INVESTIGATION BY SIMULATION OF MOTOR AND GENERATOR MATHEMATICAL AL MODELS FOR AN ELECTRICALLY EXCITED SYNCHRONOUS MACHINE RUNNING IN GENERATOR MODE

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1 INVESTIGATION BY SIMULATION OF MOTOR AND GENERATOR MATHEMATICAL AL MODELS FOR AN ELECTRICALLY EXCITED SYNCHRONOUS MACHINE RUNNING IN GENERATOR MODE Eng. Dan Claudiu RUS, Pof. Eng. Maia IMECS PhD, Lctu Eng. Ioan Iov INCZE PhD, Lctu Eng. Csaba SZABO PhD Dpatmnt of Elctical Machins and Divs, Faculty of Elctical Engining, Tchnical Univsity of Cluj-Napoca, Romania REZUMAT. În luca sunt pzntat cuaţiil gnal al maşinii sincon cu înfăşua d xcitaţi i, din ca sunt ddus modlul matmatic d moto, spctiv d gnato în vda simulăii ii în gim d gnato.. Gnatoul sincon st antnat d căt un moto d inducţi i cu oto în colivi c şi contolat în cuplu şi dbitază ază p o zistnţă tifazată pasivă zistiv-inducti inductivă. Sunt pzntat zultatl simulăii în cazul contolului scala al gnatoului în ca glaa amplitudinii tnsiunii, spctiv a fcvnţi i statoic sunt alizat indpndnt în bucl spaat. Cuvint chi: gnato sincon, modl matmatic d moto şi d gnato, simula, contol scala. ABSTRACT. Th pap psnts th mathmatical dsciption of an lctically xcitd synchonous machin using gnato and moto mathmatical modls. In simulation th synchonous machin is unning in gnato mod,, it is divn by a squil-cag induction moto and gnats ngy on a passiv sistiv-inductiv inductiv load. Simulation sults a psntd fo a scala contolld ld synchonous gnato, in which th stato-voltag amplitud and fquncy of th gnato a indpndntly contolld in two spaatd loops. Kywods: synchonous gnato, moto and gnato mathmatical modl, input and output vaiabls. 1. INTRODUCTION Th lctically xcitd synchonous machin (EE- SyM) is th main suppli with lctical ngy of th national pow gid. Th contol of th synchonous gnatos fding th AC lin is indispnsabl to maintain th fquncy and voltag constant at thi atd valus. Th opation of th pow ntwok is basd on this condition as wll as on th optimum unning of th consums. Considing that th total activ and activ pow consumd in th ntwok is fluctuating, cafully dsignd contol statgis must b applid. Although, significant advancs w mad in th fild of pow switching dvics, pmannt magnt capabilitis and ddicatd pocssing units, th usag of pmannt magnt synchonous gnatos (PM-SyG) in conjunction with back-to-back fquncy convts is still limitd by th low pow lvl at which this dvics can opat (MW p unit) [1]. Considing that th pic of th magntic matial is high and still ising du to th vaious factos, th EE- SyM bcoms a solution vn in isolatd low pow gnation applications such as isolatd and inaccssibl communitis, mot sach facilitis o mot vacation houss. Th main advantag of th EE-SyM is that it can opat at any abitay pow facto such as unity pow facto o lading pow facto du to th indpndnt contol of th lctical xcitation. Considing this chaactistic, th EE-SyM is usd fo activ pow gnation in od to balanc th gid. Ths advantags howv a balancd by a sis of sious disadvantags. Th EE-SyM, in spons to vn small load paks, tnds to poduc oscillations which a only pooly dampd. Analyzing th fundamntal poptis of th EE-SyM, a div unit which povids a stady diving toqu at fixd spd must b usd to ovcom this poblm. In nwabl ngy applications, such as wind tubins, coupling an EE-SyM dictly to a fixdfquncy gid, it focs th gnato to un at constant spd. On th oth hand, th wind tubin oto wants to follow th vaiations in wind spd. In btwn th is th mchanical div tain of th wind tubin. High dynamic loads on th mchanical componnts and sv fluctuations in th lctical pow output a th consquncs. Rduction of th dynamic loads can only Bultinul AGIR n. 4/2012 octombi-dcmbi 1 67

2 CONFERINŢA NATIONAL NAŢIONALĂ CONFERENCE DE ACŢIONĂRI OF ELECTRICAL ELECTRICE, DRIVES diţia XVI, CNAE SUCEAVA b achivd by allowing th wind oto spd a dg of fdom fom th gid fquncy. This can b achivd by using a continuous vaiabl tansmission (CVT) gabox [2].Th mathmatical modling and simulation of lctic gnatos hav a ky ol in dvloping nw and impovd contol statgis, considing th mo and mo stingnt cods applid in pow gnation and tansmission. Th synchonous machin with salint pols and damp windings givs th most gnal mathmatical modl (MaMo), fom which paticula modls may b obtaind, such as in cas of th non-salint pol machins o in th cas of th machins without damp windings. In this pap, th MaMo of th salint pol EE-SyM with damp windings without taking into account th satuation is considd [3]. Using th sam simulation conditions, a compaison btwn th moto MaMo (M-MaMo) and th gnato MaMo (G-MaMo) of th EE-SyM bhavio is psntd. Th classical contol pincipl of th EE-SyM unning in gnato mod is wll known: th fquncy and amplitud of th stato voltag a contolld by adjusting th activ and activ pow of th gnato. Th MaMo of th nti stup is considd which includ th squilcag induction moto (SqC-IM), its fquncy convt, th xcitation chopp and th load. 2. MATHEMATICAL MODELS In a synchonous machin th avag spd is dictly popotional to th fquncy of th AC supply to that it is connctd. Th MaMo of th EE-SyM basd on th two action thoy and on th spac-phaso thoy is valid fo both, stady stat and dynamic opation [3], [4]. Considing th oto quantitis fd to th stato and th d-q fnc fam, wh is th lctical angl of th oto position, diffntial quations with constant paamts a obtaind, which dscib th bhavio of th machin und any opation conditions. Th G-MaMo is dscibd by th following voltag-, flux- and motion quations, and lctomagntic toqu xpssion [4]: sd usd = Rsisd + ωψ sq ; (1) sq u sq = Rsisq + + ωψ sd ; (2) u = Ri + = 0; (3) Aq uaq = RAq + = 0; (4) u = Ri ; (5) + Ψ L i L ( i i ); = + + (6) sd sq sd sd = Lsqisq md Ψ + L (7) ; mqiaq Ψ = L i + L i + i ); (8) md ( sd Ψ = L i + L i ; (9) Aq Aq Aq mq sq Ψ = L i + L i + i ); (10) md ( sd SM 3 m = z p ( Ψ sd isq Ψ sq isd ); (11) 2 dω z p IM SM = ( m + m ), (12) Jtot wh R s, R, R Aq and R a th stato, dict damp, quadatu damp and xcitation sistancs and L sd, L sq, L, L Aq and L dict and quadatu stato, dict and quadatu damp and xcitation inductancs; L md and L mq mutual dict and quadatu stato inductancs; i sd and i sq dict and quadatu stato cunts; i and i Aq dict and quadatu damp cunts; i xcitation cunt; Ψ sd and Ψ sq dict and quadatu stato fluxs; Ψ and Ψ Aq dict and quadatu damp fluxs; Ψ xcitation cicuit sultant flux; u sd and u sq dict and quadatu stato voltag; u xcitation voltag; ω lctical angula spd of th oto; z p numb of pol pais; m SM and m IM lctomagntic toqu of th EE-SyG and SqC-IM. Th motion quation is a common mchanical on which uss th toqus of th EE-SyG and SqC-IM and th common oto spd. In this cas th angula spd is an input vaiabl fo th MaMo of th both lctical machins. In th cas of th G-MaMo th input vaiabls a i sd, i sq, u and ω and th output ons a u sd, u sq and m SM. It can b obsvd that th MaMo consists of a systm of lvn quations with th sam numb of unknown vaiabls. Considing (8) and (10) th xpssions of i and i a obtaind, xpssd with th Ψ and Ψ. In th nxt stp w plac ths xpssions in (3) and (5) and obtain though som basic mathmatical manipulations a systm of two diffntial quations with Ψ and Ψ unknown vaiabls. Futhmo using (9) and (4) with a simila appoach Ψ Aq and i Aq a computd. By gouping (1), (2), (6) and (7) and considing th sam pocdu, u sd 2 68

INVESTIGATION BY SIMULATION OF MOTOR AND GENERATOR MATHEMATICAL MODELS FOR AN ELECTRICALLY EXCITED SYNCHRONOUS MACHINE RUNNING IN GENERATOR MODE and u sq a found.

3 INVESTIGATION BY SIMULATION OF MOTOR AND GENERATOR MATHEMATICAL MODELS FOR AN ELECTRICALLY EXCITED SYNCHRONOUS MACHINE RUNNING IN GENERATOR MODE and u sq a found. In th last stp, considing (11) th lctomagntic toqu is computd. Fo th M-MaMo almost th sam systm of quations is usd, th diffnc appas only in quations (1), (2) and (12), which a placd by: u sd = Rsisd + Ψ ; (13) sd ω sq sq u uq = Rsisq + + ωψ sd ; (14) dω z p IM SM = ( m m ). (15) Jtot In this cas u sd, u sq, u and ω a considd inputs vaiabls, whil i sd,i sq and m will b computd by th modl. Using simila mathmatical manipulations as in pvious cas th systm of quations is computd. Th simplifid block diagams of th modls a psntd in Fig. 1 and Fig. 2. basd on th gnal quations [5], and it is dscibd by th following stat-spac quations: s Rs Rs = u s Ψ s + Ψ ; (16) σ L σ (1 + σ ) L R = + j ω σ L s Ψ R + σ (1 + σ ) L s s Ψ ; (17) 3 Lm * m Im = z p Ψ s Ψ, (18) 2 σ Ls L wh Im indicats th imaginay pat, * th complx conjugat valu, and R s and R stato and oto sistancs; L s, L and L m stato, oto and mutual inductancs; σ s, σ, σ stato-, oto- and sultant lakag cofficints; ω lctical angula spd of th oto; z p numb of pol-pais; m lctomagntic toqu; u s stato-voltag phaso; Ψ s, Ψ stato- and oto-flux spac phasos. Th R-L load is modld as a fist od lag. 3. CONTROL STRATEGY Fig. 1. Simplifid block diagam alizd with gnato MaMo fo simulation of th EE-SyM in gnato opation. In od to validat th psntd modls, a scala contol pocdu was usd in od to contol th EE-SyM stato-voltag in both cass. Two indpndnt contol loops w dsignd: on fo th fquncy contol and th oth fo contol th amplitud of th stato voltag. In Fig. 3 th PI stato-voltag-contoll gnats th fnc of th xcitation voltag which in this cas commands an idal DC-to-DC chopp, whil th stato-fquncy contoll gnats th fnc toqu fo th contol of th SqC-IM. In addition, an indict fild-ointd contol with spacvcto puls-wih modulation and an idal fquncy convt (with idal switching dvics) is usd to poply contol th SqC-IM, as is shown in Fig. 3. Fig. 2. Simplifid block diagam alizd with moto MaMo fo simulation of th EE-SyM in gnato opation. Th flux-mamo of th SqC-IM using spac phasos and fixd stato-ointd coodinats was dducd Fig. 3. Scala contol statgy of th EE-SyM unning in gnato mod. Bultinul AGIR n. 4/2012 octombi-dcmbi 3 69

CONFERINŢA NATIONAL NAŢIONALĂ CONFERENCE DE ACŢIONĂRI OF ELECTRICAL ELECTRICE, DRIVES diţia XVI, CNAE SUCEAVA 2012-2012 4.

Each modl was submittd to th sam simulation conditions in od to mphasiz btt th bhavio of th systm.

4 CONFERINŢA NATIONAL NAŢIONALĂ CONFERENCE DE ACŢIONĂRI OF ELECTRICAL ELECTRICE, DRIVES diţia XVI, CNAE SUCEAVA SIMULATIONS In od to analyz th abov dscibd modling and contol mthods, simulations w pfomd using MATLAB-Simulink nvionmnt. Each modl was submittd to th sam simulation conditions in od to mphasiz btt th bhavio of th systm. Th modls includd two majo sub-systms: in th fist on th contol stuctu and th SV-PWM block [6] w modld using disct sampl tim ( s), whil th hadwa componnts of th xpimntal stup (PWM-modulato, VSC, chopp, EE-SyM, SqC- IM, R-L load) w simulatd in continuous sampl tim. With this appoach th simulation modl has a simila bhavio to a al xpimntal stup. Th simulation modls w dvlopd fo a 1.5 kw, 1415 pm SqC-IM and 1 kw 1500 pm EE-SyM (limitd by th laboatoy tst bnch). Simulation stats with 230 V fnc fo th voltag amplitud and 1500 pm (50 Hz) fquncy fnc. Aft 1 s th amplitud fnc is st to 200 V, and at 2 s simulation tim th fquncy fnc is st to 1200 pm (40 Hz). Fig. 6. Excitation voltag simulatd with th G- and M-MaMo, spctivly. In Fig. 4-6 it can b obsvd that th systm has good static and tansint bhavio, and also, th a small diffncs btwn th two appoachs dspit th idntical conditions in which th simulations w mad. A caus fo ths diffncs could b th diffnt mathmatical computation stps applid in th two cass. A high sttling tim in both cass is obsvd but that is not an issu fo th goals of this pap. Fig. 4. Stp spons on th contol loop of th stato-voltag amplitud simulatd with th G- and M-MaMo, spctivly. Fig. 5. Stp spons on th contol loop of th stato-fquncy simulatd with th G- and M-MaMo, spctivly. Fig. 7. Spac-phaso diagam of th stato voltag of th EE-SyM simulatd with th G- and M-MaMo, spctivly. 4 70

5 INVESTIGATION BY SIMULATION OF MOTOR AND GENERATOR MATHEMATICAL MODELS FOR AN ELECTRICALLY EXCITED SYNCHRONOUS MACHINE RUNNING IN GENERATOR MODE 5. CONCLUSIONS In this pap th mathmatical dsciption of an lctically xcitd synchonous machin using gnato and moto mathmatical modls is psntd. Th modls w validatd by simulations and good sults w obtaind fo tansint and stady stat opation. Simulation sults a psntd fo a scala contol of th synchonous gnato, in which th stato-voltag amplitud and fquncy of th gnato a indpndntly contolld. In od to impov th stp spons of th systm a vcto-contol statgy may b usd fo th lctically xcitd synchonous gnato [7]. ACKNOWLEDGMENT This pap was suppotd by th pojct ntitld "Doctoal Studis in Engining Scincs fo Dvloping th Knowldg Basd Socity-SIDOC contact no. POSDRU/88/1.5/S/60078, pojct co-fundd fom th Euopan Social Fund though Sctoial Opational Pogam Human Rsoucs BIBLIOGRAPHY Fig. 8. Spac-phaso diagam of th stato cunt of th SqC-IM simulatd with th G- and M-MaMo, spctivly. Fig. 7 and Fig. 8 show th spac-phaso diagam fo th stato voltag of th EE-SyG and stato cunt of th SqC-IM. Both modls bhav wll in tansint and stady stat, but small diffncs may b obsvd dspit th idntical conditions in which th simulations w pfomd. [1] Chamund, D. J., Coulbck, L., Nwcomb, D. R., Waind, P. R., High pow dnsity IGBT modul fo high liability applications. IEEE 6th Intnational Pow Elctonics and Motion Contol Confnc IPEMC '09, May, 2009, Wuhan, China, pp , [2] Hau, E., Wind Tubins: Fundamntals, Tchnologis, Application, Economics. Sping, Blin, 2006, ISBN [3] Klmn, A., Imcs, Maia, Vcto Contol of AC Divs. Volum 2: Vcto contol of Synchonous Machin Divs, Ecitu Publish, Budapst, 1993, ISBN [4] Bolda, I., Synchounous Gnatos. Boca Raton, FL, CRC Pss, Taylo & Fancis Goup, [5] Klmn, A., Imcs, Maia, Vcto Contol of AC Divs, Volum 1: Vcto Contol of Induction Machin Divs, OMIKK-Publish, Budapst, 1991, ISBN [6] Rus, D. C., Pda, N. S., Incz, I. I., Imcs, Maia, Szabó, Cs., Compaativ analysis of PWM tchniqus: Simulation and DSP implmntation. IEEE Intnational Confnc on Automation Quality and Tsting Robotics (AQTR), May, 2010, Cluj-Napoca, Romania, Vol. 3, pp [7] Klmn, A., Imcs, Maia, Mtodă şi sistm d gla automată vctoială a putii activ şi activ a gnatoalo sincon, Invntion Patnt, RO, , Bultinul AGIR n. 4/2012 octombi-dcmbi 5 71

6 CONFERINŢA NATIONAL NAŢIONALĂ CONFERENCE DE ACŢIONĂRI OF ELECTRICAL ELECTRICE, DRIVES diţia XVI, CNAE SUCEAVA About th authos Eng. Dan Claudiu RUS, PhD studnt, Tchnical Univsity of Cluj-Napoca, Faculty of Elctical Engining, Dpatmnt of Elctical Machins and Divs, Mmoandumului St. 28, Cluj-Napoca, Romania Rcivd th Dipl. Eng. dg in Elctical Engining fom Tchnical Univsity of Cluj-Napoca, Romania in 2008, wh h is cuntly woking towad th PhD dg in Elctical Engining. H was PhD gust studnt fo 6 months at th Institut of Engy Tchnology, Aalbog Univsity, Dnmak in His sach intsts includ: high pfomanc AC div contol, contol of synchonous gnatos, discontinuous PWM statgis fo pow lctonic convts. Pofsso Maia IMECS, Dipl. Eng., PhD, Tchnical Univsity of Cluj-Napoca, Faculty of Elctical Engining, Dpatmnt of Elctical Machins and Divs, Mmoandumului St. 28, Cluj-Napoca, Romania. maia.imcs@md.utcluj.o Gaduatd at th Polytchnical Institut of Cluj-Napoca, Elctotchnical Faculty in 1970, pomotion chif and Rcto s Awad fo th Diploma Wok. Industial xpinc: sach in micolctonics at th I.P.R.S. Bănasa Buchast, dsigning ngin fo foodstuff industy at ththnofig-icpiaf Cluj-Napoca. In 1989 sh civd th PhD dg in Elctical Engining. In 1991 DAAD-Scholaship Univsity of Elangn-Nünbg, Gmany; Visiting Pofsso in 1998 at th Aalbog Univsity, Dnmak and at th Pannon Univsity, Vszpém, Hungay, Pof. HC Faculty of Mchanics and Infomatics, Univsity of Miskolc, 2008; Taian Vuia Awad of th Romanian Acadmy of Scinc in 1989, Gniusz Awad of th Hungaian Association of Invntos in Lctu Ioan Iov INCZE, Dipl. Eng., PhD, Tchnical Univsity of Cluj-Napoca, Faculty of Elctical Engining, Dpatmnt of Elctical Machins and Divs, Mmoandumului St. 28, Cluj-Napoca, Romania. ioan.incz@md.utcluj.o Gaduatd at th Polytchnical Institut of Cluj-Napoca, Elctotchnical Faculty in Aft 5 yas of xpinc in lctical quipmnts in pulp and pap industy h statd to wok at th Elctonic Rsach Institut Buchast, Subsidiay Cluj in dvlopmnt of mdical and industial lctonic quipmnts. Fom 2000 h joind th Tchnical Univsity of Cluj-Napoca, Faculty of Elctical Engining, Dpatmnt of Elctical Divs and Robots (sinc 2011 Dpatmnt of Elctical Machins and Divs). H obtaind th PhD dg in 2004 at th TU of Cluj-N. His main aa of intst is contolld lctical divs and pow lctonics. Lctu Csaba SZABO, Dipl. Eng., PhD, Tchnical Univsity of Cluj-Napoca, Faculty of Elctical Engining, Dpatmnt of Elctical Machins and Divs, Mmoandumului St. 28, Cluj-Napoca, Romania. csaba.szabo@md.utcluj.o Gaduatd at th Tchnical Univsity of Cluj-Napoca, Faculty of Elctical Engining, study pogam Elctical Divs in 1997, in 1998 h civd th vancd Study dg in Engy Efficint Contolld Elctical Divs. and in 2006 h obtaind th PhD dg in Elctical Engining at th TU of Cluj-N. Sinc 2000 statd to wok at th sam TU, Faculty of Elctical Engining, Dpatmnt of Elctical Divs and Robots (sinc 2011 Dpatmnt of Elctical Machins and Divs). His main aa of intst is contolld lctical divs, modlling and simulation of lctical and lctomchanical systms. 6 72

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