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Indirect 3D-Space Vector Modulation for a Matrix Converter

Ahmed Mohamed, profile picture
Ahmed Mohamed

This paper presents a novel indirect space vector modulation (SVM) technique for a four-leg matrix converter, aimed at improving control over unbalanced or nonlinear loads. The proposed method simplifies modulation processes for digital controllers and allows for effective regulation in high-frequency applications. Simulations conducted using a repetitive controller demonstrated the effectiveness of this technique for managing output voltages in 400 Hz power supply systems.

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Engineering, Technology & Applied Science Research Vol. 8, No. 2, 2018, 2847-2852 2847 www.etasr.com Abdelrehim et al.: Indirect 3D-Space Vector Modulation for a Matrix Converter Indirect 3D-Space Vector Modulation for a Matrix Converter Ahmed Abdelrehim Department of Electrical Engineering Alexandria University Alexandria, Egypt ahmed.abdelrehim@siemens.com Mohamed El-Habrouk Department of Electrical Engineering Alexandria University Alexandria, Egypt eepgmme1@yahoo.com Samir Deghedie Erfan Department of Electrical Engineering Alexandria University Alexandria, Egypt deghedie@gmail.com Karim Hassan Youssef Department of Electrical Engineering Alexandria University Alexandria, Egypt khmyoussef@yahoo.com Abstract—This paper discusses the indirect space vector modulation for a four-leg matrix converter. The four-leg matrix converter has been proven to be a reliable, cost-effective, and compact power electronic interface to supply unbalanced or nonlinear loads. However, the added fourth leg has shifted the inverter side modulation from simple two-dimension SVM into complex three-dimension. This paper employs a new technique to implement indirect 3D SVM in digital controllers with further simplification in the modulation process. Moreover, Simulink simulation using repetitive controller has been performed to regulate the output voltage for 400 Hz Power supplies. Keywords-repetitive controller; 3D SVM; four-leg matrix converter I. INTRODUCTION The matrix converter is a static and direct AC to AC converter with unique features of unity input power factor, high power to volume ratio, high reliability and MTBF factor which has gained interest in applications aiming to produce a realization of a compact three-phase drive for military, industrial and aerospace systems [1-3]. Moreover, researchers utilized the matrix converter as an electronic interface layer between all resources (wind, solar, storage, etc.) of the energy matrix model and as an electronic transformer competing with the traditional magnetic transformer. The added fourth leg is placed to provide a return path for the zero-sequence current during unbalancing and add the capability of supplying different connected single-phase loads. Four-leg converters have a superior ability to produce balanced output voltage waveform even under severely unbalanced load or non-linear load conditions [4]. A four-leg matrix converter topology is shown in Figure 1. This paper investigates the indirect space vector modulation which decouples the modulation into two stages (rectifier + inverter) without intermediate energy storage. This decoupling is efficient and allows separate control to each stage, while as there is no intermediate energy storage, a proper synchronization between the two stages is mandatory to fulfill the power balance equation as instantaneous input power shall be equal to the instantaneous output power for the load [5]. At high-frequency applications with precise control requirements as for naval and aerospace applications where the 115V-400Hz system is commonly used, traditional controllers have failed to achieve a proper regulation, due to the limited bandwidth so the repetitive controller is introduced as an optimum solution for this control problem [6]. II. MATRIX CONVERTER MODEL Matrix converter can be represented mathematically by matrix M and switches are identified as , where X is the output phase, Y is the input phase and S is the linking switch between input and output. Rectifier switches are numbered from to while inverter side switches are numbered from to . The rectifier is represented in Figure 1. Governing equations are: Vout=M*Vin (1) Iout=MT *Iin (2) Vout=Mi*VDC (3) VDC=MR*Vin (4) Vout=Mi*MR*Vin (5) where , , , , , , , and are output voltage, input voltage, output current, input current, DC intermediate voltage, inverter side switching matrix, rectifier side switching matrix, matrix converter switching matrix and transposed matrix converter switching matrix respectively. and Mi are described by (6) and (7) respectively: = 1 3 5 2 4 6 (6)
spl rec ach out ass A. con con rec Engineerin www.etasr Fig. 1. M = S7 S8 S9 S1 S11 S1 S13 S1 M equals to M M = S7 S8 S9 S10 S11 S12 S13 S14 Equation (8) = S1 ∗ S7 S2 S1 ∗ S9 S2 S1 ∗ S11 S2 S1 ∗ S13 S2 = SaA SaB SbA SbB ScA ScB SnA SnB In Figure 1 v The mathema Fig. 2. III. INDIREC Indirect spac litting the mo ctifying stage hieve decoupl tput voltage sumption of vi Rectifying St The main fu ntrol on the d ntrol the amp ctifying stage, ng, Technology r.com Schematic of a f 8 10 12 14 Mi*MR: 8 0 2 4 * S1 S3 S5 S2 S4 S6 can be further ∗ S8 S3 ∗ S7 ∗ S10 S3 ∗ S9 ∗ S12 S3 ∗ S11 ∗ S14 S3 ∗ S13 SaC SbC ScC SnC voltages are: V atical modelin Mathematical CT SPACE VECT ce vector mod odulation into and the seco ling between t control.as per irtual DC link tage unction of the displacement a plitude of the , only two sw y & Applied Sci four-leg direct ma 5 6 r synthesized i 7 S4 ∗ S8 S S4 ∗ S10 S 1 S4 ∗ S12 S5 3 S3 ∗ S14 S5 = V V V V and V ng is summariz modeling of matr TOR MODULAT dulation can b o two stages, ond is called the input curr r (5) and (9) as shown in F e rectifying sta angle of the in virtual DC l witches must b ience Research A atrix converter (7) (8) into S5 ∗ S7 S6 ∗ S8 5 ∗ S9 S6 ∗ S10 5 ∗ S11 S6 ∗ S1 5 ∗ S13 S6 ∗ S1 (9) V = V V V . zed in Figure 2 rix converter TION be implement the first is inversion sta rent control an and based o Figure 1. age is to achi nput current a link voltage. I be closed at a h V Abdelrehim et a 8 0 12 14 2. ted by called ge, to nd the on the ieve a and to In the time, just sim num com wil B. abc ang con sim ther com mo the ind is n wil Fig vec sele the the rect mat The be Vol. 8, No. 2, 20 al.: Indirect 3D t one upper s multaneously to mbered from o mbinations are l occur as show Fig. 3. Ni Rectifier Spac SVM for the c to αβ coord gle by which w nverter modul mulation that sw re is no nee mmonly hap dulations as sh Fig In Figure 4, θ actual hexa dex=Iref/IDC , 0 no need to syn l be switched gure 5. Modula ctor during t ections have b number of th range of on tifying stage trix converter e displacemen zero. To impl 018, 2847-2852 D-Space Vector M switch and on o avoid short c one to six as sh e only allowed wn in Figure 3 ine switching com ce Vector Mod rectifying sta dination and c we can define lation requirem witching one v ed to synthes ppens with hown in Figur g. 4. Synthesi θc is the angle agon sector, 0<mc<1. For nthesize the re d during ever ation process the time inte been translated he current sec ne to six. To and one of t is to have uni nt angle betwee lement this, th 2 Modulation for ne lower swi circuit. The re hown in Figure to guarantee t 3. mbinations for the dulation age works by calculating th e the working ment, it has vector per sect size two vect conventional re 4. is of reference cu e of the refere mc the cu matrix conver ference vector ry sector dura happens by as erval of eve d into a train ctor, numbers o achieve the the most inter ity power facto en input curren he reference s 2848 r a Matrix Con itch can be c ectifier switche e 1. Nine switc that no short c e rectifying stage transforming he reference v sector. For m been approve tor is sufficien tors per secto l rectifier urrent ence current w urrent modul rter, mc=1 and r as just one v ation as show ssigning one a ry sector. V of pulses car are represent e second targ resting featur or at the input nt and voltage signal given t verter closed es are ching circuit input vector matrix ed by nt and or as SVM within lation there vector wn in active Vector rrying ted in get of res of t side. shall to the
mo ins mo con app fun out add the thr app unb app neu rol leg coo inv the inv com by tur (ne coo con be ana Pri vec A. Engineerin www.etasr odulation proc stead of the inp Fig. 5. Inversion st odulation, and nverter, we w proach for th nction of inve tput voltage ded fourth leg e zero-sequenc ree-phase syste + + And the tra plied as it ha balanced syst plied. Due to utral current p le of 3D SVM gs. + + Transformati ordination du version stage, e same time in verter with mbinations ar p or n for ea rned on (posi egative). If th ordination, th nventional SV divided into alog to secto ism number m ctor angle on α Prism Identif If 0<θ<60 60<θ<12 120<θ<1 180<θ<24 ng, Technology r.com cess has been put phase curr . Rectifying s III. INV tage is conce d as this pa will address he four-leg ersion stage i under balanc g is responsibl ce component em follows (10 =0 ansformation f as happened tem (10) is n the unbalanc passing throug M to provide ≠ 0 ion to statio ue to the zer switches on th n order to avo eight switc re sixteen. Sw ach leg, where tive) and n in he sixteen-ve he result is VM are turned six prisms (F ors representat may be ident αβγ coordinati fication the 0 the 80 the 40 the y & Applied Sci taken from i rent. stage SVM vector VERSION STAGE erned with in aper discusse the 3D SVM matrix conve is to provide ced and unba e for providin t during unbal 0). from abc to with the rect no longer vali cing of the sy gh the system accurate swit onary frame ro-sequence c he same leg ca oid short circu ches, the p itching combi e p indicates ndicates the l ectors are rep a 3D hexago into prisms. T Figures 6-7). tion on conv tified by defi ion. en P=1 en P=2 en P=3 en P=4 ience Research A input phase v rs selection E nverter side es four-leg m M as a modu erter. The pr a control ove alanced loads ng a current pa lance. The bal (10 αβ coordinati tifier stage. F id and (11) is ystem, there w m and it is the tching pulses (11 happens into component. I an’t be turned uit. For the fo possible swit inations repres the upper swi lower switch presented into on and secto The 3D hexago The prisms a entional 2D ining the refe h V Abdelrehim et a oltage SVM matrix ulation rimary er the . The ath for lanced 0) ion is For an s now will be basic to all ) o αβγ In the d on at our-leg tching sented itch is is on o αβα ors of on can are an SVM. erence 8. E B. and imp bes thre swi Vol. 8, No. 2, 20 al.: Indirect 3D 240<θ<30 300<θ<36 Vectors are d Each prism con Fig. 6. 3D re Fig. Fig. Switching Vec As the referen d tetrahedron plemented by side each tetr ee switching v itching vector 018, 2847-2852 D-Space Vector M 00 then 60 then distributed into ntains four act epresentation of sw 7. Prisms ide 8. Vector dist ctor Selection nce vector loca number, sel choosing the n rahedron[8, 9] vectors, to ca the reference 2 Modulation for n P=5 n P=6, where θ o each prism a tive vectors. witching vectors i entification for 3D tribution into each ation is define ection of sw nearest referen ]. Each tetrah alculate the du e required volt 2849 r a Matrix Con θ= tan as shown in F in αβγ coordinatio D SVM h prism ed by prism nu witching vecto nce vectors lo hedron consis uty cycle for tage is transfo verter Figure on umber ors is ocated sts of each ormed
firs sw wh the and ma var tetr po SV the nu act (re cha rep rep tw ma val var suc var Th op sho 10 Engineerin www.etasr st to αβγ coor witching vector V V V = d The duty cyc d d d = ∗ S = 1 here S is the d e reference vec d d represents atrix is depend rying values rahedron. S m ssible coincid VM code check e current value The rectifyin mbers from 1 tive rectifier ectifier matrix arge of genera presenting the presented on o matrices as i atrix converter Fig. 9. M A Simulink lidate the effe rying types o ccessfully va rious scenario he input and eration. The s own in Table -26. ng, Technology r.com rdination and rs [9] as per (1 d d V V V cles can be furt ∗ V V V duty cycle mat ctor, (V1 V2 V3 s the duty cy dent on the sel depending matrix calcula ence between ks the prism a es of S. IV. MATR ng stage is de 1 to 6, these n switches and x). At the sam ating another current active (inverter in (5) allows u r. The procedu Matrix converter V. SIMUL k simulation ectiveness of m f loads. The alidated as w os such as bala output wavef simulation was I. The simula y & Applied Sci then is divid 2). ther calculated trix [8-10], (V 3)T is the curren ycle for each s lected switchin on each se ations have b prisms and te and tetrahedron RIX CONVERTE edicated to gen numbers repre d would be re me time the in series of num e inverter swit matrix) as we us to find all p ure is shown in code generation f LINK SIMULATI was successf matrix conver proposed indi well. Simulati anced and unb forms ensured s carried out u ation results ar ience Research A ed by the ava (12 d as shown in (13 (14 Vα-ref Vβ-ref Vδ-r nt switching v switching vec ng vectors, so elected prism been done for etrahedrons. Th n number to e ER nerating a ser esenting the c epresented on nversion stage mbers from 1 tches that wou ell. Multiplyin possible switch n Figure 9. from Mi and MR ION fully develop rter operation irect 3D SVM ion worked balanced linear d proper con using the param re shown in F h V Abdelrehim et a ailable 2) (13). 3) 4) ref)T is vector, ctor. S it has m and r each he 3D extract ries of current n e is in to 16, uld be ng the hes for ed to under M was under r load. nverter meters igures R A. Vol. 8, No. 2, 20 al.: Indirect 3D Source sys Load syst Switching freq Input filter Output filter Repetitive Contr Tracking con Unbalanced Balanced l Nonlinear l Non-Linear L Fig. 12. FF 018, 2847-2852 D-Space Vector M TABLE I. tem em quency (LC) r (LC) roller Q(z) ntroller d load 5Ω load load Load Fig. 10. O (a) P (b) P (c) P (d) N Fig. 11. O FT analysis for ou 2 Modulation for SYSTEM PARAM 440V 115V- 1280 56Ω/0.8m 180uH+70 1.72377 1.663 1.868 Ω+5.5mH, 10Ω+6 5Ω +5 3phase diode Output voltage Phase A Phase B Phase C Neutral Output current utput phase voltag 2850 r a Matrix Con METERS V-60Hz -400Hz 00Hz mH/10uF 0uH/100uF 2 1 76 0.75754 3 0.9914 8 0.8735 6.2mH, 20Ω+7.5m 5.5 mH e bridge +50Ω ge (THD=3.3%) verter mH
B. Engineerin www.etasr Fig. 13. Unbalanced Fig. 17. Inp ng, Technology r.com FFT analysis fo Fig. 14. Load Fig. 15. (a) P (b) P (c) P (d) Fig. 16. O put current multip y & Applied Sci or output current Error signal Output voltage Phase A Phase B Phase C Neutral Output Currents plied by factor 50 ience Research A (THD=1.8%) and input voltage h V Abdelrehim et a e C. Vol. 8, No. 2, 20 al.: Indirect 3D Fig. 19. Fig. 20. FF Non Linear L F Fig. 22. 018, 2847-2852 D-Space Vector M Fig. 18. FFT analysis fo FT analysis for ou Load Fig. 21. Output FFT analysis fo 2 Modulation for Error signal or input current (T utput phase voltag t voltage 115V/40 or input current (T 2851 r a Matrix Con THD=48%) ge (THD=3.3%) 00H THD=48%) verter
mo bee con lim (11 con eff rep vo [1] [2] [3] [4] [5] [6] [7] Engineerin www.etasr Fig Fig. 25. Inp This paper odulation for en implement ntroller was s mited bandw 15V/400Hz). nditions (bal fectiveness o petitive contro ltage in an exc P. Zanchetta, Empringham, “ AC power s Electronics Sp 16, 2005 C. Klumpner, process of th Electronics Sp 1083–1088, Ju D. Casadei, G torque control Electronics, Vo F. Yue, P. W. W space vector m Electronics Co R. Zhang, Hig unbalanced loa State Universit R. Cárdenasa, control system Electric Power T. Friedli, J. evaluation of t back-to-back Electronics, Vo ng, Technology r.com Fig. 23. . 24. Repetitive put current multip VI. C introduced th four-leg matri ted and simu selected to reg width for The simulat anced, unbal f the propos oller showed t cellent way. REFE J. C. Clare, P. “Control Design upply using ge pecialists Confere F. Blaabjerg, P he matrix conve ecialist Conferenc une 17-21, 2001 G. Serra, A. 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Indirect 3D-Space Vector Modulation for a Matrix Converter

  • 1. Engineering, Technology & Applied Science Research Vol. 8, No. 2, 2018, 2847-2852 2847 www.etasr.com Abdelrehim et al.: Indirect 3D-Space Vector Modulation for a Matrix Converter Indirect 3D-Space Vector Modulation for a Matrix Converter Ahmed Abdelrehim Department of Electrical Engineering Alexandria University Alexandria, Egypt ahmed.abdelrehim@siemens.com Mohamed El-Habrouk Department of Electrical Engineering Alexandria University Alexandria, Egypt eepgmme1@yahoo.com Samir Deghedie Erfan Department of Electrical Engineering Alexandria University Alexandria, Egypt deghedie@gmail.com Karim Hassan Youssef Department of Electrical Engineering Alexandria University Alexandria, Egypt khmyoussef@yahoo.com Abstract—This paper discusses the indirect space vector modulation for a four-leg matrix converter. The four-leg matrix converter has been proven to be a reliable, cost-effective, and compact power electronic interface to supply unbalanced or nonlinear loads. However, the added fourth leg has shifted the inverter side modulation from simple two-dimension SVM into complex three-dimension. This paper employs a new technique to implement indirect 3D SVM in digital controllers with further simplification in the modulation process. Moreover, Simulink simulation using repetitive controller has been performed to regulate the output voltage for 400 Hz Power supplies. Keywords-repetitive controller; 3D SVM; four-leg matrix converter I. INTRODUCTION The matrix converter is a static and direct AC to AC converter with unique features of unity input power factor, high power to volume ratio, high reliability and MTBF factor which has gained interest in applications aiming to produce a realization of a compact three-phase drive for military, industrial and aerospace systems [1-3]. Moreover, researchers utilized the matrix converter as an electronic interface layer between all resources (wind, solar, storage, etc.) of the energy matrix model and as an electronic transformer competing with the traditional magnetic transformer. The added fourth leg is placed to provide a return path for the zero-sequence current during unbalancing and add the capability of supplying different connected single-phase loads. Four-leg converters have a superior ability to produce balanced output voltage waveform even under severely unbalanced load or non-linear load conditions [4]. A four-leg matrix converter topology is shown in Figure 1. This paper investigates the indirect space vector modulation which decouples the modulation into two stages (rectifier + inverter) without intermediate energy storage. This decoupling is efficient and allows separate control to each stage, while as there is no intermediate energy storage, a proper synchronization between the two stages is mandatory to fulfill the power balance equation as instantaneous input power shall be equal to the instantaneous output power for the load [5]. At high-frequency applications with precise control requirements as for naval and aerospace applications where the 115V-400Hz system is commonly used, traditional controllers have failed to achieve a proper regulation, due to the limited bandwidth so the repetitive controller is introduced as an optimum solution for this control problem [6]. II. MATRIX CONVERTER MODEL Matrix converter can be represented mathematically by matrix M and switches are identified as , where X is the output phase, Y is the input phase and S is the linking switch between input and output. Rectifier switches are numbered from to while inverter side switches are numbered from to . The rectifier is represented in Figure 1. Governing equations are: Vout=M*Vin (1) Iout=MT *Iin (2) Vout=Mi*VDC (3) VDC=MR*Vin (4) Vout=Mi*MR*Vin (5) where , , , , , , , and are output voltage, input voltage, output current, input current, DC intermediate voltage, inverter side switching matrix, rectifier side switching matrix, matrix converter switching matrix and transposed matrix converter switching matrix respectively. and Mi are described by (6) and (7) respectively: = 1 3 5 2 4 6 (6)
  • 2. spl rec ach out ass A. con con rec Engineerin www.etasr Fig. 1. M = S7 S8 S9 S1 S11 S1 S13 S1 M equals to M M = S7 S8 S9 S10 S11 S12 S13 S14 Equation (8) = S1 ∗ S7 S2 S1 ∗ S9 S2 S1 ∗ S11 S2 S1 ∗ S13 S2 = SaA SaB SbA SbB ScA ScB SnA SnB In Figure 1 v The mathema Fig. 2. III. INDIREC Indirect spac litting the mo ctifying stage hieve decoupl tput voltage sumption of vi Rectifying St The main fu ntrol on the d ntrol the amp ctifying stage, ng, Technology r.com Schematic of a f 8 10 12 14 Mi*MR: 8 0 2 4 * S1 S3 S5 S2 S4 S6 can be further ∗ S8 S3 ∗ S7 ∗ S10 S3 ∗ S9 ∗ S12 S3 ∗ S11 ∗ S14 S3 ∗ S13 SaC SbC ScC SnC voltages are: V atical modelin Mathematical CT SPACE VECT ce vector mod odulation into and the seco ling between t control.as per irtual DC link tage unction of the displacement a plitude of the , only two sw y & Applied Sci four-leg direct ma 5 6 r synthesized i 7 S4 ∗ S8 S S4 ∗ S10 S 1 S4 ∗ S12 S5 3 S3 ∗ S14 S5 = V V V V and V ng is summariz modeling of matr TOR MODULAT dulation can b o two stages, ond is called the input curr r (5) and (9) as shown in F e rectifying sta angle of the in virtual DC l witches must b ience Research A atrix converter (7) (8) into S5 ∗ S7 S6 ∗ S8 5 ∗ S9 S6 ∗ S10 5 ∗ S11 S6 ∗ S1 5 ∗ S13 S6 ∗ S1 (9) V = V V V . zed in Figure 2 rix converter TION be implement the first is inversion sta rent control an and based o Figure 1. age is to achi nput current a link voltage. I be closed at a h V Abdelrehim et a 8 0 12 14 2. ted by called ge, to nd the on the ieve a and to In the time, just sim num com wil B. abc ang con sim ther com mo the ind is n wil Fig vec sele the the rect mat The be Vol. 8, No. 2, 20 al.: Indirect 3D t one upper s multaneously to mbered from o mbinations are l occur as show Fig. 3. Ni Rectifier Spac SVM for the c to αβ coord gle by which w nverter modul mulation that sw re is no nee mmonly hap dulations as sh Fig In Figure 4, θ actual hexa dex=Iref/IDC , 0 no need to syn l be switched gure 5. Modula ctor during t ections have b number of th range of on tifying stage trix converter e displacemen zero. To impl 018, 2847-2852 D-Space Vector M switch and on o avoid short c one to six as sh e only allowed wn in Figure 3 ine switching com ce Vector Mod rectifying sta dination and c we can define lation requirem witching one v ed to synthes ppens with hown in Figur g. 4. Synthesi θc is the angle agon sector, 0<mc<1. For nthesize the re d during ever ation process the time inte been translated he current sec ne to six. To and one of t is to have uni nt angle betwee lement this, th 2 Modulation for ne lower swi circuit. The re hown in Figure to guarantee t 3. mbinations for the dulation age works by calculating th e the working ment, it has vector per sect size two vect conventional re 4. is of reference cu e of the refere mc the cu matrix conver ference vector ry sector dura happens by as erval of eve d into a train ctor, numbers o achieve the the most inter ity power facto en input curren he reference s 2848 r a Matrix Con itch can be c ectifier switche e 1. Nine switc that no short c e rectifying stage transforming he reference v sector. For m been approve tor is sufficien tors per secto l rectifier urrent ence current w urrent modul rter, mc=1 and r as just one v ation as show ssigning one a ry sector. V of pulses car are represent e second targ resting featur or at the input nt and voltage signal given t verter closed es are ching circuit input vector matrix ed by nt and or as SVM within lation there vector wn in active Vector rrying ted in get of res of t side. shall to the
  • 3. mo ins mo con app fun out add the thr app unb app neu rol leg coo inv the inv com by tur (ne coo con be ana Pri vec A. Engineerin www.etasr odulation proc stead of the inp Fig. 5. Inversion st odulation, and nverter, we w proach for th nction of inve tput voltage ded fourth leg e zero-sequenc ree-phase syste + + And the tra plied as it ha balanced syst plied. Due to utral current p le of 3D SVM gs. + + Transformati ordination du version stage, e same time in verter with mbinations ar p or n for ea rned on (posi egative). If th ordination, th nventional SV divided into alog to secto ism number m ctor angle on α Prism Identif If 0<θ<60 60<θ<12 120<θ<1 180<θ<24 ng, Technology r.com cess has been put phase curr . Rectifying s III. INV tage is conce d as this pa will address he four-leg ersion stage i under balanc g is responsibl ce component em follows (10 =0 ansformation f as happened tem (10) is n the unbalanc passing throug M to provide ≠ 0 ion to statio ue to the zer switches on th n order to avo eight switc re sixteen. Sw ach leg, where tive) and n in he sixteen-ve he result is VM are turned six prisms (F ors representat may be ident αβγ coordinati fication the 0 the 80 the 40 the y & Applied Sci taken from i rent. stage SVM vector VERSION STAGE erned with in aper discusse the 3D SVM matrix conve is to provide ced and unba e for providin t during unbal 0). from abc to with the rect no longer vali cing of the sy gh the system accurate swit onary frame ro-sequence c he same leg ca oid short circu ches, the p itching combi e p indicates ndicates the l ectors are rep a 3D hexago into prisms. T Figures 6-7). tion on conv tified by defi ion. en P=1 en P=2 en P=3 en P=4 ience Research A input phase v rs selection E nverter side es four-leg m M as a modu erter. The pr a control ove alanced loads ng a current pa lance. The bal (10 αβ coordinati tifier stage. F id and (11) is ystem, there w m and it is the tching pulses (11 happens into component. I an’t be turned uit. For the fo possible swit inations repres the upper swi lower switch presented into on and secto The 3D hexago The prisms a entional 2D ining the refe h V Abdelrehim et a oltage SVM matrix ulation rimary er the . The ath for lanced 0) ion is For an s now will be basic to all ) o αβγ In the d on at our-leg tching sented itch is is on o αβα ors of on can are an SVM. erence 8. E B. and imp bes thre swi Vol. 8, No. 2, 20 al.: Indirect 3D 240<θ<30 300<θ<36 Vectors are d Each prism con Fig. 6. 3D re Fig. Fig. Switching Vec As the referen d tetrahedron plemented by side each tetr ee switching v itching vector 018, 2847-2852 D-Space Vector M 00 then 60 then distributed into ntains four act epresentation of sw 7. Prisms ide 8. Vector dist ctor Selection nce vector loca number, sel choosing the n rahedron[8, 9] vectors, to ca the reference 2 Modulation for n P=5 n P=6, where θ o each prism a tive vectors. witching vectors i entification for 3D tribution into each ation is define ection of sw nearest referen ]. Each tetrah alculate the du e required volt 2849 r a Matrix Con θ= tan as shown in F in αβγ coordinatio D SVM h prism ed by prism nu witching vecto nce vectors lo hedron consis uty cycle for tage is transfo verter Figure on umber ors is ocated sts of each ormed
  • 4. firs sw wh the and ma var tetr po SV the nu act (re cha rep rep tw ma val var suc var Th op sho 10 Engineerin www.etasr st to αβγ coor witching vector V V V = d The duty cyc d d d = ∗ S = 1 here S is the d e reference vec d d represents atrix is depend rying values rahedron. S m ssible coincid VM code check e current value The rectifyin mbers from 1 tive rectifier ectifier matrix arge of genera presenting the presented on o matrices as i atrix converter Fig. 9. M A Simulink lidate the effe rying types o ccessfully va rious scenario he input and eration. The s own in Table -26. ng, Technology r.com rdination and rs [9] as per (1 d d V V V cles can be furt ∗ V V V duty cycle mat ctor, (V1 V2 V3 s the duty cy dent on the sel depending matrix calcula ence between ks the prism a es of S. IV. MATR ng stage is de 1 to 6, these n switches and x). At the sam ating another current active (inverter in (5) allows u r. The procedu Matrix converter V. SIMUL k simulation ectiveness of m f loads. The alidated as w os such as bala output wavef simulation was I. The simula y & Applied Sci then is divid 2). ther calculated trix [8-10], (V 3)T is the curren ycle for each s lected switchin on each se ations have b prisms and te and tetrahedron RIX CONVERTE edicated to gen numbers repre d would be re me time the in series of num e inverter swit matrix) as we us to find all p ure is shown in code generation f LINK SIMULATI was successf matrix conver proposed indi well. Simulati anced and unb forms ensured s carried out u ation results ar ience Research A ed by the ava (12 d as shown in (13 (14 Vα-ref Vβ-ref Vδ-r nt switching v switching vec ng vectors, so elected prism been done for etrahedrons. Th n number to e ER nerating a ser esenting the c epresented on nversion stage mbers from 1 tches that wou ell. Multiplyin possible switch n Figure 9. from Mi and MR ION fully develop rter operation irect 3D SVM ion worked balanced linear d proper con using the param re shown in F h V Abdelrehim et a ailable 2) (13). 3) 4) ref)T is vector, ctor. S it has m and r each he 3D extract ries of current n e is in to 16, uld be ng the hes for ed to under M was under r load. nverter meters igures R A. Vol. 8, No. 2, 20 al.: Indirect 3D Source sys Load syst Switching freq Input filter Output filter Repetitive Contr Tracking con Unbalanced Balanced l Nonlinear l Non-Linear L Fig. 12. FF 018, 2847-2852 D-Space Vector M TABLE I. tem em quency (LC) r (LC) roller Q(z) ntroller d load 5Ω load load Load Fig. 10. O (a) P (b) P (c) P (d) N Fig. 11. O FT analysis for ou 2 Modulation for SYSTEM PARAM 440V 115V- 1280 56Ω/0.8m 180uH+70 1.72377 1.663 1.868 Ω+5.5mH, 10Ω+6 5Ω +5 3phase diode Output voltage Phase A Phase B Phase C Neutral Output current utput phase voltag 2850 r a Matrix Con METERS V-60Hz -400Hz 00Hz mH/10uF 0uH/100uF 2 1 76 0.75754 3 0.9914 8 0.8735 6.2mH, 20Ω+7.5m 5.5 mH e bridge +50Ω ge (THD=3.3%) verter mH
  • 5. B. Engineerin www.etasr Fig. 13. Unbalanced Fig. 17. Inp ng, Technology r.com FFT analysis fo Fig. 14. Load Fig. 15. (a) P (b) P (c) P (d) Fig. 16. O put current multip y & Applied Sci or output current Error signal Output voltage Phase A Phase B Phase C Neutral Output Currents plied by factor 50 ience Research A (THD=1.8%) and input voltage h V Abdelrehim et a e C. Vol. 8, No. 2, 20 al.: Indirect 3D Fig. 19. Fig. 20. FF Non Linear L F Fig. 22. 018, 2847-2852 D-Space Vector M Fig. 18. FFT analysis fo FT analysis for ou Load Fig. 21. Output FFT analysis fo 2 Modulation for Error signal or input current (T utput phase voltag t voltage 115V/40 or input current (T 2851 r a Matrix Con THD=48%) ge (THD=3.3%) 00H THD=48%) verter
  • 6. mo bee con lim (11 con eff rep vo [1] [2] [3] [4] [5] [6] [7] Engineerin www.etasr Fig Fig. 25. Inp This paper odulation for en implement ntroller was s mited bandw 15V/400Hz). nditions (bal fectiveness o petitive contro ltage in an exc P. Zanchetta, Empringham, “ AC power s Electronics Sp 16, 2005 C. Klumpner, process of th Electronics Sp 1083–1088, Ju D. Casadei, G torque control Electronics, Vo F. Yue, P. W. W space vector m Electronics Co R. Zhang, Hig unbalanced loa State Universit R. Cárdenasa, control system Electric Power T. Friedli, J. evaluation of t back-to-back Electronics, Vo ng, Technology r.com Fig. 23. . 24. Repetitive put current multip VI. C introduced th four-leg matri ted and simu selected to reg width for The simulat anced, unbal f the propos oller showed t cellent way. REFE J. C. Clare, P. “Control Design upply using ge pecialists Confere F. Blaabjerg, P he matrix conve ecialist Conferenc une 17-21, 2001 G. Serra, A. 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L al leg with space tronics Conferenc ebruary 27, 1997 elligent commuta using novel gate Electronics Spec mon, “Matrix con icit input voltag al Electronics, Vo ion and control p nics, Vol. 3, No. mmutation techni ower Application pringham, A. Wei IEEE Transactio 8, 2002 Bidarte, I. Martin onverter protectio on chip design w cs, Vol. 26, No. w on matrix conve 5–25, 2006 “Bi-directional er applications” rol Conference, P 8 mmutation strateg Conference on , Vol. 2, pp. 560 mutation policy f Quality Confe ps commutation st r Electronics Spec –731, May 22, 19 vini, “Matrix con and input voltag ower Electronics –P10, 2003 n, C. Brunson, or matrix conver onference Wor 1), Tallinn, Eston verter ison of verter”, osition nsional , IEEE 2002 Lee, S. vector ce and ation of drive cialists nverter ge sign ol. 49, policies 1, pp. que of s, Vol. nstejn, ons on nez de on and with an 1, pp. erters”, switch , 8th Prague, gies in Power 0–564, for low erence, trategy cialists 98 nverter ge sign s and P. W. rters in rkshop nia, pp.