About phases dependence in a switched reluctance generator

Transcription

1 Aout phses dependene n swthed relutne genertor Ds,. J., Coelho, A. nd Fleury, A. Deprtmento de Engenhr d Unversdde Ctól de Goás (UCG) Av. Unverstár, 144, Áre III, Bloo G, Sl 18, CEP , Goân-GO, Brsl E-mls:rentojyme@hotml.om, oelho.ee@gml.om, fleury@terr.om.r Astrt. Ths pper nlyses nd dsusses the phse s dependene of the swthed relutne genertor - SG. A 6x4 SG prototype ws ssemlng for tests. Eh one of ths SG phses n e onneted nd dsonneted when needed. A redued swthes ount onverter tht ws use to drve the SG. Expermentl results showed hnges n the hrtersts wve forms of two opertonl phses when the thrd phse s dsonneted. At frst sght, t ws n unexpeted result [1], [2]. Although mny tests were ondued onfrmng the frst result. Therefore, t should e sy tht for the prototype tested under the ondued testng ondtons eh phse ehvor depends n the other phses ehve. emrkle hnges n the wveforms those re present here. They show tht there s not ndependene etween the phses ut truly strong dependene mong them. Key words Swthed relutne genertor (SG), redued swthes ount, phse s dependene, phse voltge, mutul ndutne. 1. Nomenlture v ω λ θ t n e Phse voltge Phse urrent Phse resstne Phse ndutne Angulr speed Flux lnkge otor ngulr poston Tme Numer of phse elutne Bk eletromotve fore Mxmum ndutne mx Mnmum ndutne mn 2. Introduton The prnple of operton of the swthed relutne mhne s knew sne the egnnng of the eletrl mhnes development. Soon the drvng of these mhnes proved to e somewht omplex. The dvnes on power eletrons nd mro proessng n the lst dede renewed the expetnes. In ft, modern power eletron onverters ssoted wth mro proessed ontrol hrdwre hve rought ompettveness to SG drven systems, llowng ther effent nd relle use. Therefore, the SG sprouted gn n new sene. Ths pper fouses the SG. In these mhnes phse ols re onentrted wndngs n the sttor poles. There re no wndngs n ts rotor. The douly slent poles struture s hrterst nherent to these mhnes. Therefore, there s mnml therml loss n the rotor. A SG s esy to onstrut nd to mntn. Its ommonly quoted dvntges re the sene of permnent mgnets, low mnufturng osts, rellty, roustness nd effeny. The opertonl speed rnge s very wde. Though these dvntges hve lredy een onfrmng, some spets of these mhnes must e mentonng here: there s strong mgnet dsontnuty provdng urrent, voltge nd torque rpples tht should e properly ontrollng. The power eletrons requrements to ontrol SG re sometmes quotng s dsdvntge of ths knd of mhne. Furthermore, they re lttle nosy. Due to ts dvntges, SG re onsderng s spel eletrl genertor for wnd power. Fg. 1 shows tht swthed relutne mhne works s motor or s genertor dependng on the frng ngles [4]. Alet the deve s the sme, the Swthed elutne Genertor (SG) s dfferent from the Swthed elutne Motor (SM) n some spef nd essentl spets: the SG hs mehnl nput - the torque t ts shft - nd n eletrl nput the extton power. Its output s the eletrl power suppled to the lod. Ths mhne presents two dfferent eletr rut onfgurtons per phse: one for ts extton nd nother for the generton perod. The SM hs n eletrl nput, mehnl output nd just one mn eletr rut per phse E&PQJ, Vol. 1, No.6, Mrh 28

2 seond term s the ndutve voltge fll nd the thrd one s the k eletromotve fore EMF s gve y: = ω θ e (6) Fg. 1 - Motor nd genertor modes for Swthed elutne Mhne. The eletrl nd mgnet ndependene of the phses re frequently quotng s dvntge of the Swthed elutne Motors. Ths rtle nlyses nd dsusses ths spet t SG. It ws reveled tht there s dependene mong the SG phses. Expermentl results those re present to proof ths pont. 3. Mthemtl model A SG s DC mhne. Its phse s extton requres DC soure. A onverter s used to drve the deve. Fg. 2 shows the shem of the onverter used to get the expermentl results presented here. The sttor wndng s feedng n DC. As ω nd re oth postve, the sgn of e s the sme s tht of. From (6) t n e seen tht when > the k eletromotve fore s postve. In ths se, eletr power s onvertng to mehnl power nd the mhne works s motor. However, when < the k eletromotve fore s negtve nd t nreses the urrent onvertng mehnl power nto eletrl power [4]. The dynm mehnl equton for the SG s gvng y (3). It s to e notng tht the eletromgnet torque C emg omes s negtve quntty,. e., tng gnst the rotor mehnl speed. dω C + C J D. ω = (7) m emg y: The o-energy of phse of ths mhne s gven o W = λ d (8) And the orrespondng eletromgnet torque for n n phse SG s gven y: C Wx x θ = n emg = 1 o (9) The mthemtl model of the SG regrdng three-phse prototype s show elow: Fg. 2 - Eletrl sheme of the onverter topology used. The phse wndng voltge tht s gven y: λ v = + t (1) As λ s: Therefore: Where = λ (2) d d dθ λ = + dθ d d v + + ω d θ (3) = (4) dθ = ω The frst term of the seond memer of the equton (4) s the voltge fll over the resstne of the ol. The (5) Where: v v v = r Cm o + o r J r D 1 θ & & θ & & ω & θ 1 + ω θ (1) o W r = ; W r = nd W r = (11) 78 E&PQJ, Vol. 1, No.6, Mrh 28

3 If the mtres ove re desgntng [V], [], [I], [] nd [ I ] extly n the order they pper n (12), the mtrx of sttes for the SG hs the form: 4. Smulton [ I ] = [] -1 [V] - [] -1 [][I] (12) The smultons were do usng from smll prototype of SG. Its prmeters nd dmensons re gvng n Tle I. TABE I. Chrterst of SG used Prmeter Vlue Unts Sttor Dmeter 14 mm otor Dmeter 7 mm Stk ength 17 mm Ar Gp ength.4 mm Sttor Teeth Wh 19 mm otor Teeth Wh 2 mm Sttor Slot 22.5 mm otor Slot 11.7 mm Sttor Yoke 12 mm otor Yoke 12.4 mm Shft Dmeter 22 mm Numer of turns per 5 Turns/phse phse Inert.28 Kg.m 2 Coeffent of Frton.26 N.m.s Indutne 36 mh Shft Dmeter 22 mm Numer of turns per 5 Turns/phse phse Inert.28 Kg.m 2 Coeffent of Frton.26 N.m.s Indutne 36 mh Shft Dmeter 22 mm Numer of turns per 5 Turns/phse phse Inert.28 Kg.m 2 Coeffent of Frton.26 N.m.s nstntneous rotor poston. Therefore, the mtrx of sttes ws evlutor onsderng the sturton effets. The powers omng from n AC soure, whh, long wth retfer rdge tht, exte the SG. As result, t supples the lod through ts wndngs. The extton perod of eh phse egns when ts swthes re turnng on nd they strt to ondut. At ths moment the ndutne s stll nresng, the dodes re not ondutng nd the phse wndngs generte postve k eletromotve fore. The genertng perod strts when the ontrolled swthes re turnng off, the phse urrent s devted to the lod through the dode nd the phse wndngs generte negtve k eletromotve fore due to the hnge of sgn. Fg. 3 shows the proess desred ove. od voltge otned from equton (2). Fg. 3 - Extton nd generton perods. The mtrx of sttes ove equton (8) - ws hek usng omputng progrm whose nputs re the phse voltges nd the mehnl torque. The outputs re the phse urrents, the ngulr speed nd the rotor poston. Eh new set of vlues for the phse voltges nd the torque ws use to evlute the next stte. The progrm uses dynm vlues tht result from the reltonshp mong the omponents of the onverter rut nd from the reltons mong them nd the AC soure, the retfer rdge, the mhne nd the lod. Only the nformton of the rotor poston s neessry to ontrol the gte sgnls. Fg. 4 shows tht the mesured vlues for the voltge over wndng mth the results predted y smulton. Indutne 36 mh Indutne (Unlgned 3 mh Poston) Condutng Angle 3 degrees Mesurements of the flux lnkge (λ) were done for mny rotor postons (θ), lso onsderng dfferent urrent vlues for eh one of them. These mesurements resulted n lrge nk of the funton λ (θ, ). Usng ths nk, progrm for polynoml nterpolton ws onstrutng to represent the ndutne of phse s funton of ts urrent nd the Fg. 4 - Voltge nd urrent over wndng. Smulton nd expermentl results for the voltge E&PQJ, Vol. 1, No.6, Mrh 28

4 5. Expermentl esults The nlyss of the lk of phse n Swthed elutne Motors s known n some smultons [1], [2]. The prototype onstruted for testng enles to test the effets of the lk of ny phse n Swthed elutne Genertor expermentlly. Ths llows one to nlyze the dependene or ndependene mong the phses. The expermentl results hve een hevng from the prototype lredy spefed. The onverter used ws not the onventonl hlf rdge one ut tht showed n Fg. 2. The omprtve lwys were otned from the phse A wndngs. The speed of the mhne stood t 1155 rpm ll the tme. The extton voltge ws lwys of 35.5V. The sme resstve lod remned n the output n ll the tests ondued. Fg. 5 shows extton nd the generted voltges n the phse when ll the three phses were onnet nd tvted. The extton voltge ws 35.5V wth urrent of 1.6A. The lod ws feedng wth 74.47V, 6.89A. Therefore, the SG ws genertng net power of 136.8W nd delverng t to the lod. Extton voltge mesurements over the lod were 64.1V nd 5.94A. Thus, the net generted power delvered to the lod ws 79.36W. As wted ths vlue s dfferent from tht found wth ll the three phses. However, wth 33% off, 136.8W stll gves 91.19W s result. Ths vlue s expressvely greter thn the 79.3W found. Ths dfferene shows tht there s strong dependene mong the phses of the SG. When phse s dsonneted, the other two phses generte eh one less power thn they do when ll they work together. Extton voltge Generted voltge 1) Ch 2: 2 Volt 2 ms Fg. 7 - Extton voltge nd generted voltge wth the lk of phse B. Fg. 8 shows the wveform for the urrent n the two tve phse wndngs. Generted voltge 1) Ch 2: 2 Volt 2 ms Fg. 5 - Extton nd generted voltge over phse wndng. A B C Delng wth resstve lod the voltge nd the urrent were n phse. The wveform of the urrent s showng n Fg. 6. 1) Ch 1: 5 mvolt 2 ms Fg. 8 - Wveform for the urrent n the two tve phse s wndngs. 4. Conlusons A B C 1) Ch 1: 5 mvolt 2 ms Fg. 6 - Current wveform when the SG opertes wth ts three phses. In Fg. 7 t n e seen the extton voltge nd the generted voltge wth the lk of the phse B. The extton ws of 35.5V nd 8.49A. The orrespondng Mny mportnt works show the ndependene of the phses n swthed relutne motor. Ths pper fouses ths mtter regrdng for SG. It presents expermentl results tht showng tht the phses presented ler dependene onsderng the prototype nd the onverter used n testng. In ft, these results show hrd mutul nfluene mong the three phses. Not only the wveforms ut lso the vlues hnge when just one phse s dsonneted. Ths result lms for deeper nvestgton. Ths nvestgton must onsder the mutul ndutne. eferenes [1] Hussn, I., dun, A., Nrus, J., Fult Anlyss nd extton requrements for Swthed elutne E&PQJ, Vol. 1, No.6, Mrh 28

5 Genertors, IEEE Trnstons on Energy Converson, Volume 17, Issue 1, mrh 22, pp [2] Swt, T., Kjer, P. C., Cossr, C., Mller, T. J. E., Hysh, Y., Fult-Tolernt Operton of Sngle Phse S Genertors, IEEE Trnstons on Industry Applton, Volume 35, Issue 4, July-Aug 1999, pp [3] Fleury, A., Andrde, D. A., Slv, F. S., Domngos, J.., Swthed elutne Genertors Behvor under Dfferent Condtons, ISIE 7 reords, 27. [4] Swt, T., The Swthed elutne Genertor, Eletron Control of Swthed elutne Mhnes, Edted y T. J. E. Mller, Newness Power Engneerng Seres, 21, pp E&PQJ, Vol. 1, No.6, Mrh 28