Simulation investigation of the Z-source NPC inverter

Transcription

1 octoral school of energy- and geo-technology Janary 5 20, Kressaare, Estonia Simlation investigation of the Z-sorce NPC inverter Ryszard Strzelecki, Natalia Strzelecka Gdynia Maritime University, epartment of Ships Atomation rstrzele@am.gdynia.pl; nstrzele@am.gdynia.pl Abstract The paper describes constrction and the principles of activity, attribtes and potential of 3- phase Z-type inverters. The paper focses on the basic system and sggested 3-level system of a NPC type Z-inverter, which was elaborated by athors. Simplified theoretical analysis of both systems has been verified by detailed simlation research. In the last section of the article, the possibility to bild mltilevel Z-inverters based on iode Clamped typology is presented Keywords Power electronics, boost-bck converter, Z-inverter, NPC-inverter Introdction Alternating Voltage Inverters (Converters) spplied by low-voltage sorces C (ex. fel cell, photovoltaic cell) are most freqently realized on the basis of the three fndamental typologies: a) PWM voltage inverter with non-transformer converter C/C in the boost-converter system, b) PWM voltage inverter with transformed converter C/C in the boost-converter system, c) PWM crrent converter. However none of these soltions is claimed to be the best one and dominates over the other two. Search for new and better soltions contines and among them one finds Z-inverter [], which featres are very interesting. The paper aims to present work principles, theoretical analysis and selected reslts of simlation research on 3-phase NPC Z-type inverter system, which will confirm its seflness. Work principles of Z-type inverter Figre. presents a scheme of basic 3-phase Z- inverter. In distinction from VSI and CSI inverters, on C side of Z-inverter occrs a diode and a Z- sorce of X shape, composed of two capacitors C and C 2 and two chokes L and L 2. The diode prevents forbidden reversed crrent flow. For this reason application of Z-inverter is possible only where there is no necessity for energy retrn to U IN sorce, frther it is even forbidden in case of fel cell or photo-voltaic cell. It shold be marked that the same as diode fnction can be server by other power electronics systems inclding ex. diode rectifier or typical boost-converter. Sorce Z serves as power storage and garantees doble filtration grade at the inpt of the inverter, and therefore dmping crrent ripples and voltage plsation in the C circit. Conclding, reqirements for chokes and capacitors in Z-sorce are less restrictive than in VSI or CSI inverters. In a case where chokes L and L 2 have very low indctance ( 0), Z-sorce is created only from parallel connected capacitors C and C 2. Then Z- inverter simply becomes VSI system and condensers in C circit are the only storage for energy and at the same point are a cell for filtration of voltage plsation. Analogically when capacitors C and C 2 are of low capacity ( 0), Z-sorce is diminished to two chokes L and L 2 that are parallel connected, and Z-inverter system becomes CSI system. Chokes in C circit of CSI system and capacitors in C circit of VSI system mst be of greater indctance and capacity (their dimensions) than in case of Z- inverter. Fig.. Basic scheme of the 3-phase Z-inverter Typical 3-phase VSI system can assme eight allowed (permitted) states: six active states (while exchange of instantaneos power between the load and C circit) and two nll states (when the load is shorted by lower or pper grop of transistors). Whereas, 3-phase Z-inverter system (fig.) can assme nine permitted states, that is one more than in VSI system. Additional ninth state is the third nll state, occrring when the load is being shorted simltaneosly by lower and pper grop of transistors. This state, is defined as shoot-throgh state and may be generated in seven different ways, however eqivalent procedres: independently throgh every branch (3 procedres), simltaneosly throgh two of the branches (3 procedres), simltaneosly throgh all of the three branches ( procedre). The main, niqe characteristic of Z- inverter is that shoot-throgh state permits to rise otpt voltage, above the spply voltage U IN. 23

2 Figre 2. describes simple eqivalent schemes of Z- inverter, examined from the clap site of C, where a sorce d shapes inverter bridge V -V 6 (Fig.). In the shoot-throgh states (Fig.2b) a diode is polarized reversely and does not condct the inverter bridge inpt voltage d =0, and energy stored in capacitors C and C 2 is transferred to the chokes L and L 2. In non-shoot-throgh states, where every combination of the chokes V -V 6 that is allowed in VSI system is possible, the diode condcts, and the voltage d increases stepwise from 0 to its maximm d *. Since Z-sorce is symmetric circits (Fig.2), when C =C 2 and L =L 2 and low voltage plsation C and C2 dring implse period T, it can be recorded: = C = C 2 UC, L = L2 = L () where: U C mean vale of voltage in capacitors, L instantaneos voltage in chokes. Considering () and eqivalent schemes of Z- inverter (Fig.2), voltage d is calclated on the basis of following dependences: a) in shoot-throgh states (Fig.2b) in time T Z L C, f C = 2 U, = 0 (2) b) in non-shoot-throgh states (Fig.2c) in time T N L IN UC, f IN, d UC L = UC U IN d = 2 (3) where: f Z-sorce inpt voltage. a) general b) in shoot-throgh states c) in states non-shoot-throgh states Fig. 2. Eqivalent schemes of the Z-inverter If taken into consideration, that in a time period T=T Z +T N, in steady state overage voltage in chokes U L =0, then on the basis of (2) and (3) we obtain: 24 ( U U ) TZ UC + TN IN C U L = = 0 T and (4) TN UC d IN IN T T N Z where: =T Z /T - shoot-throgh coefficient, satisfying a condition <0,5. Similar procedre, on the basis (3) and (4) determines the vale d * of voltage d in nonshoot-throgh states: d C L IN (5) where: /(-2 )=T/(T N -T Z ) peak factor, determining the vale d * voltage U IN. The vale d * determines otpt voltage amplitde OUT(max) of Z-inverter. When applying sinsoidal PWM algorithm the amplitde eqals: OUT * d M U IN ( max) = M = (6) where: M modlation index, of maximm vale limited by ineqity M -, related to time T Z of shoot-throgh states As it reslts from the eqation (6), Z-inverter otpt voltage amplitde OUT(max), can be as well lower as higher than in typical VSI system with sinsoidal PWM, e.g. OUT(max) =M U IN /2. This possibility is acknowledged when looking at the 3 diagram of dependences: OUT( max) M K = = (7) U 2 2 IN in domain Ω= (0 M ; <0,5 -M) acceptable changes of and M, presented at the Figre 3. Fig. 3. Illstration of the dependence (7) 2 Reslts of simlation of the Z-inverter Simlation research of the system (Fig.) was condct in software package: PSIM Professional. To

3 control chokes V -V 6 algorithm of sinsoidal PWM was applied, modified by shoot-throgh states. The essence of this modification is explained on the Fig 4. Selected reslts of the research are presented on the Figres 5-8. Elementary parameters of the system that were assmed in the research are presented in Table. Any changes of these parameters are described by eqivalent diagrams. Table. Parameters of researched Z-inverter (Fig.) Spply C U IN 50V Z-sorce Chokes L, L 2 0,2 mh Capacitors C, C 2 0,2mF Otpt Chokes L f 00 µh filter Capacitors C f 50 µf Load (resistance) R 0 6 Ω PWM freqency carrier /T 0 khz Condct simlation research of Z-inverter confirmed theoretical dependence (7) with great accracy. Small terror did not depended on assmed vales of loads R 0 and parameters L =L 2 and C =C 2 of Z- sorce, and a harmonic distortion coefficient in inpt voltage OUT, that was conted each time, have never crossed 3%. The research also showed that transitions in Z-inverter, reslting from changes of load and factors M and (in open control system) are relatively fast. Frthermore, they inspired the athor to elaborate and condct preliminary simlation research of 3-level Z-NPC inverter. A premise to do the research was that it is impeded to increase of otpt voltage amplitde of Z-inverter over 0-times vale of spply voltage U IN. Fig. 6. Selected crrents and voltages before and after change of coefficient =0,48 0,47 for the time t=0 ms (M=0,48) Fig. 4. Simple Control algorithms implementing in simlation models of the Z-inverter Fig. 5. Selected voltages and crrents in case of changes of resistance load R 0 (M==0,48) Fig. 7. Voltages and crrents at the characteristic points of the system (Fig.) in the time t m marked at the Fig.6 25

4 where: =T Z /T and =T Z /T - short-trogh coefficients of pper and lower branches. a) b) Fig. 8. The crrents and voltages like on the Fig.5 in case of stepwise changes of the factors and M 3 Z-NPC Inverter Proposed system of 3-level Z-NPC inverter [2] is presented on the Figre 9. Instead of two voltage sorces or two capacitors with common point, as it applies to typical systems VSI-NPC [3], in this inverter two Z-sorces with inpt voltage U IN and U IN2 withot common point were applies. This allows joint and separated voltage d and d2 control. The possibility is explained by eqivalent diagrams of Z-NPC inverter in shoot-throgh states, showed at the Figre 0. b2) b3) Fig. 9. Proposed system of 3-level Z-NPC inverter In the state of short-trogh pper branches (Fig.0-b), transistors V -V 6 & V -V 3 are attached, however in states of short-trogh lower branches (Fig.0-b2) transistors V - V 6 & V 4 -V 6 (Fig.9). These two states with the dration time T Z and T Z in time period T (Fig.), case averages voltages increase U C and U d,, and maximal d * p to vale: a) on otpt of pper Z -sorce UC d IN d IN (8) b) on otpt o lower Z 2 -sorce U C 26 d 2 IN2 d 2 IN (9) Fig. 0. Eqivalent schemes of the Z-NPC inverter: a) general, b) in states of shoot-throgh : pper branches (b), lower branches (b2) and fll (b3) Occrring physical process and following dedced dependences (8) and (9), are analogical to those in a basic system of Z-converter (Fig.) and the eqations (4) and (5). It is also nchanged by fll short-trogh state (Fig.0-b3), occrring when short circit of pper and bottom branched happen simltaneosly at the time T Z - T Z (Fig.). Fig.. Exemplary schedle of branches shorttrogh in T period Considering Z-NPC inverter, which is spplied by a sorce of different voltage U IN U IN2 and controlled on the basis of sinsoidal PWM, and taking into accont (8) and (9), we can determine inpt voltage peak-to-peak vale on the basis of the following dependence:

5 OUT U IN U IN 2 ( p p) = M + M (0) where: M i M modlation index for positive and negative half of otpt voltage. Hence, if the following condition is not flfilled: U IN U IN 2 M = M () then the voltage com between reference potential V 0 (Fig.9) and a common point of symmetric 3-phase load (e.g. C-offset): com = V 0 d M π 2 2 d 2 M 2 2 (2) is different than zero. Then, in otpt voltage occr additional distortion, mainly related to even harmonics. Meeting condition (), that eliminates inpt voltage distortion and C-offset, is possible throgh: a) selection of different modlation index s M and M for the positive and negative half; b) selection of different short-trogh coefficient and for pper and bottom branches. In the first case, where = and the following ratio remains valid: M M = U IN 2 U IN (3) voltage amplitde OUT can be varied within the limits: 0 OUT( max) min U IN, U IN 2 ( ) Whereas, in the second case, where M=M and the following ratio remains valid: ( 2 ) ( 2 ) IN 2 U IN (4) the amplitde can vary within the limits: U IN U IN 2 0 OUT( max) = ( ) ( ' ) where maximal voltage in transistors V -V 6 & V -V 6 (Fig.9) are eqal. Evidently it is the possibility to joint both procedres to meet condition (). 4 Research reslts of the Z-NPC inverter Parameters for the simlated Z-NPC system were assmed analogically to the Z-type inverter (Tab.). Evental changes of the parameter are marked at the Figres 3-7, presenting the most important simlation research reslts, condcted in the software package PSIM Professional. The research confirmed correct work of Z-NPC inverter (Fig.9) with the system s power spply from sorces for eqal as well as different voltage U IN and U IN2 (Fig.2-Fig.5). In each case, when U IN =U IN2, content of harmonics in voltage OUT is like in basic Z-inverter system (Fig.). Similarly rn also transitory processes (Fig.2, Fig.5). Perceptible are only somewhat greater low-freqency voltage and crrent plsations in Z-sorces of Z-NPC inverter (compare Figre 5, and Figre 2). This is also characteristic, however to less extent, of typical NPC-VSI system with capacitor spply voltage divider. When spplying Z-NPC system from sorces with voltage U IN U IN2, selection of short-trogh coefficients pper branches and bottom branches satisfy relation (4) appeared to be a effective method to eliminate otpt voltage distortion OUT and C-offset (Fig.3-Fig.5). Sch a coefficients selection, as expected, cased also maximal voltages compensation in the transistors V -V 6 i V -V 6 and otpt voltage implse amplitde Fa directly at the inverter terminals (Fig.3, Fig.6). Fig. 2. Selected voltages and crrents in Z-NPC inverter after enclosre and after change of short-trogh coefficient =0,48 0,47 at the moment t=0 ms (M=0,48) 5 Conclsions As one concldes from the article, Z-sorce cold be sccessflly applied in mltilevel inverters realized on the basis of typology iode Clamped. As example serves the system presented at the Figre 7. It is necessary to notice that when inverters with Z sorces are spplied by diode rectifiers from alternating voltage grid, then there is no need to se neither capacity filters nor inpt diodes of inverters. Presented reslts encorage to contine research on systems with Z-sorces, especially in practical 27

6 aspect. The athors wold like to draw attention to the reqirements for accracy of realized controllers, related to sensibility of described systems to changes of short-trogh coefficients. a) eqal coefficients = 2 b) after 2 coefficients correction on the basis (4) Fig. 6. The voltage implses on inpt and otpt terminals of a Z-NPC inverter in the case presented at figre 5c Fig. 3. The otpt phase voltage, C-offset voltage and otpt voltage Fa in the inverter terminals, in case of differentiated voltages U IN U IN2 a) b) c) Fig. 4. The otpt phase voltages and C-offset in cases: a) eqal U IN =U IN2 and = 2 ; b) differentiated U IN U IN2 and eqal = 2 ; c) differentiated U IN U IN2 and after correction of coefficient 2 on the basis of dependence (4) Fig level Z-inverter system of C type References. Peng F. Z.: Z-Sorce Inverter, IEEE Trans. on Indstry Applications, No.2 (2003), p Strzelecki R., et al.: Trójpoziomowy falownik typ Z-NPC, Przegląd Elektrotechniczny, No.0 (2006), p Rodrigez J., Jih-Sheng L., Peng F. Z., Mltilevel inverters: a srvey of topologies, controls, and applications. IEEE Trans. on Indstrial Electronics, No.4 (2002), p Science Work fonded from the research resorces in of Polish Ministry of Science Higher Edcation as a project Nr 3 T0A Fig. 5. The corses of otpt phase voltages and C-offset voltage, in case of stepwise changes of work conditions for Z-NPC inverter selected on the figres 4 a,b,c 28