Continuous PWM Techniques for Sinusoidal Voltage Generation with Seven-Phase Voltage Source Inverters

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1 Coninuous PWM Techniques for Sinusoidal Volage Generaion wih Seen-Phase Volage Source Inerers D.Dujic, E.Lei, M.Jones Lierpool John Moores Uniersiy School of Engineering Lierpool L AF, UK d.dujic@6.ljmu.ac.uk G.Grandi, G.Serra, A.Tani Uniersiy of Bologna Deparmen of Elecrical Engineering 46 - Bologna, Ialy gabriele.grandi@mail.ing.unibo.i Absrac Muli-phase moor dries are ypically supplied from wo-leel olage source inerers (VSIs. I is hus necessary o deelop pulse widh modulaion (PWM schemes for inerer conrol in order o uilise he benefis offered by muliphase moor dries. This paper deals wih seen-phase VSI and deelops coninuous PWM schemes ha enable generaion of sinusoidal olages a he oupu. Carrier-based sinusoidal PWM, sinusoidal PWM wih he 7 h harmonic injecion, and sinusoidal PWM wih he riangular zero-sequence injecion, as well as he space ecor PWM are elaboraed. Presened PWM schemes are analysed in erms of DC bus uilisaion and direc correlaion beween carrier-based and space ecor approach is esablished. All schemes are implemened in a digial signal processor and are compared hrough experimenaion on a seen-phase cusomdesigned VSI supplying a seen-phase sar-conneced saic load. I. INTRODUCTION Muli-phase dries hae cerain adanages ha make hem aracie for elecric ship propulsion, locomoie racion, EVs, HEVs, ec. Regardless of he AC machine ype and regardless of he number of phases, he power supply of a muliphase drie is ypically a wo-leel VSI, which requires a mehod of PWM for is operaion. If a muli-phase machine is wih sinusoidal field disribuion, PWM scheme mus generae sinusoidal harmonic-free oupu olages in order o aoid appearance of low-order saor curren harmonics []. Howeer, if a muli-phase machine is wih concenraed windings, i is adanageous o supply he machine wih a olage ha conains, in addiion o he fundamenal, a cerain amoun of harmonic(s of a specified order, so ha saor curren harmonic injecion enhances orque producion [-]. Numerous PWM schemes for muli-phase VSIs hae already been repored [-4]. Mos of he work has been relaed o space ecor PWM. Carrier-based PWM mehods hae been analysed o a lesser exen [-,4]. From he poin of iew of he VSI phase number, [-6] deal wih space ecor PWM of he fie-phase VSI, [,,,4] wih asymmerical six-phase VSI, and [7] wih symmerical sixphase VSI. PWM sraegies for a seen-phase and a ninephase VSI, respeciely, are discussed in [8] and [9]. An exension of symmerical componen ransformaion on muli-phase sysems leads o definiion of muliple olage space ecors posiioned in differen muually orhogonal d-q planes of an n-dimensional space. This is a generalisaion of he approach of [] and i enables decoupling of fundamenal and harmonic componens ino differen planes, which simplifies furher conrol implemenaion. Sinusoidal oupu olage generaion in he case of an n-phase sysem requires applicaion of n- acie space ecors in a swiching period [9]. If sinusoidal olage oupu is required, only he firs d - q plane (sub-space has o be considered. As noed, PWM for a seen-phase VSI has been considered only in [8], where space ecor PWM was deeloped. Alhough carrier-based PWM mehods are in general easier o implemen when compared o he space ecor approach, here is no eidence ha such an approach has been followed in conjuncion wih he seen-phase VSI. Howeer, as shown in [], injecion of he n h -harmonic (zero-sequence ino reference signals in case of an n-phase sysem effeciely increases linear modulaion region wihou affecing oupu olage waeforms and enables he same DC olage uilisaion as he space ecor PWM []. The aim of his paper is herefore o inesigae a se of coninuous PWM mehods for sinusoidal oupu olage generaion using seenphase VSI. Three sinusoidal carrier-based mehods (sinusoidal PWM, sinusoidal PWM wih he 7 h harmonic injecion, and sinusoidal PWM wih he riangular zero-sequence injecion are compared wih space ecor PWM ha produces sinusoidal olages in order o deermine direc link beween hese approaches. All he mehods are implemened in a DSP and esed on a seen-phase VSI supplying a seen-phase load. Experimenal resuls are presened, hus enabling a comparison of carrier-based and space-ecor PWM mehods. II. SEVEN-PHASE VOLTAGE SOURCE INVERTER Topology of a seen-phase olage source inerer supplying seen-phase sar-conneced load is gien in Fig.. By defining swiching funcions m i ( i a, b, c, d, e, f, g for inerer legs wih m i and m i when upper swich is on and off, respeciely, insananeous alues of phase-oneural olages of a seen-phase load can be calculaed using he following expressions i V mi ( ma mb mc md me m f mg ( /7/$. 7 IEEE 47

2 There are 7 = 8 swiching configuraions during operaion of a seen-phase VSI. Since only linear modulaion region is under scope of ineres here, modulaion index is defined as he raio of he fundamenal componen ampliude of he line-o-neural inerer oupu olage o one half of he DC bus olage, M V. 5 ( i V III. CONTINUOUS CARRIER-BASED PWM FOR SEVEN-PHASE VSI Carrier-based PWM echniques include modulaion signals and carrier signals. Generalised srucure of he modulaor, including zero-sequence signal calculaor, is shown in Fig.. Modulaion signals are compared wih high frequency carrier signal and, as a resul, swiching signals are generaed for each phase. A uniersal represenaion of modulaion signals for seen-phase carrier-based modulaor can be wrien as ( ( ( ( i i no where no ( represens zero-sequence signal and i ( are fundamenal signals (seen sinusoidal signals displaced in ime by 7. Since zero-sequence signal does no appear in eiher line-o-line or phase olages, selecion of his signal can be used o modify modulaion signal waeforms. This is a degree of freedom ha can be uilised o design arious modulaion schemes. Analysis is here resriced o coninuous PWM schemes wih swiching aciiy in each of he inerer legs oer he carrier signal period, as long as peak alue of he modulaion signal does no exceed carrier magniude. For he sake of simpliciy in he analysis, ampliude of carrier signal is scaled o fi ino range ( V V and is frequency is assumed o be much higher han he frequency of fundamenal signals. While operaing in linear regime modulaor gain has he uniy alue and peak alue of inerer oupu fundamenal olage is equal o he peak alue of he fundamenal sinusoidal signal. Sinusoidal Pulse Widh Modulaion SPWM: Selecion of zero-sequence signal as no ( leads o SPWM. Modulaion signals for all seen phases are equal o sinusoidal fundamenal signals. In he linear region, he maximum modulaion index is equal o uniy, M. V V A a a B ad ac ab b b C c c D d d SPWM Fig.. Topology of a seen-phase olage source inerer. n E e e F f f G g g a b c d e f g Zero -sequence signal calculaor no a b c d e f g Carrier signal Fig.. Principle of carrier-based PWM for a seen-phase VSI. SPWM wih Seenh Harmonic Injecion SHIPWM: Thirdharmonic injecion for a hree-phase VSI leads o an increase in he DC bus uilisaion in he linear region. A generalised concep of n h harmonic injecion for n-phase inerers [] is applied here o he seen-phase VSI. Opimal leel of he n h harmonic componen is found from: V n V sin( n n (4 where (4 akes he posiie sign for n = (, 7,, 5 and negaie sign for n = (5, 9,, 7. Thus, for a seen-phase sysem, he seenh harmonic is in phase wih he fundamenal and has he ampliude: V V sin( V (5 7 Wih zero-sequence signal defined by no ( V7 sin(7, he resuling modulaing signal has he form (phase a a ( M i.5v sin(.8m i.5v sin(7 (6 In he linear region, for maximum alue of he modulaion index, one has a (. 5V. General expression for maximum possible modulaion index in he linear region in case of he n h harmonic injecion has he form [] M i cos( n (7 from where i can be found ha maximum alue of he modulaion index is M SHIPWM. 57. This is an increase of.57% in he DC bus uilisaion when compared o SPWM. SPWM wih Triangular Zero-Sequence Injecion TIPWM: If he zero-sequence is seleced according o no ( [max( a, b,... g min( a, b,... g ] (8 no jus he seenh harmonic, bu addiional 7k (k =,,5... harmonics are included ino he modulaion signal as well. Maximum modulaion index has he alue equal o he one in he preious case, M TIPWM. 57. Characerisic waeforms of SHIPWM and TIPWM schemes are shown in Fig.. Similariy in waeforms is obious. Addiional 7k harmonics are naurally included, hus leading o riangular m a m b m c m d m e m f m g 48

3 shape of he zero-sequence signal in TIPWM. Plos show siuaion for maximum alue of he modulaion index, hus fundamenal signal exceeds uniy alue, while resuling modulaion signal says inside he linear region. IV. SPACE VECTOR PWM FOR SEVEN-PHASE VSI (SVPWM By using ransformaion in real marix form as C 7 / cos( sin( cos( sin( cos( sin( / cos( sin( cos(4 sin(4 cos(6 sin(6 / cos( sin( cos(6 sin(6 cos( sin( / cos(4 sin(4 cos( sin( cos(5 sin(5 / cos(5 sin(5 cos( sin( cos( sin( / cos(6 sin(6 cos(5 sin(5 cos(4 sin(4 / decomposiion of a seen-phase sysem ino componens in hree wo-dimensional and muually orhogonal planes (single dimensional zero-sequence sub-space can no be excied due o he isolaed neural of he sar-conneced load can be realised. Applying (9 o phase-o-neural olages of a seenphase load deermined wih (, all 8 space ecors (wo zero and 6 acie space ecors of a seen-phase sysem are deermined. In general, space ecors occupy he same posiions in all hree planes, ha are labelled here d -q, d -q and d -q, alhough one swiching combinaion of he inerer leads o a differen space ecor in each plane wih regard o he magniude and phase. Considering he magniudes, acie space ecors can be classified ino eigh groups [8], while each plane can be diided ino 4 secors (each spanning /7, as shown in Fig. 4. Transforming olages of a seen-phase VSI ino hree wo-dimensional planes effeciely separaes families of odd harmonics according o he rule: 7k harmonics, k = een d q plane, (,, 5,... 7k harmonics, k = odd d q plane, (5, 9, 9,. 7k harmonics, k = een d q plane, (,, 7,. 7 k harmonics, k = odd zero-sequence (7,, 5,. Therefore, as long as pure sinusoidal oupu olages are required, space ecor modulaor mus eliminae all harmonic componens in he d -q and d -q planes, while realising fundamenal componen synhesis in d -q plane. Neighbouring n acie space ecors are seleced in each secor [8,9], hus proiding symmerical PWM paern wih single commuaion in each inerer leg oer he swiching Ampliude (p.u Seenh-harmonic Fundamenal TIPWM SHIPWM TIPWM zero-sequence signal Time (s Fig.. Characerisic signals of carrier-based PWM mehods. (9 V q.7v.59v.9v.86v.56v.44v Fig. 4. Space ecors of seen-phase VSI..55V 7.64V period, saring from ( up o ( and ice ersa. Since seleced acie space ecors are along same wo lines ha separae he secors, ficional space ecors a and b can be used a firs o simplify calculaion (Fig. 5a. This is he same as assuming ha only space ecors wih he larges magniude are inoled in he PWM paern. Such an approach, based on [5] for a fie-phase VSI, is followed here and i is differen from he preiously proposed mehodology for he seen-phase VSI in [8]. Ulimaely, howeer, boh mehods lead o he same oupu olages. Applicaion imes of ecors a and b can be found for any secor j from sin( j 7 sin( ( j 7 a s, b s ( L sin( 7 L sin( 7 where L. 64V represens magniude of he larges space ecor group from Fig. 4 while s is he swiching period. Time of applicaion of zero space ecors is o s a b ( Calculaed imes of applicaion of ficional space ecors a and b mus be properly disribued among acie space ecors, saisfying consrains gien wih a a a a b b b ( In secor acie space ecors ha are used are 64, 5, 97,, 96, (Fig. 5b, where number in subscrip represens decimal alue of binary coded inerer swiching sae (e.g. 64 =. Posiions and ampliudes of hese ecors in oher wo planes are shown in Figs. 5c and 5d. In order o eliminae low-order harmonic componens in inerer oupu olages, aerage alues in planes d -q and d - q mus be kep a zero. Thus, from Fig. 5c, for d -q plane he following consrains apply V d 49

4 q b b s b q. 86V a, b a, b a,. 55V. 64V 96 b 7 m a m b o 4 a b a a Secor b o b a a b a o 4 7 a a s a d 64 a b b a a a 5 d 97 m c m d m e q q. 86V a, b a, b a,. 56V. 59V d. 86V a, b a, b a,. 7V. 9V d m f m g Fig. 6. Swiching paern for secor c d Fig. 5. Principle of calculaion of imes of applicaion of acie space ecors (pars a,b,c,d defined in ex. a a a a a a b b b b ( Similarly, for d -q plane, from Fig. 5d one finds a a a a a a (4 b b b b Afer soling sysem (-(4 dwell facors for acie space ecors are obained as: a.98 a b.98 b a.57 a b.57 b ( a a b By using he ol-second principle [5] i can be shown ha for any gien reference magniude he corresponding fundamenal a he oupu is only 8%. This is so since he calculaion of imes in ( corresponds o he maximum fundamenal achieable wih large ecors only (.659V, while applicaion of six acie ecors according o (5 resrics he maximum achieable fundamenal o.5v. The raio of he wo maximum fundamenals is.. Thus he reference olage magniude has o be scaled wih he facor /.8 =. in order o ge he desired fundamenal a he oupu. Obained swiching paern for secor is shown in Fig. 6. Time of applicaion of zero space ecors is equally shared beween and 7. V. EXPERIMENTAL RESULTS All four PWM schemes are implemened in he TMSF8 DSP ha is used o conrol seen-phase VSI (Fig. 7 supplying a seen-phase sar-conneced R-L load. DC link olage is obained using single-phase diode recifier and is 45 V. Measuremens are done for he fundamenal oupu frequency of 5 Hz and he inerer swiching frequency is khz. Load curren and is specrum were measured using Tekronix curren probe and HP5665A dynamic signal analyser, DSP oupus wih Tekronix TDS 4 digial scope and inerer oupu olages wih FLUKE 4B power harmonic analyser in oscilloscope mode. Fig. 7. Experimenal se-up. On he basis of he heoreical consideraions i is expeced ha, during operaion wih he maximum modulaion index alue in he linear region, hree of he considered four PWM mehods will proide he same fundamenal a he oupu (SHIPWM, TIPWM and SVPWM, while he oupu of he SPWM will be slighly lower. This is confirmed in Fig. 8, where one period of he load curren is shown for all four PWM mehods. Furher eidence is proided by harmonic analysis (Fig. 9, where curren specrum is illusraed for sinusoidal PWM (SPWM and he SPWM wih riangular zero-sequence injecion (TIPWM (curren specrum for SHIPWM and SVPWM is idenical o he one shown for Load Curren (A SPWM SHIPWM,TIPWM,SVPWM Time (s Fig. 8. Measured load curren for all four PWM mehods for operaion wih he maximum fundamenal in he linear modulaion region (5 Hz reference frequency. 5

5 .5. Load Curren Specrum (A rms Frequency (Hz.5. Load Curren Specrum (A rms Frequency (Hz Fig. 9. Specrum of load curren of Fig. 8 for SPWM (op and carrier-based space ecor PWM (TIPWM, boom. TIPWM. I can be seen from he specra ha an increase in he fundamenal curren harmonic, commensurae wih he increase in he fundamenal oupu olage harmonic in he linear modulaion region of.57%, has been obained wih TIPWM (he same applies o SHIPWM and SVPWM, when compared o he fundamenal for sinusoidal PWM. Considering ha SHIPWM, TIPWM and SVPWM all lead o in essence he same oupu olage/curren, olage is furher illusraed for SVPWM only, for operaion in he limi of he linear modulaion region. Swiching paern, generaed by he SVPWM during one swiching period and measured a he DSP oupus, is illusraed for all seen inerer legs during operaion in secor in Fig.. As can be seen, PWM paern is symmerical and six acie ecors are applied, in agreemen wih heoreical consideraions. Inerer oupu phase olage is shown in Fig.. I aains six differen nonzero olage leels, in accordance wih (. Maximum fundamenal oupu phase olage in he linear modulaion region for SHIPWM, TIPWM and SVPWM equals.5v for sinusoidal oupu olages. This is well below he maximum fundamenal ha can be obained in he limi of he linear modulaion if only he larges ecors of Fig. 4 are uilised, which is hen.659v. Such operaion of he seen-phase VSI corresponds o he injecion of no only zerosequence harmonics bu also harmonics in he d -q and d -q planes (he rd and he 5 h harmonic. Inerer oupu curren when only he larges space ecors are used in he SVPWM, for operaion in he limi of he linear modulaion region, is illusraed in Fig., ogeher wih he specrum. As can be Fig.. Swiching paern for space ecor PWM (SVPWM using six acie ecors, during one swiching period in secor. Inerer legs A, B, C and D in upper par and inerer legs E, F and G in lower par. Fig.. Measured inerer oupu phase olage, generaed using SVPWM in he limi of he linear modulaion region. seen, he curren conains around 5% and % of he rd and he 5 h harmonic, respeciely. This is undesirable if a machine wih sinusoidal winding disribuion is supplied. Direc comparison of he load curren waeforms, obained using only wo larges acie ecors (Fig. and six acie ecors (Fig. 8, is proided in Fig., from which he difference in boh harmonic conen and he magniude is eiden. The final se of experimenal resuls, shown in Fig. 4, illusraes common mode olage (CMV. Waeform is shown for operaion wih he maximum fundamenal oupu in he linear modulaion region for SVPWM. The same resul was obained for SPWM. The CMV flucuaes beween V / and i conains all olage leels. 5

6 Load Curren (A Load Curren Specrum (A rms Time (s Frequency (Hz Fig.. Experimenally recorded curren and is specrum when only he larges ecors are used in SVPWM (limi of he linear modulaion region, olage fundamenal of.659v. Load Curren (A SVPWM ( ACTIVE SPACE VECTORS SVPWM (6 ACTIVE SPACE VECTORS Time (s Fig.. Comparison of he load curren for SVPWM using six acie ecors and SVPWM using only wo acie ecors. Fig. 4. CMV recorded for operaion wih he maximum sinusoidal oupu in he linear modulaion region using SVPWM. VI. CONCLUSION The paper analyses coninuous PWM schemes for seenphase olage source inerers, which enable operaion wih purely sinusoidal oupu olages. Carrier-based schemes (sinusoidal, sinusoidal wih he 7 h harmonic injecion and sinusoidal wih riangular zero-sequence injecion, as well as he space ecor PWM are elaboraed. I is shown ha SHIPWM, TIPWM and SVPWM all enable an increase in he maximum obainable fundamenal oupu in he linear modulaion region, of.57%, compared o he simples carrier-based sinusoidal PWM. Theoreical consideraions are confirmed by experimenaion on he seen-phase VSI. ACKNOWLEDGMENT The auhors acknowledge suppor proided by he EPSRC (gran no. EP/C795, Semikron, MOOG and Vereco. REFERENCES [] Y.Zhao, T.A.Lipo, Space ecor PWM conrol of dual hree-phase inducion machine using ecor space decomposiion, IEEE Trans. on Indusry Applicaions, ol., no. 5, 995, pp. -9. [] R.O.C.Lyra, T.A.Lipo, Torque densiy improemen in a six-phase inducion moor wih hird harmonic curren injecion, IEEE Trans. on Indusry Applicaions, ol. 8, no. 5,, pp [] H.M.Ryu, J.H.Kim, S.K.Sul, Analysis of muli-phase space ecor pulse widh modulaion based on muliple d-q spaces concep, IEEE Trans. on Power Elecronics, ol., no. 6, 5, [4] P.S.N.deSila, J.E.Flecher, B.W.Williams, Deelopmen of space ecor modulaion sraegies for fie-phase olage source inerers, Proc. IEE Power Elecronics, Machines and Dries Conf. PEMD, Edinburgh, UK, 4, pp [5] A.Iqbal, E.Lei, Space ecor PWM echniques for sinusoidal oupu olage generaion wih a fie-phase olage source inerer, Elecric Power Componens and Sysems, ol. 4, no., 6, pp [6] D.Casadei. G.Serra, A.Tani, L.Zarri, Muli-phase inerer modulaion sraegies based on duy-cycle space ecor approach, Proc. of Ship Propulsion and Railway Sysems Conf. SPRTS, Bologna, Ialy, 5, pp. -9. [7] M.B.R.Correa, C.B.Jacobina, C.R.daSila, A.M.N.Lima, E.R.C.da Sila, Vecor and scalar modulaion for six-phase olage source inerers, Proc. IEEE Power Elec. Spec. Conf. PESC, Acapulco, Mexico,, pp [8] G.Grandi, G.Serra, A.Tani, Space ecor modulaion of a seen-phase olage source inerer, Proc. In. Symp. Power Elecronics, Elec. Dries, Auomaion and Moion SPEEDAM, Taormina, Ialy, 6, CD- ROM paper S8-6. [9] J.W.Kelly, E.G.Srangas, J.M.Miller, Muli-phase space ecor pulse widh modulaion, IEEE Trans. on Energy Conersion, ol. 8, no.,, pp [] A.Iqbal, E.Lei, M.Jones, S.N.Vukosaic, Generalised sinusoidal PWM wih harmonic injecion for muli-phase VSIs, Proc. IEEE Power Elec. Spec. Conf. PESC, Jeju, Korea, 6, pp [] O.Ojo, G.Dong, Generalized disconinuous carrier-based PWM modulaion scheme for muli-phase conerer-machine sysems, Proc. IEEE Ind. Appl. Soc. Annual Meeing IAS, Hong Kong, 5, CD-ROM paper IAS8p. [] O.Ojo, G.Dong, Z.Wu, Pulse-widh modulaion for fie-phase conerers based on deice urn-on imes, Proc. IEEE Ind. Appl. Soc. Annual Meeing IAS, Tampa, FL, 6, CD-ROM paper IAS5p7. [] D.Hadiouche, L.Baghli, A.Rezzoug, Space ecor PWM echniques for dual hree-phase AC machine: Analysis, performance ealuaion and DSP implemenaion, IEEE Trans. on Indusry Applicaions, ol. 4, no. 4, 6, pp. -. [4] R.Bojoi, A.Tenconi, F.Profumo, G.Gria, D.Marinello, Complee analysis and comparaie sudy of digial modulaion echniques for dual hree-phase AC moor dries, Proc. IEEE Power Elec. Spec. Conf. PESC, Cairns, Ausralia,, CD-ROM paper 59. 5