Modeling, Simulation and Analysis of Matrix Converter Using Matlab&Simulink

Transcription

1 Internatonal Journal of Modelng and Optzaton, Vol., No., June 0 Modelng, Sulaton and Analyss of Matrx Converter Usng Matlab&Sulnk Hulus Karaca and Raazan Akkaya Abstract In ths paper, a atrx converter (MC) whch akes drectly AC-AC power converson s odeled usng Matlab&Sulnk and ts workng prncples are analyzed. he gate sgnals of the power swtches of MC are produced usng Optu Apltude-Venturn Modulaton (OAVM) ethod. hs ethod provdes the apltude of output voltage up to 86.6% of nput voltage, and unty fundaental dsplaceent factor at the nput regardless of the load dsplaceent factor. he sulaton results obtaned fro the odel at varous operatng condtons are presented. hese results prove effectveness of the proposed atrx converter odel wth a unty nput power factor. Consequently, the desgned Matlab&Sulnk odel can be confdently used n the constructon stage of the OAVM ethod based atrx converter. Index ers Matrx converter, AC-AC converter, odelng and sulaton, OAVM ethod. I. INRODUCION One of the ost portant processes n power electroncs s to convert electrc power to dfferent fors. In controllng of the electrc energy, the great advances are provded together wth fast proveents n seconductor power eleents and power electroncs converters. he atrx converter provdng drectly ac-ac power converson s one of the ost nterestng ebers of the power converter faly. Matrx converter frstly ntroduced n 976 started to provng after papers of Venturn and Alesna n 980 [, ]. he proposed ethod by these authors s known as the Venturn ethod or the drect transfer functon approach. In ths ethod, gate-drve sgnals for the nne bdrectonal swtches are calculated to generate varable-frequency and/or varable-apltude snusodal output voltages fro the fxed-frequency and the fxed-apltude nput voltages. he MC has soe advantages as follows accordng to tradtonal converter. Generaton of output voltages wth the desrable apltude and frequency; Energy regeneraton apttude to the ans; Snusodal nput and output currents; Controllable of nput dsplaceent factor regardless of Manuscrpt receved Aprl, 0; revsed May 4,0. H. Karaca s wth the Departent of Electrcal and Electroncs Engneerng, Selcuk Unversty, 4075, Konya, urkey, (correspondng author s phone: ; fax: ; e-al: hkaraca@selcuk.edu.tr). R. Akkaya s wth the Departent of Electrcal and Electroncs Engneerng, Selcuk Unversty, 4075, Konya, urkey (e-al: akkaya@selcuk.edu.tr). the load; Copact desgn due to the lack of dc-lnk coponents for energy storage. hese fascnatng propertes have otvated researchers to study about the MC [, 4]. But, the physcal realzaton of the MC s very dffcult, and the nuber of the devces n the power crcut s hgher than that of the nverter. herefore, t s crucal to obtan an effectve odel and to test t before constructng a workng prototype of the MC. However, popular crcut-orented sulaton software packages such as PSPICE, PSIM and Matlab&Sulnk have not got the odel of an MC as a standard block n ther lbrares [5]. In ths work, an effectve odel of the MC s developed by usng Matlab&Sulnk n order to copensate entoned necessty. he basc concepts of atrx converter are explaned and the atheatcal odel of atrx converter s brefly gven n a clear for. Optu Apltude-Venturn Modulaton (OAVM) ethod s used to produce the gate sgnals drvng bdrectonal power seconductors, and a axu voltage transfer rato (0.866) was obtaned. An nput flter s used at nput sde of converter. It soothes dstorton of the nput current around the swtchng frequency and elnates the generaton of overvoltage produced durng coutaton of currents due to the presence of the short-crcut reactance of any real power supply. he workng prncples of MC producng the output voltages at varous apltude and frequency are analyzed. Also, sulaton results of OAVM ethod based atrx converter are gven. II. HE BASIC OPOLOGY OF MARIX CONVERER he atrx converter s a sngle-stage converter, whch has an array of x n bdrectonal power swtches. Each bdrectonal swtch s coposed of two IGBs and two fast dodes connected ant-parallel. heoretcally, the nuber of nput phases, ust be at least three, and the nuber of output phases, n can be chosen fro one to nfnty. he basc atrx converter topology whch connects a three-phase voltage source to a three-phase load s shown n Fg.. hs s the ost portant atrx converter topology fro a practcal pont of vew. A atrx converter s an unlted frequency changer, whch can generate both saller and bgger output frequency than nput frequency of the converter. he output voltage wavefors are constructed by pecng together selected segents of the nput voltage wavefors. 8

2 Internatonal Journal of Modelng and Optzaton, Vol., No., June 0 -Phase AC Source N Input Flter L I A I B Matrx Converter S Aa S Ab S Ac S Ba S Bb S Bc So, odulaton atrx can be gven as n (4). M Aa Ab Ac Ba Bb Bc Ca Cb Cc (4) C I C S Ca S Cb S Cc I a I b I c Under deal nput voltage condtons, the three-phase snusodal nput voltages of the MC wll be as follows, Fg.. Crcut of a x atrx converter Each swtch s characterzed by a swtchng functon, defned as follows and can connect or dsconnect phase K of the nput stage to phase j of the load. 0 Swtch, S S Swtch, S K {A,B,C}, j {a,b,c} s open s closed Output voltages can be syntheszed by swtchng accordng to a proper cobnaton of these swtches. Control of the atrx converter ust coply wth the followng basc two rules. Frstly, any two nput ternals should never be connected to the sae output lne to prevent short-crcut, because the MC s fed by a voltage source. he other s that, an output phase ust never be open-crcuted, owng to the absence of a path for the nductve load current whch leads to the over-voltages. he above two constrants can be expressed by (). Aa Ab Ac Ba Bb Bc Ca Cb Cc When these rules are provded, the x atrx converter can allow only 7 dfferent swtchng states aong the possble 5 swtchng cobnatons. III. MODELING OF OAVM MEHOD BASED MARIX CONVERER In ths paper, V sk are the source voltages, sk are the source currents, v jn are the load voltages wth respect to the neutral pont n of the star connected load, and j are the load currents. Also, other varables have been defned to be used as a bass of the odulaton and control strateges: v KN are the MC nput voltages, K are the MC nput currents, and v jn are the load voltages wth respect to the neutral pont N of the grd. If t s defned as the te durng swtch S s on and s the swtchng perod, duty cycle of swtch S can be gven as follows. s () () t () n Load cos(ω t) vsk VsK cos(ωt /) (5) cos(ω t 4/) In accordance wth ths, each output phase voltages wth respect to the neutral pont N of the grd can be expressed by (6). v M v jn KN (6) In the sae way, the nput currents are also shown by the followng expresson. M K j (7) Where, [M] s the transpose atrx of [M]. he apltude of the output voltage s lted to 50 percent of the nput voltage n the ntal approach of Venturn Modulaton ethod. o obtan a axu voltage transfer rato, thrd haroncs of the nput frequences are added to the target output phase voltages and thrd haroncs of the output frequences are subtracted fro t as gven n (8). A Matlab&Sulnk odel s llustrated to copute the reference output phase voltage n Fg.. In ths fgure, only odel of target voltage of the output phase a (V a_ref ) s clearly gven. Also, odels of target voltages of the output phase b and c are lke ths odel. v jn qv KN cos(ωot) cos o 6 π cos(ωot ) cos 6 4π cos(ωot ) cos 6 ω t cosω t ω t cosω t o ω t cosω t Where, q s the voltage gan or voltage transfer rato. By ths way, a voltage transfer rato of whch s axu value can be obtaned. he thrd-haronc njecton of the nput and output frequences nto the target output voltages has no effect on the output lne-to-lne voltages [4, 6]. he target output voltage equals the average output voltage durng each swtchng sequence. If unty nput dsplaceent factor s requred n the OAVM ethod [6-8], the algorth can be spler n the for of (9) [, 4, 8]. o (8) 9

3 Internatonal Journal of Modelng and Optzaton, Vol., No., June 0 K v V v KN jn KN q q A,B,C, j a,b,c sn and β ω t β snω t K K π 4π 0,, (9) hen, duty cycles of bdrectonal swtches are calculated accordng to (0). s t + t Bj t X 0 t Y t + t Bj 0 Fg.. Gate sgnals of the power swtches connected to the sae output phase vknv jn q t snω t βk sn ωt (0) s VKN 9q Fg.. hrd-haronc njecton of the nput and output frequences nto the output phase voltages As shown n Fg., sgnals, X and Y are obtaned by coparng saw tooth sgnal wth swtchng frequency and these calculated duty cycles. Fg.4. Matlab&Sulnk odel of the x atrx converter 0

4 Internatonal Journal of Modelng and Optzaton, Vol., No., June 0 Fnal gate drve sgnals (S), deternng turn-on-te of the power swtches can be obtaned accordng to the logc stateents n () by usng duty cycles [5]. Consequently, only duty cycles of sx swtches are suffcent to calculate the gate sgnals for all of the power swtches X t Y t t Bj S S S Bj Cj (X) not (X) not (X) and and (Y) not (Y) () A global Matlab&Sulnk odel of atrx converter whch ncludes odels of three-phase source, flter, reference voltage, load, and especally the swtchng pattern s gven n Fg. 4. As a result, nput and output currents, output phase voltages wth respect to N (v an, v bn, v cn ) and n (v an, v bn, v cn ), output lne-to-lne voltages (v ab, v bc, v ca ) of atrx converter controlled wth OAVM ethod are attaned usng ths odel. Fg. 6. Output phase voltage wth respect to star pont of source and output current: n 0 Hz n 60 Hz IV. SIMULAION RESULS AND DISCUSSION Paraeters used n the developed sulaton odel have been gven n able I. ABLE I. SIMULAION PARAMEERS Source voltage apltude, V Flter nductance, H Flter capactance, 5 μf Flter resstance, Ω Load nductance, 0 H Load resstance, 0 Ω Input frequency, 50 Hz Voltage transfer rato, 0.8 Output frequency, 0 and 60 Hz Sulaton of atrx converter has been perfored to produce output wth varable frequency fro nput wth fxed frequency. In ths paper, sulaton results have been presented for only output frequences of 0 and 60 Hz fro an nput of 50 Hz. In Fg. 5 and Fg. 5, output lne-to-lne voltages for 0 and 60 Hz have been respectvely gven. As shown, these voltages have pulses wth swtchng frequency but ther averages consttute a snusodal wavefor. hat s, thrd-haronc njecton does not have a negatve effect on the output lne-to-lne voltages. Fg. 5. Output lne-to-lne voltage: n 0 Hz n 60 Hz Fg. 7. Output phase voltage wth respect to star pont of load and output current: n 0 Hz n 60 Hz Fg. 8. hree phase output current: n 0 Hz n 60 Hz In Fg. 6 and Fg. 6, output phase voltage wth respect to neutral of source and output current have been shown at output frequences of 0 and 60 Hz, respectvely. In Fg 7 and Fg. 7, output phase voltage wth respect to neutral of load and output current have been shown. As understood fro these fgures, output phase voltages have pulses wth khz frequency and average of ts wavefor s snusodal. Besdes, output current s lag fro output phase voltage due to nductve load. hree phase output currents have been llustrated at outputs of 0 Hz n Fg 8 and 60 Hz n Fg. 8. As shown, load currents are nearly a pure snusodal n the two-frequency and there s a phase dfference of 0 aong the currents. In Fg. 9, wavefors of source voltage, current drawn fro source and load current whch are obtaned usng by the pleented atrx converter odel are gven on the sae axs. As understood fro Fg. 9 and Fg. 9, both frequency of nput voltage and nput current s 50 Hz, even f frequency of output current s 0 Hz or 60 Hz.

5 Internatonal Journal of Modelng and Optzaton, Vol., No., June 0 Fg. 9. Input voltage, nput current and output current: n 0 Hz n 60 Hz Input voltage and nput current are at the sae phase, whle output current of atrx converter s lag fro output phase voltage due to nductve load. hese results prove that the atrx converter can draw current n the unty dsplaceent factor fro ans at any load. In addton to, pulses wth the swtchng frequency whch are occurred on nput current durng coutaton have been soothed usng a sall three nput flter. V. CONCLUSION he workng prncple and analyss of the MC that connects drect three-phase source to three-phase load and controlled wth the OAVM ethod has been presented. Modulaton strateges and fundaental atheatcal equatons of the MC have been presented clearly. Also, odelng and sulaton of the OAVM ethod, whch can gve an output voltage wth axu apltude, has been pleented. he desgned odel has satsfactorly gven the behavor of the MC ncludng the pact of the nput flter. he sulaton results show that the odulaton algorth provdes a unty nput dsplaceent factor even f the load has an nductve characterstc. As a result, the Matlab&Sulnk odel presented can be confdently used n the constructon stage of the atrx converter. REFERENCES [] M. Venturn, A New Sne Wave n Sne Wave out, Converson echnque Whch Elnates Reactve Eleents, n Proceedngs of Powercon 7, pp. E/-E/5, 980. [] M. Venturn and A. Alesna, he Generalzed ransforer: A New Bdrectonal Snusodal Wavefor Frequency Converter wth Contnuously Adjustable Input Power Factor, IEEE PESC 80, pp.4-5, 980. [] H. Karaca and R. Akkaya, Modellng and Sulaton of Matrx Converter under Dstorted Input Voltage Condtons, Sulat. Modell. Pract. heory (00), do:0.06/j.spat , 00. [4] P. W. Wheeler, J. Rodrguez, J. C. Clare, et al., Matrx Converters: A echnology Revew, IEEE ransacton on Industral Electroncs, vol. 49, no., pp.76-88, 00. [5] J. Rodrguez, E. Slva, F. Blaabjerk, et al., Matrx Converter Controlled wth he Drect ransfer Functon Approach: Analyss, Modellng and Sulaton, Internatonal Journal of Electroncs, aylor & Francs, vol.9, pp.6-85, 005. [6] H. Karaca, R. Akkaya, and H. Dogan, A Novel Copensaton Method Based on Fuzzy Logc Control for Matrx Converter Under Dstorted Input Voltage Condtons, 8th Internatonal Conference on Electrcal Machnes, ICEM 008, vol. -4, , 008, Sep , Portugal. [7] H. Karaca and R. Akkaya, Control of Venturn Method Based Matrx Converter n Input Voltage Varatons, n Proceedngs of the Internatonal MultConference of Engneers and Coputer Scentsts IMECS 09, vol II, 4-46, 009, March 8-0, Hong Kong. [8] H. Karaca and R. Akkaya, An Approach for Controllng of Matrx Converter n Input Voltage Varatons, Engneerng Letters, 009, vol. 7-, H. Karaca was born n Yozgat, urkey, n 979. He receved the B.S., M.S. and Ph.D. degrees n electrcal and electroncs engneerng fro Selcuk Unversty, Konya, urkey, n 00, 004 and 00, respectvely. He s currently a Research Assstant wth the Departent of Electrcal-Electroncs Engneerng, Selcuk Unversty, Konya. Hs research nterests nclude atrx converters, electrcal achnes and drves and power electroncs. R. Akkaya was born n Aksaray, urkey, n 96. He receved the B.S., M.S. and Ph.D. degrees n electrcal and electroncs engneerng fro Yldz echncal Unversty, İstanbul, urkey, n 986, 988 and 995, respectvely. He s currently an Assocate Professor wth the Departent of Electrcal Engneerng, Selcuk Unversty, Konya. Hs research nterests nclude electrcal achne drves, power electroncs, solar energy systes and atrx converters.