m1=m2=0.9, m3=m4=0.72, Fs1=Fs2=1.25kHz, Fs3=Fs4=1kHz).
Fig. 12. Basic voltage waveforms of six-phase system (Mode 4, F=37Hz, Vdc1=0.75Vdc2=0.75Vdc3=0.75Vdc4, m1=0.98, m2=m3=m4=0.74, Fs1=1.33kHz).
Fig. 10. Spectra of the line-to-line voltages (Mode 3).
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Phase shift between signals of dual inverters of each inverter group is an important control parameter of the presented system. It is known, that in the case of equal dc voltages of dual inverters this shift should be equal to a half of duration of switching sub-cycle τ [6]. In the case of unequal dc-link voltages of dual inverters and controlled switching frequencies as function of dc voltage, rational value of phase shifts between signals of dual inverters can be determined for the first and the second inverter sections as functions of the corresponding sub-cycles: /4 and /4. Analysis of basic voltage waveforms and its spectra, presented in Figs. 3-20, shows, that in the case of equal dc voltages of inverters of one group (Modes 1, 3), the corresponding line and phase voltages have quarter-wave symmetry. In other cases (Modes 2, 4-6) phase voltages have half-wave symmetry, but line voltages have quarter-wave symmetry for the all presented modes. In all these cases voltage spectra contain only odd (non-triplen) harmonics.
2015 International Conference on Electrical Drives and Power Electronics (EDPE)
The High Tatras, 21-23 Sept. 2015
Fig. 15. Basic voltage waveforms of six-phase system (Mode 5, F=33Hz, Vdc1=0.75Vdc4, Vdc2=0.9Vdc4, Vdc3=0.8Vdc4, m1=0.88, m2=0.73, m3=0.82, m4=0.66, Fs1=1.33kHz, Fs2=1.11kHz, Fs3=1.25kHz, Fs4=1kHz).
Fig. 13. Spectra of the line-to-line voltages (Mode 4).
Fig.14. Spectra of the phase voltages (Mode 4).
It is necessary to mention, that due to the use of variable switching frequencies of inverters of six-phase system some inverters are controlled in the overmodulation zone under some control conditions. In particular, data of Table II show, that, under Mode 4, INV1 (m1=0.98) is controlled in the overmodulation zone. Also, under Mode 6, INV1- INV3 (m1=0.95, m2=0.92, m3=0.94) are controlled in the overmodulation zone.
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Fig. 16. Spectra of the line-to-line voltages (Mode 5).
2015 International Conference on Electrical Drives and Power Electronics (EDPE)
The High Tatras, 21-23 Sept. 2015
Fig. 17. Spectra of the phase voltages (Mode 5).
Fig. 19. Spectra of the line-to-line voltages (Mode 6). Fig. 18. Basic voltage waveforms of six-phase system (Mode 6, F=45Hz, Vdc1=0.95Vdc4, Vdc2=0.98Vdc4, Vdc3=0.96Vdc4, m1=0.947, m2=0.918, m3=0937, m4=0.9, Fs1=1.05kHz, Fs2=1.02kHz, Fs3=1.04kHz, Fs4=1kHz).
Weighted Total Harmonic Distortion factor (WTHD, 1000
WTHD = (1 / Vas1 )(
∑ (V k =2
ask
/ k ) 2 ) 0.5 ) of the phase voltage Vas
as function of modulation index has been calculated for some control modes of the system (Table III (data regarding Mode 2 are presented here), Fig. 21). Therefore, data presented in Fig. 21 show results of determination of WTHD factor for the phase voltage Vas of the first group of inverters INV1+INV2, operating under Mode 3. These diagrams illustrate the fact, that increasing of switching frequency of inverters with smaller dc voltage leads to remarkable improvement of integral spectral characteristics of the phase voltage of the corresponding group of inverters (the less is basic (nominal) switching frequency, the more is this improvement)..
EDPE 2015
Fig. 20. Spectra of the phase voltages (Mode 6).
2015 International Conference on Electrical Drives and Power Electronics (EDPE) TABLE III.
m1=m2 Fs1=Fs2= 1kHz Fs1=2kHz Fs2=1kHz
WTHD FACTOR OF THE PHASE VOLTAGE VAS (%, MODE 2)
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.57
0.60
0.62
0.69
0.76
0.65
0.68
0.81
0.89
0.94
0.88
0.83
0.75
0.84
in the case of unequal switching frequencies, the used PWM algorithm does not assure this property, and phase voltage spectra is worse than in the system with equal switching frequency of inverters (see data of Table III). 4. It has been shown, that for some operation regimes it is possible to improve spectra of the phase voltage by control of switching frequencies of the corresponding inverters as a function of dc-link voltage (Modes 3-6, Fig. 21). 5. The presented PWM strategy insures synchronous control of the system in the overmodulation zone in the case of small difference of dc-link voltages (Mode 6, three invertors INV1-INV3 operate in this case in the overmodulation zone). 6. Operation of separate inverter of the system in the second part of the zone of overmodulation (Mode 4, m1=0.98>0.952) (during linear operation regime of other inverters) leads to distortion of the phase voltage of the corresponding group of inverters, and it is necessary to try to avoid such regimes. 7. Other schemes of synchronized PWM (continuous and other discontinuous ones), like described in [10], can also be used for flexible synchronous control of multi-inverter systems. 8. Simple correction of the presented PWM algorithms can assure voltage synchronization of inverters and drive systems operating under regimes with non-linear dependences between fundamental voltage and fundamental frequency [11]. REFERENCES
Fig. 21. Averaged WTHD factor of the phase voltage Vas (Mode 3). [1]
IV. CONCLUSION AND DISCUSSION Multi-inverter power conversion systems have additional degrees of freedom for organizations of schemes and algorithms of control and modulation. Comparative analysis of modulation processes of six-phase drive system on the base of four inverters (with discontinuous synchronized PWM) with isolated dc-links with different dc-voltages, and with controlled switching frequencies of inverters, have been done in the paper. Several typical operation modes (Mode 1 – Mode 6) have been considered. Some basic deductions can be formulated based on results of simulation of processes in the system with standard scalar control: 1. It has been shown (see Modes 1–6, Figs. 3-20), that algorithms of synchronized PWM assure voltage waveform symmetries of multi-inverter system for the case of fractional frequency ratios (but not only for integral ratios) between the switching and fundamental frequencies of inverters (basic switching frequency was equal to 1kHz, and fundamental frequencies were equal to 32, 33, 34, 35, 37, 38, 45 Hz in these modes). 2. In the case of equal dc voltages and switching frequencies of inverters of one group (Modes 1, 3), the corresponding line and phase voltages of the system have quarter-wave symmetry. In other cases (Modes 2, 4-6) phase voltages have half-wave symmetry, but line voltages have quarter-wave symmetry for the all modes. In all these cases voltage spectra contain only odd (non-triplen) harmonics. 3. Phase voltage of the system operating under Mode 1 (Vdc1=Vdc2) is equal to phase voltage of three-level inverter. Phase voltage of the system operating under Mode 2 (Vdc1=0.5Vdc2, and equal switching frequency of dual inverters) is equal to the phase voltage of four-level inverter [6],[9]. But
EDPE 2015
The High Tatras, 21-23 Sept. 2015
G.K Singh, “Multi-phase induction machine drive research – a survey,” Electric Power System Research, vol. 61, pp. 139-147, 2002. [2] M. Jones, O. Dordevic, N. Bodo, and E. Levi, “PWM algorithms for multilevel inverter supplied multiphase variable-speed drives,” Electronics, vol. 16, no. 1, pp. 22-31, 2012. [3] J. Prieto, M. Jones, F. Barrero, E. Levi, and S. Toral, ‘‘Comparative analysis of discontinuous and continuous PWM techniques in VSI-fed five-phase induction motor,’’ IEEE Trans. Ind. Electron., vol. 58, no. 12, pp. 5324---5335, 2011. [4] G. Grandi, A. Tani, P. Sanjeevkumar, and D. Ostojic, “Multi-phase multi-level AC motor drive based on four three-phase two-level inverters,” Proc. IEEE Int’l Symp. on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM’2010), pp. 1768-1775, 2010. [5] G. Grandi, P. Sanjeevkumar, and D. Casadei, “Preliminary hardware implementation of a six-phase quad-inverter induction motor drive,” Proc. European Power Electronics Conf. (EPE’2011), 9 p., 2011. [6] V. Oleschuk, G. Grandi, and P. Sanjeevkumar, “Simulation of processes in dual three-phase system on the base of four inverters with synchronized modulation,” Advances in Power Electronics, vol. 2011, pp. 1-9, 2011. [7] V. Oleschuk and F. Blaabjerg, “Synchronized scheme of continuous space-vector PWM with the real-time control algorithm,” Proc. IEEE Power Electronic Specialists Conf. (PESC’2004), pp.1207-1213, 2004. [8] V. Oleschuk, R. Bojoi, G. Griva, and F. Profumo, “Dual inverter-fed traction drives with dc sources power balancing based on synchronized PWM,” Proc. IEEE Int’l Electric Machines and Drives Conf. (IEMDC’2007), pp. 260-265, 2007. [9] B.V. Reddy, V.T. Somasekhar, and Y. Kalyan, “Decoupled spacevector PWM strategies for a four-level asymmetrical open-end winding induction motor drive with waveform symmetries,” IEEE Trans. Ind. Electron., vol. 58, no. 11, pp. 5130-5141, 2011. [10] V. Oleschuk and F. Barrero, “Standard and non-standard approaches for voltage synchronization of drive inverters with space-vector PWM: A survey,” International Review of Electrical Engineering, vol. 9, no. 4, pp. 688-707, 2014. [11] V. Oleschuk and M.P. Kazmierkowski, “Dual-source fed multiphase traction system with standard and non-standard controlled regimes based on synchronized PWM,” Proc. IEEE/EPE Power Electronics and Motion Control Conf. (EPE-PEMC’2008), pp. 1571-1577, 2008.
