Synchronous operation of five-phase converters in linear modulation region Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

SYNCHRONOUS OPERATION OF FIVE-PHASE CONVERTERS IN LINEAR MODULATION REGION

FUNCTIONAREA SINCRONA A CONVERTOARELOR PENTAFAZATE IN DOMENIUL MODULARII LINIARE

СИНХРОННОЕ РЕГУЛИРОВАНИЕ ПЯТИФАЗНЫХ ПРЕОБРАЗОВАТЕЛЕЙ В ЗОНЕ ЛИНЕЙНОЙ МОДУЛЯЦИИ

V. Oleschuk, F. Profumo, A. Sizov, A. Tenconi, E. Yaroshenko

RESUME

This paper presents results of the development and application of algorithms of synchronized pulsewidth modulation (PWM) for control of five-phase voltage source inverters. Simulations give the behavior of five-phase power conversion systems with algorithms of continuous and discontinuous synchronized PWM.

Keywords: multiphase modulated inverter, five-phase load, phase voltage synchronization.

RESUMAT

Aceasta lucrare prezinta resultatele dezvoltarii si aplicarea algoritmilor modularii in durata a pulsurilor sincronizate pentru controlul invertoarelor pentafazate sursa de tensiune. Simularile prezinta comportarea sistemelor pentafazate de conversie a energiei cu algoritmi de modulare sincronizata de tipurile continuu si discontinuu.

Cuvinte cheie: invertor multifazat modulat, sarcina pentafazata, sincronizarea tensiunilor de faza.

АННОТАЦИЯ

Исследованы пятифазные инверторы напряжения, регулируемые в соответствии с модифицированными алгоритмами синхронной широтно-импульсной модуляции. Приведены результаты моделирования пятифазных преобразовательных систем с непрерывной и прерывистой разновидностями синхронной модуляции.

Ключевые слова: многофазный инвертор с широтно-импульсной модуляцией, пятифазная нагрузка, синхронизация фазного напряжения.

1. INTRODUCTION

Multiphase power electronic converters and ac drives are a subject of increasing interest in the last years due to some advantages compared with standard three-phase systems, especially in the field of high power/high current applications. In particular, multiphase topologies of electric drives allow reduction of amplitude and increasing the frequency of torque pulsation, and also reduction of the rotor harmonic losses in electrical machines. Multiphase inverters and converters allow dividing of the controlled power on more inverter legs, reducing the rated current of power switches [1]-[2]. Between different multiphase solutions the more interesting and addressed ones are the five-phase and six-phase power conversion systems [1].

In particular, five-phase adjustable speed drives on the base of five-phase inverters are now ones of the most suitable topologies of multiphase drives for such perspective fields of application, as electric vehicles, ship propulsion, aerospace, etc. So, space-vector-based control and modulation methods and techniques for five-phase systems have been developed intensively during last period [3]-[9]. Five-leg voltage source inverters for five-phase drives are characterised by additional degrees of freedom for their control in comparison with conventional three-phase systems. At the same time it is known, that almost all versions of standard space-vector modulation are based on asynchronous principle, which results in subharmonics (of the fundamental frequency) in the spectrum of the output voltage of inverters, that are very undesirable in drive systems with increased power rating, operating at low switching frequencies [10],[11]. In particular, if the ratio between the switching and fundamental frequency of drive systems is less than 20-25, it is necessary to use synchronized PWM for control of these systems [11].

In order to avoid asynchronism of standard space-vector PWM, novel method of synchronized PWM has been recently proposed for control of standard three-phase inverters [12]. So, this paper present results of the development of this new PWM method for synchronous adjustment of five-phase drive inverter in the linear modulation region, until the zone of overmodulation.

2. SYNCHRONIZED SPACE-VECTOR PWM FOR A FIVE-PHASE SYSTEM

Basic topology of power circuit of a five-phase voltage source inverter with a star-connected load with the neutral point n is presented in Fig. 1 [7]. In particular, in the case of a five-phase motor as a load, the five stator phases a, b, c, d and e are distributed with a spacing of 720.

Space-vector pulsewidth modulation is one of the most suitable control techniques for five-phase systems. Similar to three-phase space-vector PWM, it can be developed for a five-phase system, as shown in Fig. 2 for a period of the fundamental frequency [4]. In particular, Fig. 2 shows ten basic switching vectors (1, 2, 3, 4, 5, 6, 7, 8, 9, 10) for a five-phase inverter in accordance with conventional designation (in brackets) of switching state of every switch of the inverter, where “1” corresponds to the switch-on state of the corresponding switch of the upper group of switches of the phases a - e [4]. This control scheme includes also two zero switching states (00000 and 11111), providing zero voltage at the outputs of the inverter.

Although total number of available voltage space vectors in five-phase inverter is equal to 32, the using only of the mentioned above 12 vectors (ten active vectors (large vectors [4]), and two zero vectors) allows minimum number of switchings in inverter and minimum switching losses [4]. It allows also providing continuous adjustment of the fundamental voltage during both undermodulation and overmodulation control zones, until the maximum phase-to-neutral voltage at the ten-step operation mode.

Fig. 1.

Fig. 2.

2.1. Principle of Continuous Voltage Synchronization

In order to provide synchronization of the process of space-vector PWM, a novel approach has been proposed for synthesis of the output voltage of three-phase inverters [12]. The main principles of this method, developed and modified for control of the five-phase systems, are based on the following deductions.

In accordance with principle of voltage space-vector modulation for symmetrical PWM versions, applied for control of five-phase systems, the ratio of durations of the corresponding total active switching state signals Pj during a sub-cycle to the central active switching state signal P, which is formed in the centre of the 360-clock-intervals, can be written as

P, sin(36 -a,) + sin a, „ _

— =--------- ---j-------j = 1.618[sin(360 -aj ) + sin aj ] (j = 2,...i) (1)

Pi sin(36 -a1) + sin a1

where aj - angle position of the centre of the p -signal from the beginning of the 360-clock-interval; a1 = 180 - the angle position of the central p -signal.

The relative widths of the y -components of total active switching states, which have less duration regarding the corresponding (p-y )-component, are equal to:

=------- sinK--^)----------- (k=i_1, .1) (2)

Pt-k+1 sm(36 -at-k+1) + sm( a--k+1)

So, one of the basic ideas of the method of synchronized PWM is in continuous

synchronization of the positions of all central signals p in the centres of the 360-clock-intervals (to fix positions of the p -signals in the centres of the 360-clock-intervals for the five-phase systems), and then - to generate symmetrically around the centres of the 360-clock-intervals all other active p - and y -signals in accordance with (1) and (2).

2.2. Continuous Synchronized PWM in A Five-Phase Inverter

As an example, Fig. 3 presents switching state sequence, switching signals (pole voltages Va - Ve) for the phases a - e, and the phase-to-neutral voltage Van on a half of period of the fundamental frequency F for five-phase inverter with continuous synchronized PWM. Continuous scheme of space-vector modulation is characterized by continuous switchings of each inverter leg during each sub-cycle. Switching states corresponds here to designations presented in Fig. 2. The phase-to-neutral voltage Van is calculated in accordance with (3) [5]:

Van = (4/5) Va - (1/5)(V&+Vc +Vd + Ve) (3)

Fig. 4 shows more in details control and output signals of the five-phase inverter for the first 360-clock-interval. Due to the symmetrical principle of generation of control signals, the phase-to-neutral voltage of five-phase system has quarter-wave symmetry during the whole diapason.

To provide realisation of algorithms of voltage space-vector modulation during synchronized PWM, a set of control functions connecting voltage parameters with the fundamental and switching frequencies of the system can be used, which is based on simple transformation of (1) and (2). In particular, in accordance with (1):

Switching state sequence

LJ1

0 36 72 108 144 180

■*

- l±±JJL±JLJJL±JLJL±JLJLJirin

Fig. 3.

Van

Fig. 4.

At the same time, the angle position aj of the centre of the corresponding P -signal in Figs. 3-4 is equal to:

a,

= 180 -(j-1)r (j=l,..i),

(5)

where r is the width of sub-cycle. So, for j=2, ...i:

Pj = P1 cos[(j - 1)r]

(6)

To realise widespread scalar control mode (V/F=const control) of adjustable speed five-phase drive system with linear control of the fundamental voltage until the zone of overmodulation, it is reasonable to execute simple linear control of the P -signal:

P1 = 1.03mr, (7)

and it provides the maximum width of the central signal, equal to the duration of the switching period at the end of the linear modulation range.

After analogue transformation of (2) for j=i-1, .2:

yj = Pi- j+1{0.5 - 0.809 tan[(i - j)r]} (8)

Duration of the notches between the signals in Figs. 3-4 for j=1, ...i-l:

kj =r-(Pj +Pj+1)/2 (9)

To provide the mentioned above in part 2.1 continuous synchronization of the output

voltage in five-phase inverters, by the analogy with the three-phase converters [12], the

scheme of synchronized PWM includes, as an important control parameter, boundary frequencies Fi, situated on the axis of the fundamental frequency F of the system. Fi is calculated in a general form as a function of the width of sub-cycles r in accordance with

(10), and the neighboring F-i - from (11). The modulation index is m = F/Fm in the case of

the scalar V/F control. Index i is equal to the numbers of notches inside a half of the 360-

clock-intervals and it is determined from (12), where fraction is rounded off to the nearest higher integer:

F =--------------1------- (10)

- 10 (2i - 1)r v 7

F-1 =------------1------- (11)

--1 10 (2i -3)r v 7

i = 1/10 F + r (12)

2r

The process of voltage synchronization in five-phase systems is also connected with specialized control of the signals situated near the boundaries of the 360-clock-intervals. In particular, for the waveforms presented in Figs. 3 - 4, where i=4, the corresponding boundary signals are: k4 = k = k, P4 = Pt = P" , and y1. Control functions (14)-(16) for determination

of these parameters include special linear coefficient of synchronisation Ks (13), providing smooth step-by-step quasi-linear variation of these signals from the rated value to close to zero value between the boundary frequencies Fi and Fj.f.

Ks = 1- F-F^ (13)

* Fi-1 -Ft V '

Pi = P = P cos[(i - 1)r]K* (14)

k =k=(r-P K (15)

y = 5P"(k+P")FK* (16)

2.3. Disontinuous Synchronized PWM in A Five-Phase Inverter

Fig. 5 presents switching state sequence, pole voltages Va - Ve for the phases a - e, and

the phase-to-neutral voltage Van on a half of period of the fundamental frequency F for five-

phase inverter with discontinuous synchronized PWM. Discontinuous scheme of space-vector modulation for five-phase inverters is characterized by the four 180-non-switching intervals during period of the fundamental frequency.

Fig. 6 shows more in details control and output signals of the five-phase inverter with discontinuous PWM for the first 360-clock-interval. Control functions for determination of the boundary frequencies and index i are slightly modified in this case in comparison with continuous synchronized PWM:

Fi =-------1---- (17)

i 10(2i -1.5)r v 7

F 1 =------1---- (18)

i-1 10(2i-3.5)r v 7

. 1/10F + 1.5r ,1iV.

1 =---------------- (19)

2t

Fig. 5.

Fig. 6.

3. OPERATION OF THE SYNCHRONIZED FIVE-PHASE SYSTEM IN LINEAR

MODULATION RANGE

Algorithms of synchronized space-vector PWM allow continuous shock-less synchronization of waveforms of the output voltage of five-phase inverter during the whole control range including the zone of overmodulation. Fig. 7 - Fig. 10 present basic voltage waveforms (with spectral characteristics of the phase-to-neutral voltage) of the five-phase inverter controlled in accordance with two basic schemes of synchronized PWM: 1)

Continuous synchronized PWM (Fig. 7 and Fig. 9), and 2) Discontinuous PWM with the 18 -non-switching intervals (Fig. 8 and Fig. 10).

Curves in Figs. 7 - 8 correspond to the zone of low fundamental frequencies of the system (F = 20 Hz, modulation index m = 0.4 in the case of the scalar V/F control). The average switching frequency is 1.5 kHz. Fig. 7 (continuous PWM) and Fig. 8 (discontinuous PWM) present the pole voltages Va - Ve, line voltage Vac, and phase-to-neutral voltage Van (together with spectrum of the phase-to-neutral voltage) of the five-phase system with synchronized PWM.

Fig. 7.

Fig. 8.

Fig. 9 - Fig. 10 present basic voltage waveforms (with spectral characteristic of the phase-to-neutral voltage) of the five-phase inverter with continuous synchronized PWM (Fig. 9), and with discontinuous synchronized modulation (Fig. 10), operating in the zone of higher fundamental frequencies, where F = 40Hz (modulation index m=0.8 in the case of V/F control). The average switching frequency is 1.5 kHz.

Fig. 9.

Fig. 10.

Algorithm of synchronized PWM provides continuous symmetry of the phase-to-neutral voltage of the five-phase system. So, its spectrum includes only odd (non fifth-order) harmonics for both continuous and discontinuous versions of synchronized PWM for any fundamental frequencies and for any (integer and fractional) ratios between the switching frequency and fundamental frequency. In particular, the control mode of the inverter, presented in Figs. 9-10, is characterized by the fractional ratio between the switching frequency and fundamental frequency, equal to 1500/40=37.5, but the phase-to-neutral voltage has quarter-wave symmetry in this control mode too.

During synthesis of algorithms of synchronized PWM for five-phase inverters it is necessary to take into consideration real parameters of inverter switches (turn-on and turn-off delays), and to provide minimum duration of switching states, dead-time compensation, etc., in accordance with the corresponding technical solutions [10],[11].

Analysis of spectral composition of the phase-to-neutral voltage of five-phase inverter, controlled in accordance with the scheme of space-vector modulation with ten active voltage vectors and two zero vectors, presented in Fig. 2, shows presence in its spectrum of the large third harmonic during the whole control range for both continuous and discontinuous versions of PWM. Due to this big third harmonic content, total harmonic distortion of the phase-to-

neutral voltage, and also weighted total harmonic distortion factor, are practically identical for continuous and discontinuous schemes of synchronized PWM.

Fig. 11 shows variation of the magnitude of the third harmonic of the phase-to-neutral voltage of five-phase inverter with standard V/F control mode. The magnitude of the third harmonic is in practically linear dependence of modulation index m, and its value is practically identical for both continuous and discontinuous versions of synchronized PWM. And relative (to the magnitude of the fundamental harmonic) value of the third voltage harmonic is close in this case to the constant ratio equal to 0.28.

Fig. 11.

It is necessary to mention, that due to the specific peculiarities of the five-phase drives on the base of the electrical machine with concentrated windings, it is possible to utilize the third harmonic stator current injection to enhance the torque production [4],[5],[8]. So, the presented twelve-vector-based scheme of synchronized PWM, which is characterized by big third harmonic in the spectrum of the phase-to-neutral voltage, can provide increased torque per ampere ratio in the five-phase drives with the motors with concentrated winding.

CONCLUSION

A novel method of synchronized PWM has been developed and modified for control of five-phase voltage source inverters. The proposed control algorithms, based on space-vector approach for determination of the pulse patterns, allow minimum number of switchings in five-phase systems and minimal switching losses.

Both continuous and discontinuous schemes of synchronized PWM provide smooth symmetrical shock-less voltage control in five-phase inverter systems during the whole linear control range for any ratio (integral or fractional) between the switching frequency and fundamental frequency. The phase-to-neutral voltages of inverters have symmetry during this

control diapason, and its spectra do not contain even harmonics and sub-harmonics, which is especially important for the drive systems with increased power/current ratings.

Due to the specific peculiarities of the five-phase drives, the presented twelve-vector-based schemes of synchronized PWM, producing controlled third harmonic in the spectrum of the phase-to-neutral voltage, can provide increased torque per ampere ratio in the five-phase drives with the motors with concentrated winding.

ACKNOWLEDGMENT

This research has been supported in part by Marie Curie International Fellowships Award of the FP6 Program of the European Commission.

REFERENCES

[1] R. Bojoi, F. Farina, F. Profumo and A. Tenconi, “Dual-three phase induction machine drives control - a survey”, CD-ROM Proc. of the 2005 IEEE Int’l Power Elect. Conf., 10 p.

[2] V. Oleschuk, R. Bojoi, F. Profumo, A. Tenconi and A.M. Stankovic, “Multifunctional six-phase drives with algorithms of synchronized PWM”, Proc. of the 2006 IEEE Ind. Electr. Soc. Conf., pp.1852-1859.

[3] H.A. Toliyat, “Analysis and simulation of five-phase variable-speed induction motor drives under asymmetrical connections,” IEEE Trans. on Power Electr., vol. 13, no.4, 1998, pp.748-756.

[4] R. Shi and H.A. Toliyat, “Vector control of five-phase synchronous reluctance motor with space vector pulse width modulation (SVPWM) for minimum switching losses,” Proc. of the 2002 IEEE Appl. Power Electr. Conf., pp.57-63.

[5] H. Xu, H.A. Toliyat and L.J. Peterson, “Five-phase induction motor drives with DSP-based control system,” IEEE Trans. on Power Electr., vol.17, no.2, 2002, pp.524-533.

[6] A. Iqbal and E. Levi, “Space vector modulation schemes for a five-phase voltage source inverter,” CD-ROM Proc. of the 2005 European Power Electr. Conf., 12 p.

[7] A. Iqbal, E. Levi, M. Jones and S.N. Vukosavic, “Generalised sinusoidal PWM with harmonic injection for multi-phase VSIs,” CD-ROM Proc. of the 2006 IEEE Power Electr. Spec. Conf., 7 p.

[8] H.M. Ryu, J.H. Kim and S.K. Sul, “Analysis of multiphase space vector PWM based on multiple d-q spaces concept,” IEEE Trans. on Power Electr., vol.20, no.6, 2005, pp.1364-1371.

[9] A. Iqbal and E. Levi, “Space vector model of a five-phase voltage source inverter,” Proc. of the 2006 IEEE Int’l Conf. on Ind. Technology, pp.488-493.

[10] J. Holtz, “Pulsewidth modulation for electronic power conversion,” Proc. of IEEE, vol. 82, no. 8, 1994, pp. 1194-1213.

[11] N. Mohan, T.M. Undeland and W.P. Robbins, Power Electronics, 3rd ed., John Wiley & Sons, 2003.

[12] V. Oleschuk and F. Blaabjerg, “Direct synchronized PWM techniques with linear control functions for adjustable speed drives,” Proc. of the 2002 IEEE Appl. Power Electr. Conf., pp.76-82.

Valentin Oleschuk, D.Sc., is Director of the Research Laboratory of the Power Engineering Institute of the Academy of Sciences of Moldova. He is author and co-author of two books and more than 170 publications in the field of Power Electronics and Electric Drives, including 40 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.

Francesco Profumo, Ph.D., is Professor of electrical machines and drives of the Politecnico di Torino, Italy. He is author and co-author of more than 250 prestigious publications (mainly in the IEEE transactions and proceedings) on Power Electronics and Electric Drives. His fields of interests are high-power devices, integrated electronic/electromechanical design, high response speed servo drives, and new electrical-machine structures.

Alexandr Sizov is Scientific Collaborator of the Laboratory of Automated Electric Drives of the Power Engineering Institute of the Academy of Sciences of Moldova. He is author and co-author of about 50 publications and 10 patents and authors certificates. His research interests include elaboration, modelling and simulation of control algorithms and control systems for power electronic converters and drive systems.

Alberto Tenconi, Ph.D., is Professor of the Department of Electrical Engineering of the Politecnico di Torino, Italy. He is author and co-author of more than 100 papers published in international journals and international conference proceedings. His fields of interest are high-performance-drive design, new power-electronic-device applications and nonconventional electric machine development.

Evgeni Yaroshenko is Scientific Collaborator of the Laboratory of the Automated Electric Drives of the Power Engineering Institute of the Academy of sciences of Moldova. He is author and co-author of more than 50 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.