Conrol and Proecion Sraegies for Marix Converers Dr. Olaf Simon, Siemens AG, A&D SD E 6, Erlangen Manfred Bruckmann, Siemens AG, A&D SD E 6, Erlangen Conrol and Proecion Sraegies for Marix Converers To reach accepance of he marix converer opology in indusrial producs, i is necessary o offer an undersandable conrol and a secure operaion under all operaion condiions including faul siuaions. A undersandable conrol providing a secure bidirecional swich commuaion wihou precise addiional measuremens is explained. Furhermore, measures o preven over volages a he swiches in case of a urn off wihou he need of addiional componens in he power circui are presened. marix converer, space vecor conrol, over volage proecion, save commuaion. Inroducion Many drives applicaions require energy recovery o he grid for energy efficien operaion. Mos convenional converers wih diode bridges a he inpu can only use a resisor for energy dissipaion if braking of he drive is necessary and herefore do no offer an opimal energy saving soluion. A possible alernaive soluion is he marix converer ha direcly convers a hree phase ac sysem ino anoher hree phase ac sysem wih conrollable magniude and frequency. Alhough he marix converer is known for a quie long ime i hasn become an indusry based soluion ye. Neverheless, due o he advanageous feaures of he marix converer he Siemens AG has been ineresed o know if he marix converer is echnically realizable. Two main quesions ha prevened he usage of marix converers so far have been invesigaed. Firs, he conrol of he marix converer which is quie obscure, oday, and he problem of converer proecion and reliabiliy where known soluions are unsaisfacory for indusry producs. The conrol of he marix inverer has been improved and wo innovaive soluions concerning he over volage proecion on urn off or gae drive fauls and secure commuaion are presened.. Marix Converer The marix converer direcly connecs hree ac inpu phases wih hree ac oupu phases. Therefore nine bidirecional swiches are necessary which migh be realized
wih wo ani serial IGBT s in common collecor mode whereas each IGBT has one ani parallel diode (figure ). Each bidirecional swich S is labeled by wo indices, he firs indicaing he corresponding inpu phase and he second indicaing he corresponding oupu phase. inpu () () S S S Figure : Marix converer S S S ui () ii S i O S S () () () u O oupu (load) Because no shor circui is allowed beween wo inpu phases and no open circui is allowed beween wo oupu phase only one bu a leas one swich needs o be closed in each row which is called one oupu phase of he marix converer. Therefore, weny seven swich combinaions are allowed. To indicae a swich combinaion a group of hree numbers is used. The firs number indicaes which inpu phase is conneced o he firs oupu phase, he second which inpu phase is conneced o he second oupu phase and so on. For example he swich sae () indicaes ha swich S, S and S are conducing and all ohers are open.. Recifying and Invering ecor Modulaion (RIM) For calculaing he necessary swiching saes during one modulaion period o creae a desired average oupu volage wo main procedures are known. The firs procedure is based on a phase by phase calculaion and was presened by enurini and Alesina [ ]. The creaion of an oupu volage for each phase is very undersandable bu unforunaely he algorihm doesn give an undersandable mehod o achieve desired inpu currens. Addiionally, hird harmonics need o be added o he reference oupu volage o reach bes performance concerning he oupu volage range. The second mehod which has been presened by Huber, Borojevic and Burany [ ] is based on space vecor heory and reas he marix converer as one piece. They have presened an algorihm o calculae he swiching saes and corresponding swiching imes o creae a desired oupu volage o reach he full oupu volage range. Unforunaely hey only presened an algorihm bu no close mahemaical formulaion for he volage and curren ransfer funcions as done in paragraph..
olages and currens will be saed in space vecors defined by equaion ( ). ( x + a x + a x ) π wih a e j x = = ( ). Space ecor Modulaion of olage DC Link Converers Firs, he space vecor modulaion of a convenional volage dc link converer shall be explained as an inroducion. Figure shows he possible oupu volage space vecors of he dc link converer if hey are normalized by wo hird of he dc link volage U D. value range (-+-) Im (++-) uo U D Figure : Space vecors of he dc link volage converer ó (+--) (-++) ì 4 ö Re (--+) ú (+-+) 6 Any desired oupu volage u O can be described by he space vecor if he volage ransfer funcion saed in equaion ( ) is applied. ( ) u O = U D Because only he space vecors.. 6 and are applicable by differen swich combinaions, he desired space vecor needs o be creaed by pulse widh modulaion. The geomeric locaion of wihin he hexagon defines he imes per modulaion period.. 6 (modulaion indices) each corresponding swiching sae.. 6 has o be applied. = + + + 4 4 + + 6 ( ) 6 Usually only wo modulaion indices of.. 6 are unequal o zero. The remaining ime of he modulaion period needs o be filled wih he zero space vecors using he swiching saes (+++) or (---). Because he space vecor defines he modulaion indices, iself can be called he complex modulaion index for he oupu volage of he dc link converer. From he complex modulaion index all swiching imes and corresponding swiching saes can be derived.
complex modulaion index modulaion indices 4 6 swiching saes ( + ) ( + + ) ( + ) ( + + ) ( + ) ( + + ) Figure : Derivaion of swiching saes from he complex modulaion index. Recifying and invering vecor modulaion (RIM) of he marix converer The procedure of he dc link converer can be applied o he marix converer in an similar manner. Wih respec o he load he marix converer behaves like a volage source converer, whereas wih respec o he line i behaves like a curren source acive converer, because curren pulses are injeced ino he line filer. This principal behavior can be mirrored o he modulaion conrol algorihm. To creae a desired oupu volage he marix converer is reaed as a volage source converer and he same complex modulaion index as described in he previous paragraph is chosen o define he angle of he oupu volage space vecor. To define he inpu curren he marix converer is reaed as a curren source converer. Therefore, he complex modulaion index of a curren source converer called M III, defining he inpu curren angle, is chosen (figure 4) in he same manner as for volage source converers. To achieve uniy power facor he inpu curren needs o be in phase wih he inpu volage. Therefore, M III will be chosen in phase o he inpu volage, usually. This echnique is based on he volage and curren ransfer funcion of he marix converer ( 4 ), which can be derived from space vecor heory. Oupu volage ransfer funcion: u = Re{ M u } III I 44 4 4 U D * Inpu curren ransfer funcion: i I = M III { i O } * Re O 44 ID To define he ampliude of M III and he resul of he real par funcion Re{} is reaed as a ficiious dc link volage or dc link curren, respecively. Saring wih a chosen reference value of he ficiious dc link volage (U D ) M III can be calculaed wih he knowledge of he inpu volage u I. and choosing he angle of M III equal o he negaive angle of u I. Anoher angle may be used o creae reacive inpu curren. Aferwards wih he knowledge of he ficiious dc link volage and he desired oupu volage can be calculaed. The limis of are he same known from he volage dc link converer whereas he limis of M III can be aken from figure 4 and are similar o he complex modulaion index known from he dc curren source converer. ( 4 )
(4) value range of Im () () ó ì ö ú () Re () (4) value range of M III ì () Im ó ö ú M III () (6) Re Figure 4: alue ranges of he complex modulaion indices () (6) secor number () Aferwards he swiching imes and saes need o be calculaed. Each complex modulaion index defines a se of six modulaion indices for each acual reachable sae. There are wo adjacen saes used in each se. If each se is reaed as a vecor a marix produc * T M can be calculaed leading o a six by six seized modulaion index marix. Only four adjacen elemens are unequal o zero. komplex modulaion indizes M M i j b a modulaion indizes h c 4 6 / d e T M n-shape g f M u-shape M ( ) M swiching saes M M M c III M 4 M M 6 Figure : Derivaion of swiching saes from he complex modulaion indices of he marix converer
This modulaion index marix corresponds o he swiching sae marix of figure. Now, he necessary swiching saes and corresponding imes per modulaion period are known. During he remaining ime of he modulaion period he zero vecor corresponding o he swiching saes (), () or () needs o be used. A useful sequence of hese five necessary swiching saes ha minimizes he number of commuaions is given in figure. The example uses a n-shape sequence (a,b,...,j) which needs o be applied if he sum of secor numbers of and M III is even. Oherwise an u-shape has o be used. In he given example oupu phase and commuae from inpu phase o and from o and vice versa. Oupu phase has no commuaion. Therefore four forh and back commuaions are necessary wihin each modulaion period. The proposed RIM conrol has been implemened wihin an 7. kw marix converer prooype. Measuremens are shown in figure 6. 8 8 6 4 u_in_ i_in_ 6 4 u_ou_ - -4-6 -8 - - - - volage / ime / ms curren / A Figure 6: - - - - -4-6 -8 i_ou_ - - - - volage / ime / ms curren / A olage and Curren measuremen a he inpu (lef) and oupu (righ) of he 7. kw marix converer prooype - - - 4. Secure olage Conrolled Commuaion Looking a he example of he previous paragraph all oupu phases use a well defined sequence of inpu volages during he modulaion period which is u,u and u. This sequence is followed forh and back during each modulaion period. Therefore, no commuaion occurs beween he inpu volages u and u. This sequence is dependan of M III, only. If he inpu power facor is chosen o, he sequence is direcly dependen of he inpu volage. The occurring sequences over one period of he inpu volage are shown in figure 7. In secor of M III which is he secor of he above example we can see ha no commuaion happens beween he wo inpu volages which are close o each oher. This rule is valid for all secors. Thus he commuaion volage is always greaer han half of he magniude of he inpu volage. Therefore he commuaion volage sign for he occurring commuaions can be measured easy and secure or even derived from he inpu volage secor which is calculaed from he analog inpu volage measuremen. There is no necessiy o find he borders of he secors exacly because no change of he volage sign beween wo inpu volages occurs near he border. As a consequence for a commuaion process no exac measuremen of he volage sign is necessary. The analog volage measuremen which is used for he
oupu volage conrol in any case is sufficien if he proposed space vecor modulaion is applied. Therefore, he RIM is a differen way o implemen a save commuaion similar o he ideas given in [ ]. U U U inpu volage Figure 7: Commuaion sequence depending of he inpu volage 6 4 secor M III commuaion sequence. Over olage Proecion If all gae signals of he marix converer are urned off, which migh happen if he inpu volage fails e.g. due o a hree phase shor circui of he line, an exising oupu curren pah would be opened and a damage of he semiconducor devices would resul. To avoid his problem sae of he ar measures are clamp circuis o provide an alernaive pah for he oupu curren. Usually a diode bridge wih a capacior and a parallel resisor is used. This is quie disadvanageous because addiional componens mus be implemened in he power circui which is expensive and voluminous. An advanced soluion is presened here. Over volage proecion is realized by adding suppressor diodes (ransil diodes) beween he collecor and he gae of each IGBT [ 4 ]. In case of an occurring over volage he suppressor diode injecs a curren ino he Gae and urns he IGBT on wihou any furher acion a he gae driver, hus limiing he Collecor Emier volage approximaely o he blocking volage of he suppressor diodes. Figure 8: Gae drive circui of over volage proecion G C G E In his case he inducive energy of he oupu will be deposed wihin he silicon of he IGBT which is possible for low power converers. To avoid he sress of he IGBT during urn off varisors can be added a he oupu of he marix converer in
riangular configuraion. A simplified schemaic of his proecion mehod is given in figure 9. U sn R G D rann 6 U i T N U i U sn R G D rann 6 U i T N Figure 9: Simplified circui of he over volage proecion es wihin he marix converer U ran U ran U U i ran D ranp U ran D ranp U ran T P T P U sp R G 6 U ge U sp R G 6 U o i a r ar U o i U o i var i L U ar ar L L R L Figure shows measuremens afer a gae signal urn off demonsraing he feasibiliy of a simple urn off of he marix converer almos equivalen o a volage source converer. A he begin of he measuremen he bidirecional swiches and are urned on. Thus a posiive curren i L is flowing hrough boh swiches and he inducive load driven by he inpu volage U I. A = he gae signals of boh bidirecional swiches are urned off. Due o he inducive load curren he volage a he varisor U ar increases. The greaes volage reachable a he varisor is defined by Uar, max = Uran U ( ) I,max where U ran is he clamping volage of he suppressor diodes. The varisor mus be designed ha he greaes oupu curren can be carried a his volage. If U ran is designed o k he varisor volage migh reach up o.4 k a a 4 line. The blocking volage is almos symmerically disribued over boh bidirecional swiches (U,U ) and always limied o 8 in his case, by limiing he blocking volage of each IGBT wih he suppressor diodes Afer he gae signal urn off he load curren (I L ) commuaes from he swiches (I ) o he varsor (ar ) and he inducive energy is dissipaed and he oupu curren decreases o zero.
vol ag e / 8 6 4 - U var U,U cur ren / A I I L,I ar -4 - ime / µs - - ime / µs Figure : olages (lef) und currens (righ) a he swiches (,) and he varisor afer gae signal shu down 6. Summary The recifying and invering space vecor modulaion (RIM) o conrol he marix converer has been presened. I has been shown ha he marix converer behaves like a volage dc link converer a he load and like a curren dc link converer a he line. Procedures known from he dc link converers for modulaion can be ransferred o he marix converer. A simple pair of complex equaions describes his behavior of he marix converer and simplify undersanding, simulaion and realizaion. I has been shown ha a secure commuaion wihou a risk of a false inpu volage sign measuremen can be applied, hus achieving a large robusness of he marix converer necessary for indusry applicaions. Furhermore a snubberless soluion for over volage proecion has been presened. Avoiding he clamp circuis leads o a small and cheap soluion for a marix converer drive applicaion. Experimenal resuls prove he echnical progress made for he marix converer opology. References [ ] Alesina, A.; enurini, M. - Inrinsic ampliude limis and opimum design of 9- swiches direc PWM AC-AC converers - PESC 88 Record. 9h Annual IEEE Power Elecronics Specialiss Conference, -4 April 988, Kyoo, Japan [ ] Huber, L.; Borojevic, D. - Space vecor modulaed hree-phase o hree-phase marix converer wih inpu power facor correcion - IEEE Transacions on Indusry Applicaions, ol., No. 6, Nov/Dec 99 [ ] Ziegler, M.; Hofmann, W. - A new wo seps commuaion policy for low cos marix converers - PCIM Europe, Conference Proceedings, Nürnberg, Germany, [ 4 ] Mahlein, J; Braun, M; - A marix converer wihou diode clamped over-volage proecion - rd IPEMC; ; Beijing; China