Algorithms of space vector PWM in overmodulation area

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1 DSpace VSB-TUO hp:// Advances in Elecrical and Elecronic Engineering (AEEE) AEEE. 2006, vol. 5 Algorihms of space vecor PWM in overmodulaion area T15:56:34Z hp://hdl.handle.ne/10084/83774 Downloaded from DSpace VSB-TUO

2 Advances in Elecrical and Elecronic Engineering 90 ALGORITHMS OF SPACE VECTOR PWM IN OVERMODULATION AREA Z. Perouka, T. Glasberger Universiy of Wes Bohemia / Deparmen of Elecromechanics and Power Elecronics, Plze, Czech Republic perouka@ieee.org, glasber@kev.zcu.cz Summary The aim of his paper is he comparison and evaluaion of differen space vecor PWM (SVPWM) sraegies enabling he coninuous ransiion from he linear modulaion o he six-sep mode. One of he imporan facors o be explored is he frequency analysis of he moor quaniies in order o be able o evaluae he possible impac of he drive on he racion mains specifically he impac on he railway signaling. This research has been suppored by he Minisry of Indusry and Trade of he Czech Republic under he projec MPO R FI-IM2/ INTRODUCTION Space vecor PWM (SVPWM) is eligible for he modern conrol algorihms of adjusable speed drives and acive recifiers. The operaion of his modulaion scheme in he overmodulaion area as well as coninuous ransiion ino he six-sep mode is sill under he research (e.g. [1] [3]). The operaion in he overmodulaion area and he ransiion ino he six-sep mode can cause he problems no only from he conrol viewpoin, bu can also be he source of he serious problems in he racion applicaions e.g. adverse ineracion of he racion drive wih he railway signaling, wha is one of our imporan research objecive. 2. SVPWM IN OVEMODULATION AREA A. Overmodulaion Sraegy 1 (OS1) This algorihm [2] is quie simple for he implemenaion. The principle of he overmodulaion algorihm 1 is illusraed in he Fig. 1. The demanded volage vecor u* (conrol command) is produced so long, unil is circular rajecory inersecs he hexagon edge (Fig. 1a, in his mode u* = u, where u is he real converer oupu volage vecor). When he vecor u* inersecs he hexagon edge (Fig. 1b), he real converer oupu vecor u says in his consan posiion (γ so called hold angle), while he demanded vecor u* moves o (π/6) in he given secor. Thereafer he real vecor jumps o he posiion (π/3 - γ ), (Fig. 1c). When he vecor u* achieves posiion (π/3 - γ ) i means ha u* inersecs he hexagon edge again, hen he converer produces he real vecor u, which corresponds wih demanded vecor u* (u = u*) symmeric acion in he hexagon verexes (Fig. 1d). B. Overmodulaion Sraegy 2 (OS2) This overmodulaion sraegy is based on [3]. In his mehod, he overmodulaion area is divided using he modulaion index mi 1 (1) ino wo sub-areas: overmodulaion area I and II (OAI and OAII respecively). The modulaion index is defined as: u * mi1 =, (1) U where u* is size of he demanded volage vecor, U max = (2/3U dc ) is maximum phase volage accessible in he six-sep mode and U dc is he converer dc-link volage. Thus, he index mi 1 shows he acual uilizaion of he converer volage capabiliy. In he overmodulaion area I, he reference vecor size is changed, while he reference volage vecor angle is mainained he demanded volage vecor angle and real converer oupu volage vecor angle max Fig. 1. Principle of he firs invesigaed overmodulaion algorihm (OS1): (γ posiion of he real converer oupu volage vecor u, γ 1 posiion of demanded volage vecor u*, γ hold angle) Fig. 2. OS2: Space vecor rajecory in overmodulaion area I is he same. If he demanded volage vecor u* is inside he hexagon (beween poins A-B), he

3 91 Algorihms of space vecor PWM in overmodulaion area modulaion employs common sraegy for linear modulaion area [4]. When he demanded vecor u* rajecory passes ouside he hexagon (he demanded volage vecor is ou of he converer volage capabiliy), he swiching imes mus be calculaed wih (2), he zero vecor is no used and he real converer oupu volage vecor u moves along he hexagon edge, ha is beween poins B-C as is shown in he Fig. 2. T pwm 1. α T =, (2a) 3 π / 3 T = T T, (2b) 2 pwm 1 where T 1 is he swich on ime of he firs ouer vecor, T 2 is he swich on ime of he second ouer vecor and T pwm is PWM period. γ = 0 for 0 γ γ, (3a) γ γ π γ = for γ γ π /3 γ, π / 6 γ 6 γ = π / 3 for π /3 γ γ π /3, (3c) In he overmodulaion area II, he real converer oupu volage vecor u rajecory changes gradually from hexagon o he discree six-sep rajecory. A firs in he swiching period, he real converer volage vecor u says in he ouer posiion, which corresponds wih he six-sep mode (Fig. 3a). When he demanded volage vecor u * posiion reaches he hold angle γ, hen he real converer oupu volage vecor u moves along he hexagon edge (Fig. 3b). This operaion is symmerically repeaed on he second side of he secor in order o produce symmerical pulse paern of he converer oupu volage (Fig. 3c,d). (3b) The posiion (γ ) of he converer oupu volage vecor u corresponding o he given demanded vecor u* is calculaed by (3). C. Overmodulaion Sraegy 3 (OS3) This algorihm based on [1] uses he modulaion deph (mi 2 ) in order o divide he modulaion area ino he linear modulaion area (mi 2 1) and wo overmodulaion ranges: overmodulaion area I (OAI: mi 2 (1, 1.05)) and overmodulaion area II (OAII: mi 2 (1.05, 1,1)). The modulaion deph is given by: * * 2 u 3 u mi = 2. U = U, (4) 3 max dc where u* is size of he demanded volage vecor, U max = (2/3U dc ) is maximum phase volage accessible in he six-sep mode and U dc is he converer dc-link volage. In he overmodulaion area I, he reference vecor moves along he circular rajecory wih he radius equal o he modulaion deph mi 2 near he hexagon verex. From he specific angle γ, he real converer oupu volage vecor u jumps on he hexagon edge and moves along his edge unil i reaches he posiion (π/3 - γ ). Thereafer he reference vecor rajecory is again circled. This algorihm is depiced in he Fig. 4. The swiching imes are in he overmodulaion area I calculaed by (5): mi1.sin(60 γ ) T1 =. T mi.sin γ + mi.sin(60 γ ) 1 1 pwm, (5a) T = T T, (5b) 2 pwm 1 In he overmodulaion area II, he reference volage vecor size and also is phase angle are disored. The modulaion sraegy in he overmodulaion area II is almos he same as in he above described sraegy OS2. Fig. 4. OS3: Converer oupu volage vecor rajecory in overmodulaion area I 3. COMPUTER SIMULATION Fig. 3. OS2: Modulaion sraegy in he overmodulaion area II: demanded (u*) and real converer oupu volage vecor (u ) rajecory The simulaion resuls of he firs overmodulaion sraegy OS1 are depiced in he Fig. 5. Fig. 6 shows he moor phase volage and moor phase curren from he second mehod (OS2). Fig. 7 presens resuls from OS3, boh in area OAI. Fig. 8 and Fig. 9 display resuls from he same mehod, bu in OAII.

4 Advances in Elecrical and Elecronic Engineering 92 Fig. 5. Behaviour of overmodulaion sraegy 1 (OS1) described in 2.A: f pwm = 4kHz, f ou = 50Hz, dc-link volage U dc = 565V, u*= 343V. Fig. 8. Behaviour of overmodulaion sraegy 2 (OS2) in he overmodulaion area II (see paragraph 2.B): u*= 346V. Fig. 6. Behaviour of overmodulaion sraegy 2 (OS2) in he overmodulaion area I (see paragraph 2.B): u*= 336V. Fig. 7. Behaviour of overmodulaion sraegy 3 (OS3) in he overmodulaion area I (see paragraph 2.C): u*= 336V. 4. EXPERIMENTAL EVIDENCE The above explored algorihms (OS1 OS3) have been implemened in he fixed-poin digial signal processor Texas Insrumens TMS320LF2812. In linear modulaion area, he approach published in [4] has been applied. The designed SVPWM has Fig. 9. Behaviour of overmodulaion sraegy 3 (OS3) in he overmodulaion area II (see paragraph 2.C): u*= 346V. been esed on he inducion machine drive of raed power of 4kW (IM: 4kW, 380V/50Hz, 1420rpm). The simple open loop V/f conrol has been seleced for he ess, because i make possible o easily change he prese ramp and, herefore, o define various condiions for he experimenal verificaion of he modulaion sraegies under he es. Based on he simulaion resuls, he sraegy OS3 has been highlighed, because i provides in our opinion very good properies. Fig. 10 Fig. 13 presens boh he waveforms and he frequency analysis (on-line FFT) of he moor phase volage and moor curren in boh overmodulaion area I (f ou = 45Hz) and overmodulaion area II (f ou = 48Hz) (sraegy OS3). Swiching frequency has been f pwm = 4kHz and dc-link volage U dc =540 V. In he linear modulaion area and overmodulaion area I, here dominae he firs harmonic componen and harmonics around he muliples of he swiching frequency f pwm (he side bands based on he f ou muliples). In he overmodulaion area II, where he converer oupu volage is near he six-sep mode, here appear he well-known harmonics: 5 h, 7 h, ec. These resuls are well-known. However, our aenion has been paid o he low frequency harmonics (up o 100Hz) ha can poenially disurb he railway signaling.

5 93 Algorihms of space vecor PWM in overmodulaion area Fig. 10. Sraegy OS3 overmodulaion area I: Frequency analysis (on-line FFT) of moor phase volage Fig. 11. Sraegy OS3 overmodulaion area I: Frequency analysis (on-line FFT) of moor phase curren Fig. 12. Sraegy OS3 overmodulaion area II: Frequency analysis (on-line FFT) of moor phase volage 5. CONCLUSIONS The firs crierion for overmodulaion algorihms comparison is he compuing ime. The mehod OS1 is quie simple; he compuing ime of his mehod is he shores. The oher wo algorihms (OS2 and OS3) have almos similar principle; hus, heir compuing imes are similar oo (compuing ime has aken 4.5µs wih DSP TI TMS320LF2812 operaing a clock frequency of 75MHz). Fig. 13. Sraegy OS3 overmodulaion area II: Frequency analysis (on-line FFT) of moor phase curren The nex crierion is behaviour (qualiy) of moor quaniies. From he resuls in he ime domain and frequency analysis can be concluded ha he sraegy OS1 provides he wors behaviour of explored moor quaniies. The moor quaniies in case of he oher wo mehods are on firs sigh comparable, bu he curren behaviour in overmodulaion area II of OS2 is more disored. In his paper, he aenion has been paid o asynchronous modulaion. The frequency analysis has been focused on he low frequency componens especially of he moor curren (up o 100Hz) in order o be able o evaluae he possible impac of he modulaion on he dc racion mains. Our observaions show ha danger low frequency componens are mainly influenced by swiching frequency (f pwm ). In he high power racion applicaions (such as locomoives) he swiching frequency is limied o hundreds herzs. Therefore, he imporan role plays he proper selecion of he raion beween f pwm and he railway signalling frequency. I is imporan o noe ha all of hese asynchronous SVPWM algorihms canno provide saisfacory operaion under very low swiching frequencies (approx. less han 800 Hz). REFERENCES [1] Bakhshai R. A., Joós G., Jain P., K., Jin H.: Incorporaing he Overmodulaion Range in Space Vecor Paern Generaors Using a Classificaion Algorihm. IEEE Transacions on Power Elecronics, Vol. 15, No. 1, Jan [2] Bolognani S., Ziglioo M.: Novel Digial Coninuous Conrol of SVM Inverers in he Overmodulaion Range. IEEE Transacions of Indusry Applicaions, vol. 33, No. 2, March/April [3] Holz J., Lozka W., Khambadkone A. M.: On Coninuous Conrol of PWM Inverers in he Overmodulaion Range Including he Six-Sep Mode. IEEE Transacions on Power Elecronics, Vol. 8, No. 4, Ocober [4] Perouka Z.: Space Vecor Pulsewidh Modulaion for Modern Conrol Algorihms. In: Elekroechnika a informaika ZU v Plzni, Plze pp , Vol. II. ISBN