dvnes in Power Eletronis Volume, rtile ID 854, 8 pges doi:.55//854 Reserh rtile omprtive Studies of Different Swithing Ptterns for Diret nd Indiret Spe Vetor Modulted Mtrix onverter min Shnpour, Ssn Gholmi, nd li Rez Seifi Shool of Eletril nd omputer Engineering, Shirz University, Shirz 745, Irn orrespondene should e ddressed to li Rez Seifi, seifi@shirzu..ir Reeived 7 My ; epted 7 Novemer demi Editor: Frneso Profumo opyright min Shnpour et l. This is n open ess rtile distriuted under the retive ommons ttriution Liense, whih permits unrestrited use, distriution, nd reprodution in ny medium, provided the originl work is properly ited. This pper presents MTL/Simulink simultion of diret nd indiret spe vetor modultion for mtrix onverter. Different swithing ptterns for oth diret nd indiret methods re simulted nd ompred. Three riteri re hosen to ompre the performne of swithing ptterns: () totl hrmoni distortion (THD); () hrmoni spetrum nlysis of output voltges; nd () numer of swithing in eh swithing period. Swithing strtegies re ompletely implemented using the power lirry in MTL/Simulink environment.. Introdution Three-phse mtrix onverter is n -to- onverter with nine idiretionl swithes. These swithes re orgnized in mtrix nd with this rrngement ny output phse n e onneted to ny input phse []. Some dvntges of using this onverter re providing idiretionl power flow; ontrol of output wveforms nd input power ftor; nd sene of D pitor []. Different pprohes for swithing of mtrix onverter hve een proposed in litertures [ 6]. Mny spets suh s output hrmoni spetrum, totl hrmoni distortion (THD), omplexity of implementtion, nd numer of swithing ply importnt roles in determintion of n pproprite modultion strtegy. Spe vetor modultion hs een suessively improved in reent yers nd is onsidered s stndrd tehnique in mtrix onverter modultions [, 5]. Despite the ft tht this onept is presented in vrious litertures, it is still miguous for engineers to ompletely omprehend its operting priniple. Spe vetor swithing methods for mtrix onverter re lssified into two different strtegies: () indiret spe vetor modultion whih tkes the dvntge of virtul d link [5] nd (() diret spe vetor modultion tht provides diret onversion []. So fr only one omprison etween the diret nd indiret spe vetor modultion is reported [7]. In [7] the diret nd indiret ontrol performnes of mtrix onverter supplying n indution motor (IM) hve een rried out; however, different swithing ptterns re not investigted. In this pper first the two methods of indiret nd diret spe vetor modultion of mtrix onverter re reviewed. Then different swithing ptterns re introdued, nd eh swithing pttern will e simulted in MTL/Simulink softwre. Simultions nd omprison re done under the sme onditions of the input power supply nd the output lod. In order to ompre the performnes of swithing ptterns three riteri re onsidered: totl hrmoni distortion, hrmoni nlysis of output voltge, nd numer of swithing. The rest of the pper is s follows: Setion explores the mtrix onverter fundmentl. Setions nd 4 desrie the indiret nd diret spe vetor modultions, respetively. The swithing ptterns re given in Setion 5. In Setion6 simultion results re disussed. Finlly the onlusion is given.. Mtrix onverter The φ-φ mtrix onverter sheme is shown in Figure. mtrix onverter omprises of nine idiretionl swithes so rrnged tht ny of the three output phses n e
-phse output dvnes in Power Eletronis S S S. Indiret Spe Vetor Modultion spe vetor is otined from three phse quntities through the following trnsformtion: S X = ( χ + αχ + α χ ), -phse input S S ( ) ( ) π π α = e j(π/) = os + j sin. (4) S S S Figure : Diret mtrix onverter. onneted to ny input phse. idiretionl swithes mke it possile to onnet ny of input phses,, or to ny of output phses,, or t ny moment. The input phses of mtrix onverter must not e shorted due to the input voltge soures, nd the output phses must not e opened due to the indutive nture of the lod. The swith funtion, S αβ, n e defined s S αβ = { Sαβ :open, S αβ : lose, The restrition is expressed s α {,, }, β {,, }. () S β + S β + S β =. () The output voltges nd input urrents of the mtrix onverter n e represented y the swithing funtion S nd the trnsposed S T,suhs [V out ] = [S] [V in ], V S S S V V = S S S. V, V S S S V [ [I in ] ] = S T [I out ], I S S S I I = S S S. I, I S S S I where V, V, nd V re input phse voltges; V, V nd V re output phse voltges; I, I,ndI re input urrents; I, I,ndI re output urrents. () Mny engineers re fmilir with the spe vetor modultion (SVM) for voltge soure inverters (VSIs) [8]; however, the modultion method for the mtrix onverter is understood to few engineers due to the high level of intriy nd limited mterils to explin its fundmentls. Hene, it would e esier nd more oneivle to illustrte the swithing opertion of mtrix onverter y dopting onventionl VSI topology nd SVM onept. The indiret spe vetor modultion (indiret SVM) ws first proposed y Huer nd orojevi. [5], where mtrix onverter ws desried to n equivlent iruit onsisting of urrent soure retifier nd voltge soure inverter onneted through virtul d link s shown in Figure. The ide of the indiret modultion tehnique is to seprte the ontrol of the input urrent nd output voltge. This is done y dividing the swithing funtion S into the produt of retifier nd n inverter swithing funtion: S S S S 7 S 8 [ ] S S S S S = S 9 S. S 5, S S S S S S S 4 S 6 (5) V S 7 S 8 [ ] V S S V = S 9 S. S 5. V S V S S S 4 S. 6 V So the spe vetor for the two voltge soure onverters shown in Figure n e pplied to the mtrix onverter shown in Figure.ForexmpleS S 7 + S 8 S in Figure is equivlent to S in Figure. Two spe vetor modultions for urrent soure retifier nd voltge soure inverter stges should e implemented, nd then the two modultion results should e omined. 4. Spe Vetor Modultion for the Retifier Stge The retifier prt of the equivlent iruit n e ssumed s urrent soure retifier (SR) with the verged vlue of I D nd is derived s follows: I D = I out m v os(θ out ). (6) I out is the pek vlue of output urrent, θ out is the output lod displement ngle, nd m v = V out /V D. The input urrent spe vetor I ref is extrted s follows: I ref = ( I + αi + α I ). (7)
-phse output dvnes in Power Eletronis I D S S S 5 S 7 S 9 S i q-xis 9 -phse input V D d δ I δ I ref i S S 4 S 6 S 8 S S d γ I γ θ i d-xis Retifition stge Inversion stge Figure : Indiret mtrix onverter. The nine retifier swithes hve nine permitted omintions to void n open iruit t the d link. These omintions inlude three zero nd six nonzero input urrents given in Tle. The referene input urrent vetor is synthesized y impressing the djoining swithing vetors (I γ )nd(i δ )with duty yles (d γ )nd(d δ ), respetively. The referene vetor n e expressed y the urrent-time produt sum of the djoining tive vetorssillustrtedinfigure : I ref = d γ I γ + d δ I δ. (8) The duty yle of the tive vetors re lulted y d γ = T ( γ π = m sin i) T s θ, d δ = T δ T s = m sin(θ i ), d o = T o T s = d δ d γ, where θ i indites the ngle of the referene urrent vetor. The urrent modultion index, m, defines the desired urrent trnsfer rtio suh s (9) m = I ref I D ; m. () 5. Spe Vetor Modultion for the Inverter Stge TheinverternessumedsseprteVSI.Theswithing method is extly similr to onventionl VSI [8], ut owing to its virtul D link, V D should e defined s follows: V D = V in m os(θ in ). () V in is the pek vlue of input voltge, nd θ in is the input displement ngle. i 7 Figure : Input urrent spe vetor in omplex plne. V V q-xis 9 d α I α 7 d β I β θ v V ref V Figure 4: Output voltge spe vetor in omplex plne. d-xis The output voltge spe vetor, V ref, is evluted s. V ref = ( V + αv + α V ). () The inverter swithes hve eight permitted omintions to void short iruit. These omintions inlude three zero nd six nonzero input urrents (see Tle ). The referene output voltge vetor is synthesized y impressing the djoining tive vetors V α nd V β with the duty yles d α nd d β, respetively. The referene vetor n e expressed y the voltge-time produt sum of the djoining tive vetorssillustrtedinfigure 4: V ref = d α V α + d β V β. ()
4 dvnes in Power Eletronis Tle : urrent vetors for retifier stge. Type Vetor I ref S S S S 4 S 5 S 6 tive I / I D < π/6 I / I D <π/6 I / I D <π/ I 4 / I D < 5π/6 I 5 / I D < 5π/6 I 6 / I D < π/ Zero I Tle : Voltge vetors for inverter stge. Type Vetor V ref S 7 S 8 S 9 S S S V /V D < V /V D <π/ tive V /V D < π/ V 4 /V D <π V 5 /V D < π/ V 6 /V D < π/ Zero V The duty yles of the tive vetors n e written s: d α = T ( α π = m v sin v) T s θ, d β = T β T s = m v sin(θ v ), d ov = T ov T s = d α d β, (4) where θ v indites the ngle of the referene voltge vetor. m v is the voltge modultion index nd defines the desired voltge trnsfer rtio suh s Vref m v = ; m v, (5) V D 6. Diret Spe Vetor Modultion In diret spe vetor modultion the tul mtrix onverter iruit is onsidered without ny ssumption of n equivlent iruit. For opertion of the mtrix onverter one nd only one swith in eh output phse must e onduting. This leds to twenty-seven possile swithing omintions for the mtrix onverter. Modultion is more omplited euse these vetors vry ontinuously nd depend on instntneous mgnitude of soures. The output voltge sttes re usully lssified in three groups: (i) 8 omintions with fixed diretions, (ii) zero vetors, (iii) 6 rotting vetors. The 6 omintions of rotting vetors in group re not used. Similr to indiret spe vetor modultion the referene output voltge vetor is synthesized y impressing the djoining tive vetors. The referene input urrent vetor is lso synthesized y impressing the djoining swithing urrent vetors. Figure 5 shows the output voltge nd input urrent referene spe vetors. For ny omintion of output voltge nd input urrent setors, four onfigurtions n e identified, whih produe output voltge nd input urrent vetors. mong the swithing tht n e seleted in eh setor, ones tht re shred input urrent nd output voltge vetors re used. Tle shows the possile onfigurtions. Duty yle lultions re given in []. If k v nd k i re the setors where V ref nd I ref re pled nd α nd β re the phse ngles within the setors V ref nd I ref, the duty yles re lulted y T = ( ) kv+ki q os(α π/) os( β π/ ) os ( ϕ i ), T = ( ) kv+ki+ q os(α π/) os( β + π/ ) os ( ϕ i ), T = ( ) kv+ki+ q os(α + π/) os( β π/ ) os ( ϕ i ), T 4 = ( ) kv+ki q os(α + π/) os( β + π/ ) T = T T T T 4. os ( ϕ i ), (6)
dvnes in Power Eletronis 5 +7, +9 Setor +, +9 V i V o V o ϕ i i i β i α i α o +, + Setor V o +, +7 () () Figure 5: The output voltge nd input urrent referene spe vetors. T T T T T () T T T T T T T T T 4 4 4 4 4 4 () Figure 6: Swithing ptterns for indiret modultion: () single sided; () doule sided. T T T T T 4 () T T T T T 4 T T T T () T T T T T T 4 T () T T T T T T 4 T T 4 T T T (d) T T Figure 7: Swithing ptterns for diret modultion: () symmetril single sided; () symmetril doule sided; () symmetril single sided; (d) symmetril doule sided. + V I + V + Soure Mtrix onverter Lod Swithing pttern genertor Disrete, T s = e 6 s Powergui Figure 8: Test se shemti in Mtl/Simulink.
6 dvnes in Power Eletronis Tle : Swithing onfigurtions. Swithes on V o I o, 5, 6 /V < / i < π/6 4,, /V < / i < π/6 4, 8, 9 /V < / i <π/ 7, 5, 6 /V < / i <π/ 7,, /V < / i < 7π/6, 8, 9 /V < / i < 7π/6 4,, 6 /V < π/ / i < π/6, 5, /V < π/ / i < π/6 4, 5, 9 /V < π/ / i <π/ 4, 8, 6 /V < π/ / i <π/, 8, /V < π/ / i < 7π/6 7,, 9 /V < π/ / i < 7π/6 4, 5, /V < 4π/ / i < π/6,, 6 /V < 4π/ / i < π/6 7, 8, 6 /V < 4π/ / i <π/ 4, 5, 9 /V < 4π/ / i <π/,, 9 /V < 4π/ / i < 7π/6 7, 8, /V < 4π/ / i < 7π/6,, 4, 5, 6 7, 8, 9 Tle 4: Test se system prmeters. Prmeter Vlue Soure voltge (pek) V System frequeny 6 Hz Lod resistne 5 Ω Swithing frequeny 6 khz Modultion index.8 Smpling time μs In these equtions ϕ i is the displement ngle etween urrent spe vetors nd input voltge spe vetors, nd q = V o /V i is the voltge rtio. 7. Swithing Pttern The order in whih the vetors re pled long one period is lled swithing pttern. proper hoie of the swithing pttern should e pplied to the swithes of the mtrix onverter in order to hieve the desired output. There re different omintions for ordering the time segments orresponding to duty rtios. In this pper two swithing ptterns re onsidered for indiret spe vetor modultion. single nd doule distriutions of time periods during swithing period re seleted. These ptterns re shown in Figure 6. Four swithing ptterns re simulted nd nlyzed for diret spe vetor modultion: () symmetril single sided, whih uses only one of the three zero vetors; () Tle 5: Simultion results. Pttern THD% Numer of Swithing for eh swith Single side indiret 69.59 88 Doule side indiret 68.5 59 symmetril single side diret 7.84 6 symmetril doule side diret 66.9 6 Symmetril single side diret 67. Symmetril doule side diret 65. 9 symmetril doule sided swithing pttern; () symmetril single sided, whih utilizes ll the three zero vetors nd (4) symmetril doule-sided pttern. Figure 7 shows these swithing ptterns. 8. Simultion Results In order to ompre the performnes of the diret nd indiret spe vetor modultion tehniques, these methods re pplied to n / mtrix onverter. This system onsists of simple soure voltge tht is onneted to resistive lod through mtrix onverter. The simultions were performed with Mtl/Simulink softwre s shown in Figure 8. The min iruits were ssumed to e idel, nd results re evluted under the sme onditions for the input power supply nd the output Lod. The prmeters of the system re shown in Tle 4. Two ptterns of Figure 6 nd four ptterns of Figure 7 re simulted. Tle 5 ompres
dvnes in Power Eletronis 7.5.5 4 6 8 4 6 8.5.5 4 6 8 4 6 8 () ().5.5 4 6 8 4 6 8.5.5 4 6 8 4 6 8 () (d).5.5 4 6 8 4 6 8.5.5 4 6 8 4 6 8 (e) (f) Figure 9: Hrmoni spetrum of output voltge: () single side indiret; () doule side indiret; () symmetril single side diret; (d) symmetril doule side diret; (e) symmetril single side diret; (f) symmetril doule side diret. THD nd the numer of swithing in eh swithing period for these methods. Furthermore, Figure 9 illustrtes hrmoni spetrum of output voltge for the six ptterns. s the higher hrmonis ould e removed esily y low-pss filter, Figure 9 only shows the low-order hrmonis, whih re hrder to e eliminted. However, the THDs of Tle 5 ll onsist of the hrmonis. sed on these simultion results, the doule-sided ptterns show the following hrteristis over the singlesided pttern: (i) lower hrmoni distortion, (ii) greter numer of swithing. In ddition, the nlysis for symmetril nd symmetril ptterns shows tht the symmetril pttern is more pproprite hoie for lower hrmoni distortion in spite of greter swithing losses. 9. onlusion This pper ompres different swithing ptterns of diret nd indiret spe vetor modultions for three-phse mtrix onverter. Two methods of indiret nd diret spe vetor modultion of mtrix onverter were ompletely desried. Doule-sided nd single-sided ptterns s well s symmetril nd symmetril ptterns were nlyzed in Simulink. omprison results were evluted sed on three riteri: () totl hrmoni distortion (THD); () hrmoni spetrum nlysis of output voltges; nd () numer of swithing in eh swithing period. s expeted the doule-sided s well s symmetril ptterns produes lower hrmoni distortions. However, the numer of swithing inreses when using doule-sided nd symmetril ptterns. Referenes [] P.W.Wheeler,J.Rodríguez, J.. lre, M. L. Empringhm, nd. Weinstein, Mtrix onverters: tehnology review, IEEE Trnstions on Industril Eletronis, vol. 49, no., pp. 76 88,. []D.sdei,G.Serr,.Tni,ndL.Zrri, Mtrixonverter modultion strtegies: new generl pproh sed on spevetor representtion of the swith stte, IEEE Trnstions on Industril Eletronis, vol. 49, no., pp. 7 8,. [] M. Venturini nd. lesin, Generlised trnsformer: new idiretionl, sinusoidl wveform frequeny onverter with
8 dvnes in Power Eletronis ontinuously djustle input power ftor, in Proeedings of the IEEE Power Eletronis Speilists onferene (PES 8),pp. 4 5, tlnt, G, US, June 98. [4]. lesin nd M. G.. Venturini, nlysis nd design of optimum-mplitude nine-swith diret - onverters, IEEE Trnstions on Power Eletronis, vol. 4, no., pp., 989. [5] L. Huer nd D. orojevi, Spe vetor modulted threephse to three-phse mtrix onverter with input power ftor orretion, IEEE Trnstions on Industry pplitions, vol., no. 6, pp. 4 46, 995. [6] J. Rodríguez, E. Silv, F. ljerg, P. Wheeler, J. lre, nd J. Pontt, Mtrix onverter ontrolled with the diret trnsfer funtion pproh: nlysis, modelling nd simultion, Interntionl Eletronis, vol. 9, no., pp. 6 85, 5. [7] M. Jussil nd H. Tuus, omprison of diret nd indiret mtrix onverters in indution motor drive, in Proeedings of the nd nnul onferene on IEEE Industril Eletronis (IEON 6), pp. 6 66, Pris, Frne, Novemer 6. [8] H. W. vn der roek, H. h. Skudelny, nd G. V. Stnke, nlysis nd reliztion of pulse width modultor sed on voltge spe vetors, IEEE Trnstions on Industry pplitions, vol. 4, no., pp. 4 5, 988.
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