Bond Graph based control of a three phase inverter with LC filter

Transcription

1 Bond Graph baed control of a three phae nverter wth LC flter Roberto Sanchez (,3) Frédérc Cola () Genevève Daphn-Tangy (3) Xaver Gllad () () LEP, (3) LAGIS, UMR CNRS 846, Ecole Centrale de Llle, BP 48, 5965 Vlleneve d Acq cedex, France. () ENSAM Llle, Art et Méter ParTech, 8 bd Lo XIV, Llle cedex, France. roberto_t@hotal.co, frederc.cola@ena.e, geneveve.daphn-tangy@ec-llle.fr, xaver.gllad@ec-llle.fr KEYWORDS Bond Graph, nverter. ABSTRACT In th paper propoed a odel of a three phae electrcal nverter wth a LC otpt flter n delta connecton ed n a renewable energy pply yte. The concept of nvere bond graph va bcaalty ed for the control law degn. The control law copared n laton wth another tradtonal one and valdated experentally. INTRODUCTION Power yte have been developed over the year to pply a varyng deand fro centralzed generaton orce of fol and nclear fel. Nowaday the renewable energy orce tart to play an portant role n the grd connecton, o the renewable orce need to be ntegrated nto the electrcal network va electronc power converter. The electronc power converter are not only ed for the connecton between a renewable energy orce and the network, they are alo ed n any ndtral applcaton. The lt phyc apect of ch yte jtfe the bond graph approach. The bond graph odel of a three phae nverter ha been addreed n everal reearch paper, a for exaple for the ot recent pblcaton: [Mezghann et al., 007; Belhadj, 006; González-Contrera et al., 007]. Each preented odel ha dfferent charactertc and ed for dfferent applcaton. They have n coon that they have been etablhed wth an electronc wtch (MTF) for odelng the cotaton cell of the converter; oreover the dfferent paper ed a PWM technqe for controllng the cotaton n thee eleent. Here we propoe to odel the three phae electrcal nverter wth only two electronc wtche [Gllad & Franco, 003] and to control t wthot ng PWM ethod. For degnng the control law, we e the nvere bond graph odel ng the bcaalty concept [Ngwopo et al, 996] A pecfc controller propoed cobnng the nvere odel and a reonant block. The otlne of th paper follow. In the econd ecton a preentaton of the global yte gven. In ecton 3 the bond graph odel of a three phae nverter wth LC flter propoed and oe caalty proble are dced. A two tage control law for the nverter gven n ecton 4. Secton 5 how the experental and laton relt. Fnally oe conclon are gven. PRESENTATION OF THE GLOBAL SYSTEM Fgre how the global chee of a renewable energy orce connected to a load. Th trctre the bac one and cold be analyzed at dfferent level of coplexty. The renewable energy orce cold be a panel of photovoltac cell, a ga trbne or a wnd trbne. It delver the prary power n the DC b whch wll be converted nto AC power va the power converter. The ntrodcton of a capactor on the DC b neceary n order to have a decoplng between the haronc generated by both converter. In th part of the yte, t neceary to ake the reglaton of voltage ( ) or crrent ( ). Fgre Global electrcal yte. Proceedng 3rd Eropean Conference on Modellng and Slaton ECMS Javer Otaend, Andrzej Bargela, Joé L Monte, L Mgel Doncel Pedrera (Edtor) ISBN: / ISBN: (CD)

2 The power electronc converter ght be condered a an aplfer. It copoed of three par of electronc wtche (Mofet, IGBT, etc.). Each par of wtche called a cotaton cell. In the flter part, the bac one known a a LR flter, whch cont only n one ndctance n ere wth a retance; t can be taken a a bae for ore coplex flter, only by addng ore coponent, for exaple LC one (fgre ) whch ha one ndctance and retance n ere wth a capactor n parallel. Each flter confgraton ha t own charactertc and ed for pecfc reqreent or analy fro the pont of vew of tablty and haronc analy. In fgre, the crrent n ndctance L, =,, 3, and the voltage of capactor C, C, C are controlled. Th, the behavor of th yte ay be alated to a voltage orce, contrary to the clacal LR flter trctre whch alated to a crrent orce. The an advantage wth ch a voltage orce n cae of connecton to the grd, becae t avod any dependence of the voltage n the C-eleent to the voltage grd. The grd wll be choen here a a pave load (R, L). MODEL OF THE INVERTER AND THE FILTER In th paper the odel of the nverter how p explctly only two of the three cotaton cell, the thrd one fxng the voltage reference. Only phae to phae voltage (, ) have to be condered for control [Gllad & Franco, 003]. The crrent 3 lnearly dependent of the two other ( and ). We are focng on the average behavor of the converter. Frtherore, we are not ntereted n the wtche theelve, bt on the pact of the converter on the LC flter. Th, we defne control gnal (, ) whch are defned a: = and = () The prary orce of the converter n the DC b repreented a a contant voltage orce ( ) by ang that t ha no varaton or flctaton. The three phae LC flter copoed of three ndctance wth ther aocated retance and three Delta connected capactor. The odel ade n two tage. Frtly, the three ndctance and ther aocated retance are taken nto conderaton; econdly the three capactor are added. The three phae nverter odel wth the LR flter hown fgre. The eleent I: L 3 ha a dervatve caalty becae of the 0-jncton placed between the bond, and 3, whch repreent the Krchhoff law ( of the crrent eqal to zero). Fgre Bond Graph odel of the three phae nverter wth a LR flter. Takng the bond graph of fgre a bae, the three C- eleent are added (fgre 3). Fgre 3 Bond Graph odel of the three phae nverter wth a LC flter. In fgre 3 the eleent C: C ha a dervatve caalty becae of the - jncton lnkng bond 4, 5 and 6, whch repreent the Krchhoff law ( of the voltage eqal to zero). The bond graph odel how p two caalty loop (followng effort and followng flow) n bond 4, 6, 4,, and two other n bond 5, 6, 0, 8 [Van Djk & Breedveld, 99], each of the wth a gan eqal to n one. Th, the odel can be lated. Thee caalty loop are ntrodced becae of the confgraton n Delta connecton of the capactor. In a tar connecton they wold not ext. The bond graph odel explctly pont, ot the phycal nght of the yte wth the two eleent n dervatve caalty (L 3 and C ).

3 Fnally, fgre 4 how the connecton of L-R eleent (load) for each branch. control law va the two cloed loop, for perforance prpoe. The calclaton of the control law n the odel ade n two tep, the frt one for the crrent and the next one for the voltage. The fgre 5 how p the nvere bond graph, whch allow dedcng the open loop crrent control law. The two crrent enor are nverted ltaneoly va bcaal bond and two djont bcaal path are drawn to the two dered nvere odel otpt correpondng to the two control gnal (, ), whch prove that the odel nvertble [Ngwopo et al, 996]. Fgre 4 Bond Graph odel wth the connecton of a load. Eleent L and R n bond 4, 5 and 6 are agned wth ntegral caalty. The for detector (Df:, Df:, De: c, De: c,) hown n fgre 4 are aocated wth the enor. CONTROL OF THE INVERTER AND THE FILTER In th ecton we propoe a new control trctre for the three phae converter, and we recall a clacal one whch wll be ed for coparon prpoe. Control va nvere odel and b-caalty bond graph The control law appled to the odel baed on the bcaalty bond graph, and degned fro the nvere bond graph. The noton of bcaalty wa ntrodced by Gawthrop [Gawthrop, 995], and can be ed to pont ot properte abot nvere dynac [Ngwopo et al, 996] and paraeter etaton [Ngwopo & Scavarda, 999]. For the forlaton of the nvere bond graph, t neceary to change the flow detector Df (ppoed deal) of the orgnal bond graph for orce (naed Se 0 Sf, becae they poe to the nvere odel zero effort-non nll flow), then propagate the bcaalty (n only one lne of power tranfer) fro th orce (SS) to the npt orce of the orgnal bond graph whch becoe a detector n the nvere bond graph [Ngwopo et al, 996]. Wth the nvere bond graph we degn the trctre of the control n open loop, whch then extended to a cloed loop control by fxng the dynac of the error. The three phae voltage have to be controlled. However, there are two dfferent way to proceed: - The frt way ae that the dynac n the I: L eleent are fater, copared wth the dynac n the C-eleent. Th only the voltage n C and C are controlled n cloed loop; the voltage n the dependent C eleent drectly related to the two other. - The other way conder the two loop n cacade, one for the crrent n the L and another one for the voltage n C -eleent. In th paper, we chooe to ake the Fgre 5 Invere bond graph for the calclaton of the crrent control law. The I-eleent are n dervatve caalty. Eqaton () derved fro the nvere bcaal bond graph of fgre 5, by ettng that the nercal vale of R and L are the ae for the 3 phae. It gve: = R + L d dt + c c () For etablhng the cloed loop control law, we et p the dynac of the error ( ε = ref ) n both expreon, a ε + k p ε = 0, where k p a contant gan to be fxed. The expreon () becoe (3) a d = + R L dt Fnally, = ε ref + c (3) ε ref c d ref ref R c L k p ref ref dt c (4) A for the deternaton of the crrent control, the voltage control law calclated; t provde the crrent reference for eqaton (4). Fgre 6 how the nvere

4 bond graph ed for the deternaton of the crrent reference. n + n + n + ωn 0 (7) In (7), the natral freqency (ω n ) adjted to the npt gnal freqency n order to obtan an nfnte open loop gan at th freqency [Lopez de Hereda et al., 006]. The calclaton of the paraeter n the reonant controller ade ng the pole placeent approach [Leclercq, 004]. On the other hand, the gan k p calclated for each phae by placng the pole of the polynoal denonator of the tranfer fncton n cloed loop derved fro Fgre 7. The dered perforance for the cloed loop odel are gven hereafter. Fgre 6 Invere Bond Graph for the voltage control law. For dervng eqaton (5) fro fgre 6, we follow the ae procedre a prevoly. Two bcaal djont path ext fro one SeSf 0 to one De 0 Df. The odel th nvertble. It lead to ref ref d = C dt d = C dt ( ) c c + r ( ) c c + r (5) Accordng to the fact that the 3 capactor are ppoed wth the ae vale capactance, th eqaton (6) how p the voltage control law for the converter. ref = ref d + cref cref c + C Ck r dt p cref cref c (6) r In eqaton (4) and (6), k p and k p are contant gan to be fxed. We chooe to change k p for a reonant controller gven eqaton (7) [Sato et al., 998; Gllad et al., 999]: Fgre 7 Block dagra for the crrent loop. In fgre 7, eleent Lˆ and Rˆ are etated vale of the actal yte paraeter. The controller block dagra of the coplete odel hown n fgre 8. It portant to notce that the trctre of the control law contan a feed-forward wth a dervatve acton on the reference. The reference gnal are nodal and they can be derved analytcally wthot any proble. The propoed control law copared by laton wth a clacal one decrbed hereafter. Control va Park tranforaton A clacal control approach cont n tranforng the nodal reference nto a contno reference by applyng a fraework change ng the Park tranforaton. By th way, a clacal proportonal ntegral controller can be ed wthot any proble, the reonant controller havng no eanng here becae of the contant vale of the reference gnal. A for the control prevoly preented, the control va Park tranforaton e the two loop cacade control trctre. Fgre 9 how the trctre of the controller. Fgre 8 Invere odel Controller block dagra n nodal reference.

5 In fgre 0, no change appear n the voltage. In the oppote, the fgre how the change n the flter crrent repone. Fgre 9 PI Controller block dagra n Park reference. Slaton and experental relt of the two yte are hown n next ecton. EXPERIMENTAL AND SIMULATION RESULTS a) Slaton The laton relt are obtaned wth the oftware 0S. The table how the nercal vale ed n the odel. Table Nercal paraeter for the yte and control. Syte L = 0. 55H R = 0. Ω C = μf = 645Ω Vale for nvere control law Lˆ = 0. 5H Rˆ = 0. Ω Cˆ = 0μF n = 0.07 n = 43. n = k p = Vale for Park control law k p =.45 T p =.46e 4 k p = T p =.e 3 For the two odel the reference are two nodal gnal wth 340 volt apltde and 50Hz freqency, dphaed of 0. The nercal vale of table have been calclated takng a te repone of 0 n the voltage loop and n the crrent one. Fgre 0 and how the laton repone n one phae for the two cloed loop odel, when one tep load change ade at te = The load balanced (ae L and R paraeter vale n the three phae). R r Fgre Slaton flter crrent relt. Fnally, n fgre preented the load crrent. Fgre Slaton: crrent n the load balanced load We obtan the ae repone n both control trctre becae the ae te repone ha been condered. Conder now the cae of an nbalanced load (thrd phae L and R paraeter vale dfferent fro the two other). Fgre 3 how the repone obtaned for the control law wth PI controller n Park reference, and fgre 4 for the repone fro the propoed nvere odel controller. Fgre 3 Slaton: voltage n C-eleent for an nbalanced load - PI controller n Park odel. Fgre 0 Slaton: voltage n one C-eleent balanced load

6 Fgre 4 Slaton voltage relt for an nbalanced load - nvere odel controller - nodal reference. It hown that the nvere odel control ha a better behavor copared to the PI one n the Park reference. Experental pleentaton (a hown hereafter) confr the robtne of the propoed new control law ver paraeter ncertante. b) Experentaton For the experental pleentaton, we ed a real te lator a hown fgre 5. Fgre 6 Three phae voltage repone for an nbalanced RL load. A expected, we can notce n the fgre 6 that the change n the load ha no pact on the voltage. In the oppote, the actal change can be een n the three load crrent (fgre 7). Fgre 7 Repone of the crrent for an nbalanced RL load tep change n load R vale at Fgre 5 Schee of the experental et p. The capactor voltage (v, v, v 3 ) are trantted to the hgh bandwdth power aplfer whch apple the voltage to the load. The crrent flowng nto the load are eared and ntrodced n the real te laton odel va an ADC (analogcal to dgtal converter). The effect of the load ntrodced n the real te lator a a three phaed crrent orce. For the experental relt, we condered the ae nercal vale a for the laton (table ). We how p the repone for the voltage and crrent for a LR ere load. The reference voltage 40 volt RMS and a three phae retve load of 645 Ω wth nbalanced ndctance (0.H, 0.07H and 0.08H). We appled one tep change n the 3 R vale (0 Ω) at econd. The three phae voltage are hown n fgre 6. The nbalancng of the load de to a dfferent vale of the ndctance n the phae appear explctly. In addton, for the flter crrent (fgre 8) we can notce a lttle change n the agntde at te The pertrbaton n the gnal are de to eareent noe. Fgre 8 Repone of the crrent n the flter, for an nbalanced RL load. The experental relt have been copared wth the laton relt and we fond that they are very lar.

7 CONCLUSIONS A new bond graph odel of a three phae nverter copled wth a LRC flter ha been propoed. Th odel keep the three branche of the AC crrent de and e only two eleent for the cotaton of the nverter. Moreover, we propoed a new trctre for the control law derved fro the nvere bond graph ng the concept of bcaal bond graph. It ha been hown throgh laton and experentaton that the propoed control trctre robt ver paraeter devaton. The ftre developent wll cont n connectng actve load to the yte, ch a an aynchrono achne. Sato Y., Ihzka T., Nez K., Kataoka T A new control trategy for voltage-type PWM rectfer to realze zero teady-tate control error n npt crrent. IEEE Tranacton on Indtry Applcaton, vol. 3, e 3, pp Van Djk J. and Breedveld P. 99. Slaton of yte odel contanng zero-order caal path I. Clafcaton of zero-order caal path. Jornal of the Frankln Inttte, 38 (5/6), pp ACKNOWLEDGEMENT The athor wold lke to thank the pport gven by the Conacyt, Mexco. REFERENCES Belhadj J Modelng, Control and Analy of Mlt- Machne Drve Syte ng Bond Graph Technqe. Jornal of Electrcal Syte -, pp 9-5. Gawthrop P Phycal Model-baed Control: A Bond Graph Approach. Jornal of the Frankln Inttte, vole 33B, No. 3, pp Gawthrop P Bcaal Bond Graph, (995) In Proceedng of the Internatonal Conference on Bond Graph Modelng and Slaton ICBGM 95, vol. 7, pp González-Contrera B.M., Rllán-Lara J.L., Vela-Valdé L.G., Clado S.A Modellng, Slaton and Falt Dagno of the Three-Phae Inverter Ung Bond Graph. IEEE Internatonal Sypo on Indtral Electronc. Gllad X., Vandecateele F., Wlverck M., Hater J.P New concept of corrector for the control of alternatve qantte. Proc. 8 th Eropean Conference on Power Electronc, EPE Laanne. Gllad X., Franco B A caal ethod for the odelng of tatc converter and the control degn. Applcaton to a Voltage Sorce Converter. 0 th Eropean Conference on Power Electronc and Applcaton, EPE 003, -4. Leclercq L Apport d tockage nertel aocé à de éolenne dan n réea électrqe en ve d arer le ervce ytèe. Thee USTL Llle. Lopez de Hereda A., Gaztañaga H., Etxeberra-Otad I., Bacha S., Gllad X Analy of Mlt-Reonant Crrent Control Strctre and Tnng Method. IEEE Indtral Electronc, IECOM 006, pp Mezghann D., Andol R., Ma A. and Daphn-Tangy G Bond graph odelng of a photovoltac yte feedng an ndcton otor-pp. Slaton Modellng Practce and Theory, pp Ngwopo R.F., Scavarda S., and Thoaet D Inveron of Lnear Te-nvarant SISO Syte Modelled by Bond Graph. Jornal of the Frankln Inttte, Vol. 333(B), No., pp Ngwopo R.F., Scarvarda S Denonng proble n yte degn ng bcaal bond graph. Slaton Practce and Theory, pp