IMECS 9, March 8 -, 9, Hong Kong Control of Venturn Method Based Matrx Converter n Input Voltage Varatons Hulus Karaca, Ramazan Akkaya Abstract Matrx converter s a sngle-stage converter whch drectly connects a three-phase voltage source to a three-phase load wthout dc-lnk components. Therefore, any harmonc dstorton and mbalance n nput voltage drectly reflect to the output of the converter. Recently, many researchers have made an effort to cope wth ths problem. In ths paper, under dstorted nput voltage condtons, behavors of the MC controlled wth Venturn method are analyzed and a PI controller based compensaton method to prevent negatve effects of nput voltage s proposed. Snce the proposed method s based on closed loop control of the output currents, t not only reduces the output harmonc contents but also ensures a stable control of the load currents. Some results are presented to prove the effectveness of the proposed compensaton technque. Index Terms Matrx converter, ac-ac converter, Venturn method, dstorted nput voltage, compensaton. I. INTRODUCTION One of the most nterestng members of the power converter famly s the matrx converter provdng drectly ac-ac power converson. Matrx converters frstly ntroduced n 976 started to mprove after the papers proposed by Venturn and Alesna n 98 and 989 [], []. The matrx converter has receved an ncreased amount of nterest and has been studed ntensely as an alternatve to conventonal ndrect power converter systems n recent years, because t has outstandng advantages n followng []-[5]. Snusodal nput and output currents No bulky dc-lnk reactve elements Possble wth unty dsplacement factor for any load Four-quadrant operaton Smple and compact desgn Regeneraton capablty. These attractve propertes have motvated researchers to study about the matrx converter [4]. However, the load sde of the MC s drectly affected by the dstorted and/or unbalanced nput voltages due to the lack Manuscrpt receved December 5, 8. Scentfc Research Project Found of Selcuk Unversty has been provded the fnancal support to ths project. H. Karaca s wth the Department of Electrcal and Electroncs Engneerng, Selcuk Unversty, 475, Konya, Turkey, (correspondng author s phone: +9--75; fax: +9--465; e-mal: hkaraca@selcuk.edu.tr). R. Akkaya s wth the Department of Electrcal and Electroncs Engneerng, Selcuk Unversty, 475, Konya, Turkey (e-mal: akkaya@selcuk.edu.tr). of dc ntermedate crcut n the MC. The dstorted and/or non-snusodal nput voltages may cause the undesrable harmonc currents. The workng performance of the load has deterorated, when t s exposed to the harmonc and non-snusodal currents. If unfavorable effects of the dstorted nput voltages are elmnated n the MC, the popularty of the MC wll more ncrease. Some papers have been presented to reduce the nfluences of the dstorted nput voltages [5]-[]. In ths paper, a PI based compensaton technque s proposed to get rd of the undesrable effects of the dstorted nput voltages for matrx converter controlled wth Venturn modulaton method. Snce ths technque mprovng the output performance of the MC performs closed loop control of the output current, three-phase output currents of the MC must be measured by usng current sensors. The proposed method not only reduces the output harmonc contents but also ensures over-current protecton and control for the load current. Some numercal and smulaton results are presented to prove the effectveness of the proposed compensaton technque. II. THE BASIC TOPOLOGY OF MATRIX CONVERTER The matrx converter s a sngle-stage converter, whch s composed of an array of m x n bdrectonal power swtches, each connected between one phase of the nput and one phase of the output. Theoretcally, the number of nput phases, m must be at least three, and the number of output phases, n can be chosen from one to nfnty. The basc matrx converter topology whch connects a three-phase voltage source to a three-phase load as shown n Fg. s the most mportant converter from a practcal pont of vew []. A matrx converter s an unlmted frequency changer, whch can generate both smaller and bgger output frequency than nput frequency of the converter. The output voltage waveforms are constructed by pecng together selected segments of the nput voltage waveforms. Each swtch s characterzed by a swtchng functon, defned as follows []. S Kj(t) = S Kj s open S Kj s closed Each swtch S Kj, K = {A, B,C}, j = {a,b, c}, can connect or dsconnect phase K of the nput stage to phase j of the load. Output voltages can be syntheszed by swtchng v jn accordng to a proper combnaton of these swtches. () ISBN: 978-988-7-7-5 IMECS 9
IMECS 9, March 8 -, 9, Hong Kong V sa I sa I A S Aa S Ab S Ac I a N V sb I sb L f I B S Ba S Bb S Bc I b Load n V sc I sc I C S Ca S Cb S Cc I c Three-phase source C f Input Flter Matrx Converter Fg.. The basc matrx converter topology Control of the matrx converter must comply wth the followng basc two rules. Frstly, any two nput termnals should never be connected to the same output lne to prevent short-crcut, because the MC s fed by a voltage source. The other, an output phase must never be open-crcuted, owng to the absence of a path for the nductve load current whch leads to the over-voltages. The above two constrants can be expressed by (). m Ka ( t ) = mkb( t ) = mkc( t ) = K = A,B,C K = A,B,C K = A,B, C When these rules are provded, the x matrx converter can allow only 7 dfferent swtchng states among the possble 5 swtchng combnatons. III. VENTURINI METHOD FOR MATRIX CONVERTER In 98, Venturn and Alesna presented a converter, whch conssts of bdrectonal power swtches constructed as matrx and they ntroduced to as matrx converter. In addton to, they proposed a PWM modulaton method for the control of matrx converter. The proposed method by these authors s known to as the Venturn method or the drect transfer functon approach. In Venturn method, the approprate frng pulses to each of the nne bdrectonal swtches must be calculated to generate varable-frequency and/or varable-ampltude snusodal output voltages from the fxed-frequency and the fxed-ampltude nput voltages. In ths paper, VsA,VsB, VsC are the source voltages, sa, sb, sc are the source currents, v jn, j = {a,b, c} are the load voltages wth respect to the neutral pont n of the load, and j, j = {a,b, c}, are the load currents. Also, other varables have been defned to be used as a bass of the modulaton and control strateges: v, = {A, B,C}, are the MC nput voltages,, = {A,B, C}, are the MC nput currents, and v jn, j = {a,b, c}, are the load voltages wth respect to the neutral pont N of the grd. If t s defned as t Kj : the tme durng whch swtch s on and Ts: the samplng nterval, m ( t ) = t T : duty cycle of swtch S Kj, modulaton matrx s gven n (). Kj Kj s () S Kj M( t ) m Aa ( t ) = m Ab ( t ) m Ac ( t ) mba ( t ) mca ( t ) mbb ( t ) mcb ( t ) mbc ( t ) mcc ( t ) Under deal condtons, the three-phase snusodal nput voltages of the MC can be gven as, [ v ( t )] () cos( ωt ) = Vm cos( ωt + π / ) (4) cos( ωt + 4π / ) In accordance wth ths, each output phase voltages can be expressed by (5). [ v ( t )] [ M ( t )][ v ( t )] jn = (5) In the same way, the nput currents are also shown by expresson n (6). T [ ( t )] [ M( t )] [ ( t )] = o (6) Where, [M(t)] T s the transpose matrx of [M(t)]. The ampltude of the output voltage s lmted to 5 percent of the nput voltage n the ntal approach of Venturn method. To obtan a maxmum voltage transfer rato s added thrd harmoncs of the nput and output frequences to the target output voltages as shown n (7). [ v ( t )] jn cos( ) cos o 6 π = qvm cos( + ) cos 6 4π cos( + ) cos 6 ( ω t) + cos( ω t) ( ω t) + cos( ω t) o ( ω t) + cos( ω t) Where, q s the voltage gan or voltage transfer rato. By ths way, a voltage transfer rato of.866 whch s maxmum value can be obtaned. The thrd-harmonc njecton of the nput and output frequences nto the target output voltages has no effect on the output lne-to-lne voltages. The target output voltage equals the average output voltage durng each swtchng sequence. If unty nput dsplacement factor s requred n the optmum-ampltude Venturn method [], [5], the algorthm can be more smple n the form of (8) []. o (7) ISBN: 978-988-7-7-5 IMECS 9
IMECS 9, March 8 -, 9, Hong Kong T s t Aj+ t Bj t Aj Control System Phase AC Source X Y t Aj t Aj+ t Bj Iref + - PI q Controller and Drver Fg.. PI feedback compensaton scheme for matrx converter 9 Ido Phase Current Measurement Load Fg.. Obtanng turn-on-tme of the power swtches vkv j q mkj = + + sn K Vm qm π 4π K = { A,B,C}, j = { a,b,c}, βk =,, ( ω t + β ) sn( ωt ) Then, duty cycles of bdrectonal swtches were calculated accordng to (9). (8) vkv j q tkj = Ts + + sn( ωt + βk ) sn( ωt ) (9) V 9q m m As shown Fgure, Sgnals, X and Y are obtaned by comparng saw-tooth wth swtchng frequency and these calculated duty cycles. Fnal gate drve sgnals (S Kj (t)), determnng turn-on-tme of the power swtches are obtaned accordng to the logc statements n () by usng duty cycles []. Consequently, only duty cycles of sx swtches are suffcent to calculate the gate sgnals for all of the power swtches. SAj = ( X) X = taj SBj = not( X) and ( Y) Y = taj + tbj S = not ( X ) and not ( Y ) Cj IV. THE PROPOSED COMPENSATION SCHEME FOR DISTORTED INPUT VOLTAGE CONDITIONS () Modulaton algorthms used n the MC have employed fxed swtchng patterns n snusodal nput voltages. For certan frequency and/or ampltude values, duty cycles of the power swtches are pre-calculated and placed nto the table. But, snce the negatve effects of the nput voltages reflect the output of the converter under the dstorted nput voltage condtons, usng the fxed swtchng patterns are not approprate. Therefore, duty cycles for swtchng patterns must be calculated nstantaneously by measurng the output currents at each samplng perod []. T s In PI feedback compensaton scheme, whch s shown schematcally n Fg., the measured output currents are used to calculate the magntude of the output current space vector (I do ) accordng to (). If the nput voltages of the MC are snusodal and balanced, the output currents wll be snusodal, too. Under ths condton, I do s constant. However, f the nput voltages of the MC are non-snusodal and unbalanced, I do wll be not constant due to the output harmonc currents. I do [ ( t ) + ( t ) + ( t )] = oa ob oc () Recevng nspraton from ths dea, f I do s kept constant, the output of the converter s not affected by dsturbances n the nput voltages. The proposed compensaton technque s based on ths prncple and a PI controller s employed for ths purpose. Accordngly, the PI controller system s fed by the nstantaneous error of I do (e(k) ) n () and produces a varable voltage-gan (q) accordng to the dsturbance of the nput voltage. Duty cycles of the power swtches are calculated, substtutng the varable-voltage-gan-value produced by the PI controller n (9). e [ ] ( k) I ( k ) I ( k) = () ref Block dagram of the PI controller based feedback system s clearly gven n Fg. 4. The nstantaneous value of the error can be calculated by subtractng the nstantaneous current-space-vector I do obtaned by the measured three-phase output current from the reference-current-space-vector I ref. Fg. 4. Smulnk dagram of PI controller based feedback system The output of the PI controller system s the voltage-gan (q) and a saturaton block has been added to the output of system, due to the magntude of q can not exceed.866 and can not be negatve. do ISBN: 978-988-7-7-5 IMECS 9
IMECS 9, March 8 -, 9, Hong Kong V. SIMULATION RESULTS Some smulaton studes have been done usng parameters n Table I. TABLE I SIMULATION PARAMETERS Source voltage ampltude, V m V Input frequency, f 5 Hz Load resstance, R Ω Load nductance, L mh Input flter nductance, L f mh Input flter resstance, R f. Ω Input flter capactance, C f 5 µf Swtchng frequency, f s khz The smulatons have been performed under the nput voltage condtons whch have % thrd harmonc and % ffth harmonc as shown Fg. 5. The varatons of q for the compensated and uncompensated systems are llustrated n Fg. 6. The voltage-gan s constant n the matrx converter wthout compensaton. But, under the abnormal nput voltage condtons, thanks to the proposed compensaton method, the voltage-gan aren t fxed anymore, are varable accordng to the dsturbance n the output currents. So, the duty cycles of the power swtches wll not fxed. The waveforms of the output currents for 5 and 5 Hz are shown n Fg. 7 and Fg. 8, respectvely. In Fg 7(a) and 8(a), the output currents of the uncompensated systems are gven under the dstorted nput voltage condtons. As for the output currents of the compensated systems are llustrated n Fg. 7(b) and 7(b). In the uncompensated system, total harmonc dstortons of the output current are respectvely 6.6% and 9.6% for 5 and 5 Hz of the output frequency. In the compensated system, total harmonc dstortons of the output current are respectvely.45% and.7% for 5 and 5 Hz of the output frequency. As t s shown, f the nput voltages of the MC are dstorted or unbalanced, the low order harmoncs occur on the output current and voltage of the MC. But, under the same condtons, the proposed PI controller based compensaton method has effectvely decreased these harmoncs. The waveforms of the output voltages for 5 and 5 Hz are shown n Fg. 9 and Fg., respectvely. In Fg 9(a) and (a), the output voltages of the uncompensated systems are gven under the dstorted nput voltage condtons. As for the output voltages of the compensated systems are llustrated n Fg. 9(b) and (b). The black pulsng dagram s the output lne voltage and the green lne s average of the output lne voltage n fgures. As t s understood from the average value of the output lne voltage, the proposed compensaton technque has satsfactorly elmnated the harmoncs of the output voltage, too Fg. 5. Input voltages whch have % thrd and % ffth harmoncs Fg. 6. Varaton of the voltage gan (a) Output currents wthout compensaton (b) Output currents wth compensaton Fg. 7. Three-phase output currents for MC the under dstorted nput voltage condtons (f o = 5 Hz) (a) Output currents wthout compensaton (b) Output currents wth compensaton Fg. 8. Three-phase output currents for MC the under dstorted nput voltage condtons (f o = 5 Hz) ISBN: 978-988-7-7-5 IMECS 9
IMECS 9, March 8 -, 9, Hong Kong (a) Output currents wthout compensaton (b) Output currents wth compensaton Fg 9. Output lne voltages for the MC the under dstorted nput voltage condtons (f o = 5 Hz) (a) Output currents wthout compensaton Internatonal Conference on Electrcal Engneerng ICEENG 8, May 8. [5] D. Casade, G. Serra and A. Tan, Reducton of the Input Current Harmonc Content n Matrx Converters under Input /Output Unbalance IEEE Trans. Ind. Electron., vol. 45, no., pp. 4-49, June 998. [6] P. Nelsen, F. Blaabjerg, J. K. Pedersen, Space Vector Modulated Matrx Converter wth Mnmzed Number of Swtchngs and a Feedforward Compensaton of Input Voltage Unbalance, IEEE-PEDES 96, vol., pp. 8-89, 996. [7] P. Nelsen, D. Casade, G. Serra, A. Tan, Evaluaton of the Input Current Qualty by Three Modulaton Strateges for SVM Controlled Matrx Converters wth Input Voltage Unbalance, IEEE-PEDES 96, vol., pp. 794-8, 996. [8] K. Sun, D. Zhou, L. Huang, K. Matsuse, Compensaton Control of Matrx Converter Fed Inducton Motor Drve under Abnormal Input Voltage Condtons, IEEE-IAS 4, pp. 6-6, 4. [9] M. E. O. Flho, E. R. Flho, K. E. B. Qundere, J. R. Gazol, A Smple Current Control for Matrx Converter, IEEE-Internatonal Symposum on Industral Electroncs, pp. 9-94, 6. [] S. Sünter, H. Altun, J. Clare, A Control Technque for Compensatng the Effects of Input Voltage Varatons on Matrx Converter Modulaton Algorthms, Taylor&Francs-Electrc Power Components and Systems, vol., pp. 87-8,. [] H. Karaca, R. Akkaya, H. Doğan, A Novel Compensaton Method Based on Fuzzy Logc Control for Matrx Converter under Dstorted Input Voltage Condtons, IEEE-Internatonal Conference on Electrcal Machnes, September 8. [] S. Campbell, H. A. Tolyat, DSP-Based Electromechancal Moton Control, CRC Press, pp. 7-5, 4. [] J. Rodrguez, E. Slva, F. Blaabjerg, P. Wheeler, J. Clare, J. Pontt, Matrx Converter Controlled wth the Drect Transfer Functon Approach: Analyss, Modellng and Smulaton, Taylor&Francs-Internatonal Journal of Electroncs, vol. 9, no., pp. 6 85, February 5. (b) Output currents wth compensaton Fg. Output lne voltages for the MC the under dstorted nput voltage condtons (f o = 5 Hz) VI. CONCLUSIONS A PI controller based compensaton technque s proposed to mprove the output performance of the MC. The proposed method has satsfactorly reduced harmoncs n the output currents and voltages under the dstorted nput voltage condtons. In addton to, ths method allows the over-current protecton and the control of the load current. Under undesrable effects of the nput supply voltage, the proposed compensaton technque s an effectve method to reduce harmoncs of the output current and voltage. Valdty of ths method s verfed by the presented smulaton results. REFERENCES [] M. Venturn, A New Sne Wave n Sne Wave out, Converson Technque Whch Elmnates Reactve Elements, Proceedngs of Powercon 7, pp. E/-E/5, 98. [] A. Alesna, M. Venturn, Analyss and Desgn of Optmum-Ampltude Nne Swtch Drect AC-AC Converters, IEEE Trans. Power Electron., vol. 4, no., pp. -, Jan. 989. [] P.W. Wheeler, J. Rodrguez, J.C. Clare, et al., Matrx Converters: a Technology Revew, IEEE Trans. Ind. Electron., Vol. 49, no., pp.76-88, Aprl. [4] H. Karaca, R. Akkaya, A Matrx Converter Controlled wth the Optmum Ampltude-Drect Transfer Functon Approach, 6th ISBN: 978-988-7-7-5 IMECS 9