ANALYSIS O VIENNA RECTI IER

Transcription

1 Electrical Power Qality and Utilisation, Jornal Vol. XI, No., 005 ANALYSIS O VIENNA RECTI IER Grzegorz RADOMSKI Technical University of Kielce, Poland Smmary: It is common to find the inexpensive bt robst electric power rectification method to flfil the demands of clean power conversion [-]. The Vienna rectifier strctre [] is one of the hopefl constrction to flfil these demands. It may be classified as the Clean Power Converter. It lets s obtain PFC rectification in simpler than the PWM converter system. The Vienna rectifier has three control points. In addition the Vienna rectifier is the three voltage level system with less crrent ripples than in the case of the PWM converter. However, it has some disadvantages. The Vienna rectifier system is an nidirectional converter. It can fnction only in the rectifier mode, the working in the inverter mode is impossible and the generation of the reactive power is strongly restricted. Usally the Vienna rectifier is controlled on the basis of the direct crrent control method [4,5,6]. However, this method is not perfect becase it lets the improper control seqences appears. In this paper the mathematical model of the Vienna rectifier is derived. The voltage space vectors and their dependencies to the phase crrents are defined. The range of the phase displacement angle and the maximm voltage space vector modle v. phase displacement angle is drawn ot for the case of the sinsoidal space vector modlation. The drawn ot relations are proven by simlation reslts. Key words: Power electronics Electric power qality P C rectifiers Improving THD(i). INTRODUCTION Limitation of the high harmonic contents in the crrents and improvement of the inpt power factor of the loads spplied by the power electronic converters is one of the most important problems of power electronics. Especially, the ratings of the rectifiers are widely considered []. Classic diode and thyristor rectifiers are sorces of the high harmonic crrent components drawn ot from the electric power tility (THD i» 30%), while the common norms demand the total harmonic distortion factor THD i 5% and power factor P ³ 94%. The developed Vienna rectifier strctre [] is devoted mainly for spplying of electronic systems. The scheme of Vienna rectifier is presented in the igre. The main advantages of this constrction are: three phase, three level inpt voltage generation, controlling only three electronic switches, less voltage stress of the electronic switches than in the case of the PWM converter. It is worth nderlining that this configration is death time problem free. However, the Vienna rectifier is nidirectional system. It can convey the electrical energy only from AC circit to the DC circit. The methods of controlling Vienna rectifier with direct inpt crrent shaping were presented in the papers [4, 5, 6]. The controlling Vienna rectifier by the voltage space vector method and its limitations is the sbject of this paper. The Vienna rectifier belongs to the class of AC/DC converters with crrent sorce inpt and voltage sorce otpt. The primary sides of inpt magnetic coils are spplied by phase voltages. The controlling this kind of the converter relies on the generation of three phase voltages at the secondary side of the inpt magnetic coils. This generation mst go in the manner that the voltages at the inpt magnetic coil impedance have low high harmonic contents, the phase angle and amplitde of the first harmonic voltage oriented to obtain the desired crrent vales near sinsoidal and sally in phase with inpt phase voltages. The principles of the converter fnctionality are presented in the fig. and fig. 3. The fig. presents the eqivalent scheme of the inpt rectifier circit while the fig. 3 illstrates the relation between the voltage and crrent space vectors in the dq reference axis. The character of the inpt impedance and power flow direction in relation to rectifier voltage space vector realisation is shown. It will be next explained that Vienna rectifier may fnction only in the rectifier mode, the working of Vienna rectifier in the inverter mode is impossible. ig.. Scheme of the Vienna rectifier Grzegorz RADOMSKI: Analysis of Vienna Rectifier 49

2 ig.. Eqivalent scheme of the rectifier ig. 3. Rectifier vector diagram. INPUT VOLTAGES O VIENNA RECTI IER Vienna rectifier is three level voltage boost converter. It differs from PWM AC/DC boost converter in realisation of matrix of power electronic switches and in three level converter phase voltage related to the mid point of the capacitive otpt voltage divider [3]. This property is a direct reslt of the different realisation of the matrix of power electronics switches. The transistor switches together with diode switches and inpt indctance create the boost converter system. Inpt magnetic coils are charged in the state when the transistor is on and discharged by the positive or negative diode when the transistor is off. While the transistor electronic switch is on, the crrent and energy cmlated in indction coil increase, when the switch is off the energy flows from the magnetic coil to the otpt circit by diode D j+ or D k depending on the actal crrent flow direction. Change in the state of transistor condction atomatically case the change in the diodes condction which reslts in death time problem free operation of the rectifier. Depending on the state of power electronic switch and the direction of crrent the inpt voltage of the rectifier takes three vales: respectively: where phase indexes: dc dc Sin, 0, () dc for s i 0 i i 0 Sin () for s 0 (3) i Sin dc for s i 0 i i < 0 Sin (4) i { a, b, c} The dynamics of the phase crrents is described by the following eqations: dii for s i ( fi Nn) L + (5) di j for 0 0 dc s j i j > fj Nn L + S dik for 0 0 dc s k i k < fk Nn L + + S i j k i,j,k { a,b,c} The fact that the positive crrent responds to the switching phase voltage Sin between vales of 0 and dc while the negative crrent responds to the switching phase voltage between vales of Sin and dc reslts in strongly limited abilities of the reactive power generation and in total impossibility of working in the inverter mode. The disadvantages of Vienna rectifier described here are illstrated by the simlation investigation reslts in figres from 0 to 5 in the next chapter. or these reasons, the Vienna rectifier may be implemented as a power spply for electronic systems, especially in telecommnication switch-boxes, electric arc spply, UPS systems, electric battery chargers. The application of the Vienna rectifier in the field of electric DC drives is restricted to the systems with low dynamics withot regenerating braking. Introdcing the switch state fnction s i where s i for the condction mode of switch and s i 0 in the case of not condction mode lets s describe vales of voltages Sa, Sb, Sc as: S (6) (7) 50 Power Qality and Utilization, Jornal Vol. XI, No, 005

3 ( ) ( ) ( ) ( ) s sign i sign i Sin i i dc+ i dc for i { a,b,c} (8) The sign fnction defined as (9) is sed in the considerations presented in this paper. dla x 0 sign( x) 0 dla x < 0 (9) or dc+ dc, which is tre in the case of large and eqal vales of the capacitance C + and C, we can state that dc dc+ dc, then voltages given by eqation (8) may be described by the simplified eqation (0). dc s sign i (0) ( ) ( ) ( ) Sin i i Phase voltages referenced to the potential of the netral point of electric power tility () may be obtained as the differences of phase voltages referenced to the netral point of otpt voltage capacitive divider and zero seqence component voltage SO Nn, see figres and 4. Si Sin Nn () Taking into accont simplification (0) the zero seqence voltage of the rectifier system may be stated in the form (). Nn S 0 ( San + Sbn + Scn ) 3 ( a) ( ( a) ) ( b) ( ( b) ) 3 s sign i + s sign i + () dc + ( sc) ( sign( ic) ) In the end we obtain symmetrical rectifier voltage generator described by eqation (3) as a reslt of electronic switches fnctionality. The voltages Sa, Sb, Sc obtained have an implse shape time plots. ( b) ( ( b) ) ( sc) ( sign( ic) ) ( a) ( ( a) ) ( sc) ( sign( ic) ) ( sa) ( sign( i a) ) ( sb) ( sign( ib) ) s sign i.. dc Sa ( sa )( sign( ia ) ) 6 s sign i.. dc Sb ( sb )( sign( ib ) ) 6 + Sc ( sc )( sign( ic ) ) dc 6 (6) ig. 4. Scheme for symmetrical components analysis of AC/DC converter 3. BASE VOLTAGE SPACE VECTORS O VIENNA RECTI IER Analysing the eqation (3), at the inpt assmption of rectifier symmetry, yo come to the conclsion that there are six zones where crrent signs have different vales (4). The described relation is illstrated in the figre 5. The zone sectors will be enmerated by the digits from 0 to 5. ( ) ( ) ( ) 0 for sign i, sign i 0, sign i 0 for sign i, sign i, sign i 0 for sign i 0, sign i, sign i 0 SectI 3 for sign i 0, sign i, sign i ( 4) 4 for sign i 0, sign i 0, sign i 5 for sign i a, sign i b 0, sign ic In the stationary reference frame with co-ordinations a, b every zone occpies the angle of radian. or the given 3 crrent zone the electronic switches state vector s [s a, s b, s c ] has eight different vales. Each vale of power electronic switches state vector has a co-responding voltage space vector. This vector may be generated when crrent space vector lays in the given zone. The voltage space vectors are defined by transformation the eqation set (3) into the stationary reference frame a, b. This transformation is performed by the left-side mltiplying of the eqation (3) by the conversion matrix C abc ab. The end points of the six voltage space vectors create a reglar hexagon, the end point of two other voltage space vectors point the centre of this hexagon. While the crrent space vector is moving throgh the crrent sectors from 0 to 5, the voltage space vector follows the crrent throgh the co-responding hexagons which may be generated for this crrent zone. Voltage space vectors with the most modle V5 3 dc belong only to one sector, with middle modle V6, dc Grzegorz RADOMSKI: Analysis of Vienna Rectifier 5

4 to two one and with small modle V347 6,,, dc to three ones. The nll space vector V0 0 dc is realised by switching on the all three power electronic switches at the same time, independently of the crrent sector zone. The next convention for assigning voltage space vectors is sed in figre 5. The voltage space vector is represented by the for nmbers ( SectI;s a,s b,sc) ( SectI; s ). The first nmber refers to a crrent sector zone nmber for which voltage space vector is generated. This nmber is the inpt parameter of voltage space vector modlator. The next three nmbers with vales 0 or refer to the state of the power electronic switches and are otpt parameters of modlator algorithm. 4. CONTROL AREA O VIENNA RECTI IER The relative placing of the sectors of the crrent space vectors and the hexagons of basic voltage space vectors ( ig. 6) case that in the case of sinsoidal modlation of the voltage s the phase displacement angle between the first harmonic of crrent and the first harmonic of the AC side rectifier voltage mst be restricted to the range expressed by expression (5). ( ) s() + ε ϕ + ε (5) 6 6 The angle e is introdced to express the inflence of the high crrent harmonics on the activation of the actal crrent sector. In the next expressions the inflence of angle e will be neglected. or the phase displacement angle j s() satisfying expression (5) the maximm available modle of the voltage space vector (in case of sinsoidal modlation) is restricted by eqation (6). max s ( cosϕs() + 3 sinϕs() ) dc (6) There also exist a potential problem that may take place in the case of crrent space vector going across the bondary between two crrent sectors. This problem arises from the fact that change of sign of any phase crrent i i in sitation when the transistor of this phase is in off state (s i 0) case the co-responding change in the sign of AC side phase voltage, which is eqivalent to the change of the actal voltage space vector. In this case, we mst make appropriate changes in power electronic switch state vector to save the actal vale of the voltage space vector. This problem will indct some secondary problems in controlling Vienna rectifier. The change of crrent sign (sign(i j )) in the phase with condcting transistor (s j ) does not case any change in the voltage space vector vale. In this case no additional action is needed. To sm p, we can say that there will be no pro- ig. 5. Voltage base space vectors of Vienna rectifier 5 Power Qality and Utilization, Jornal Vol. XI, No, 005

5 blems if the voltage space vector belongs to the common part of two hexagons and has the same electronic switch state vector in both sectors. In the other cases the actal voltage space vector has no realisation in the next crrent sector or the procedre recalclating the power electronic state vector for generating actal voltage space vector in the new hexagon mst be performed. or the voltage space vectors enmerated like in fig. 6, while crrent space vector goes to the next crrent sector, only vectors V 34,, V 6, V 7 may be realised in the new crrent sector. In the case of vectors V,V 6 7 and vector V34, realisation with two transistors switched on no additional action is needed ( ig. 5). In the case of vector V34, realisation with one transistor switched on the recalclation procedre mst be performed. 5. DC SIDE OUTPUT CIRCUITS O VIENNA RECTI IER The three level AC side voltage Sin synthesis has an inflence on the rectifier DC side otpt circit strctre. igre 7 presents eqivalent scheme of the Vienna rectifier otpt circits. Two of the three crrents i dc+, i dc, i n are independent and may be represented in the DC otpt circits by the crrent sorces controlled by the state of power electronic switches. The third crrent is a compliment of the two others. The choice of the crrents represented by the crrent sorces is arbitrary. Eqations (7), (8), (9) describe crrents that spply the rectifier DC otpt circits. ig. 6. Hexagon of the voltage space vectors generated for one crrent sector in saia + sbib + scic (7) ( ) ( ) ( ) ( ) i + s sign i i + s sign i i + dc a a a b b b ( ) ( ) + s sign i i c c c (8) ( ) ( ) ( ( ) ( ) ( ) i s sign i i + dc a a a ( ) ( )( ( )) ) + s sign i i + s sign i i b b b c c c (9) ig. 7. Eqivalent scheme of the otpt circits of Vienna rectifier C+ dc+ 0 () ic idc i0 i i i () In the case of sinsoidal modlation the average vales of the i dc+ and i dc crrents are eqal to each other and eqal to the average vale of the load crrent i 0 (0). It implicates that the average vale of the i n crrent is zero. Hence average vales of the condenser voltages are eqal to each other. In the case of great vales of the condenser capacities it may be assmed that the instantaneos vales of the condenser voltages are nearly constant and eqal to each other. In this case the simplification (0) may be applied. Idc+ ( Avg) Idc ( Avg) I0( Avg ) In( Avg) 0 (0) The dynamic of the voltage of the otpt capacitors is described by eqations from () to (8). Grzegorz RADOMSKI: Analysis of Vienna Rectifier d dc+ in idc idc+ (3) in ic ic+ (4) i ddc+ C (5) C+ + C i C ddc C (6) dc ( i i ) (7) ( i i ) + dc+ 0 d dc 0 (8) C The rectifier DC otpt voltage is a sm of the otpt circits capacitor voltages (9). 53

6 of the above mathematical eqations describing the Vienna rectifier DC otpt fnctionality. 6. RESULTS O SIMULATION INVESTIGATION O VIENNA RECTI IER ig. 8. Vienna rectifier s DC otpt circits block scheme + (9) dc dc+ dc Generally the rectifier DC otpt crrent is a non-linear fnction of the rectifier DC otpt voltage (30). The parameters of the load circit R 0, L 0, E are the parameters of the fnction (30). i ( ) f (30) 0 dc The block scheme in figre 8 is a graphical representation Vienna rectifier simlation scheme for the TCAD program is presented in the fig. 9. Simlation was performed for the next conditions: U f 30V, f 50Hz, L s 85mH, R s 0.5W, S 3kVA, C + C 00m, R 0 43W, L 0 0H, E 0V, f PWM 0kHz. The time plots of the phase crrents, the phase voltage and the otpt reglator signal for different vales of phase displacement angle are presented in the figres from 0 to 5. The voltage U a is mltiplied by scale factor of 0,03. It can be see from the previos illstrations of the simlations that Vienna rectifier fnctions properly for the vales of the phase displacement angle j s() from the closely restricted range. or the AC side rectifier inpt (behind the inpt magnetic coil) this range is done by eqation (5). The phase displacement angle j () in the case of the inpt voltage of the overall converter (before the magnetic coil) differs from the vale of the angle j s() becase of the reactive power of inpt magnetic coil. or this reason, the rectifier displacement angle j () may have larger vale than. It mst have larger vale 6 than on the other hand. In the opposite case the crrent 6 shape will be distorted from sinsoidal. Vienna Rectifier I Voltage Space Vector Modlation Control with Otpt CD Voltage Balancing ig. 9. Simlation scheme of Vienna rectifier 54 Power Qality and Utilization, Jornal Vol. XI, No, 005

7 ig. 0. The time plots of phase crrents, phase voltage and reglator otpt signal for displacement angle of j () 0 ig. 3. The time plots of phase crrents, phase voltage and reglator otpt signal for displacement angle of ϕ () ig.. The time plots of phase crrents, phase voltage and reglator otpt signal for displacement angle of ϕ () ig. 4. The time plots of phase crrents, phase voltage and reglator otpt signal for displacement angle of ϕ () 3 ig.. The time plots of phase crrents, phase voltage and reglator otpt signal for displacement angle of ϕ () 6 ig. 5. The time plots of phase crrents, phase voltage and reglator otpt signal for displacement angle of 5 ϕ () 7. CONCLUSIONS The mathematical model of the Vienna rectifier is presented in the paper. The set of voltage space vectors of the Vienna rectifier is defined. Inpt crrent zones in the relation to signs of the phase crrents are defined. The relation between the active sbset of voltage space vectors and crrent zones are carried ot. Control area limitations are derived. The eqivalent scheme of the otpt circit is presented and described by eqations and related block scheme. Simlations of the rectifier system in the case of different inpt displacement power angle are presented. The system limitations carried ot in the theory are verified by the simlation reslts. Grzegorz RADOMSKI: Analysis of Vienna Rectifier. 55

8 SYMBOLS i,i,i,i,i,i a b c i j k instantaneos vales of the phase crrents, i C+, ic instantaneos vales of the DC otpt capacitor crrents, i dc+, i dc, in instantaneos vales of the DC rectifier otpt crrents, i 0 instantaneos vale of the otpt load crrent, s a,s b,s c,s i,s j,s k electronic valves state fnctions, s vector of electronic switches state fnctions, SectI nmber of the crrent sector, fa, fb, fc, fi, fj, fk instantaneos vales of the phase voltages of the electric power tility, Nn S 0 instantaneos vale of the zero seqence component voltage of the AC side converter phase voltages, San, Sbn, Scn, Sin instantaneos vales of the AC side converter phase voltages referenced to the centre point of the capacitive voltage divider, Sa, Sb, Sc, Si instantaneos vales of the AC side converter phase voltages referenced to the netral point of the electric power tility, s vector of the AC side converter phase voltages referenced to the netral point of the electric power tility, dc, dc+, dc instantaneos vales of the DC side otpt voltages, V,...,V 0 7 e ϕ () ϕ s() base voltage space vectors of the AC side rectifier otpt in the base crrent zone (SectI0), error angle, phase displacement angle between the first harmonic of phase crrent and phase voltage, phase displacement angle between the first harmonic of phase crrent and AC side rectifier voltage, L s indctance of the phase magnetic coil, C +, C DC otpt capacitors, L 0 load indctance, R 0 load resistance, E vale of the load voltage, f PWM modlation freqency. RE ERENCES. Kolar J.W., Zach.C.: A Novel Three-Phase Utility Interface Minimizing Line Crrent Harmonics of High-Power Telecommnications Rectifier Modles. Record of the 6 th IEEE International Telecommnications Energy Conference, Vancover, Canada, Oct. 30-Nov. 3, pp , Kolar J.W., Ertl H.: Stats of the Techniqes of Three- Phase Rectifier Systems with Low Effects on the Mains. st IN- TELEC, Copenhagen, Denmark, Jne 6 9, pp. No. 4, Miniböck J., Kolar J.W.: Comparative Theoretical and Experimental Evalation of Bridge Leg Topologies of a Three- Phase Three-Level Unity Power actor Rectifier. Proceedings of the IEEE Power Electronics Specialists Conference, Vancover, Canada, Jne 7-, 3, pp , Drofenik U., Kolar J.W.: Comparison of Not Synchronized Sawtooth Carrier and Synchronized Trianglar Carrier Phase Crrent Control for the VIENNA Rectifier I. ISIE 99, Bled, Slovenia, M i n i böck J., Strö gerer., Kolar J.W.: A Novel Concept for Mains Voltage Proportional Inpt Crrent Shaping of a VIENNA Rectifier Eliminating Controller Mltipliers. Proceedings of the IEEE 6 th IEEE Applied Power Electronics Conference, Anaheim, USA, March 4 8,, pp , Strögerer F., Miniböck J., Kolar J.W.: Implementation of a Novel Control Concept for Reliable Operation of a VIENNA Rectifier nder Heavily Unbalanced Mains Voltage Conditions. Proceedings of the IEEE Power Electronics Specialists Conference, Vancover, Canada, Jne 7, Malinowski M.: Sensorless Control Strategies for Three- Phase PWM Rectifiers. Warsaw University of Technology, Warsaw 00, (PhD thesis). 8. KaŸmierkowski M. P., Krishnan R., Blaabjerg.: Control in Power Electronics selected problems. Academic Press, Elsevier Science (USA) Strzelecki R., Spronowicz H.: Wspó³czynnik mocy w systemach zasilania pr¹d przemiennego i metody jego poprawy [Alternating Crrent Sply Systems and Methods of Its Improvement]. Oficyna Wydawnicza Politechniki Warszawskiej, Warszawa Tnia H., Winiarski B.: Energoelektronika. [Power electronics]. WNT, Warszawa Radomski G.: Analysis of Modified Diode Bridge Rectifier with Improved Power actor. Electrical Power Qality and Utilisation, 9,, Radomski G.: Experimental Investigations of Modified Diode Rectifier with Improved Power actor. Electrical Power Qality and Utilisation, 9,, 003. Grzegorz Radomski was born in Kielce, Poland, in 967. He received MSc and Ph.D. degrees from Technical University of Kielce in 99 and 00, respectively. Main fields of his scientific interest are rectifiers with improved power factor clean power converters and control systems of electric drives for hybrid electric vehicles. Address: Technical University of Kielce Al. Tysi¹clecia Pañstwa Polskiego Kielce, Poland ene@t.kielce.pl 56 Electrical Power Qality and Utilization, Jornal Vol. XI, No, 005