Artigo Maquina Relutancia Variavel

7/27/2019 Artigo Maquina Relutancia Variavel

1/24

ACIONAMENTO DA MQUINA A RELUTNCIA VARIVEL COMO MOTOR/GERADOR UTILIZANDO DSP

SILVEIRA,A.W.F.V.,ANDRADE,D.A.,FLEURY,A.,GOMES,L.C.,BISSOCHI,C.A.,DIAS,R.J.

Laboratrio de Acionamentos Eltricos, FEELT, Universidade Federal de UberlndiaAv. Joo Naves de vila, N 2121, Bloco 3N, Uberlndia-MGE-mails: [email protected],[email protected]

Abstract This paper deals with the switched reluctance motor/generator drive. An alternative half-bridge electronic converter to-pology is used to attain motor operation mode. To change from motor operational mode to generation mode the electronic converterstructure is strategically modified through a relay switch, allowing the flux of power go to the load. Simulation and experimental re-sults obtained from a 6x4 switched reluctance machine prototype operating as a motor/generator are presented. They show the beha-vior of the electrical machine during the transition between both operational modes. The DSP based control is successfully tested. Re-sults presented here sustain the applicability of the switched reluctance machine as a motor/generator solution for general application.

Keywords Switched reluctance motor/generator, half-bridge converter, digital signal processor.

Resumo Este artigo trata do acionamento da mquina a relutncia varivel operando como motor/gerador. Um conversor eletr-nico de meia ponte (half-bridge) com alteraes foi utilizado para permitir os dois modos de operao. Durante a comutao de mo-tor para gerador, ou vice-versa, o circuito de desmagnetizao modificado com a utilizao de um rel de potncia. Isso permite quedurante a operao motora a energia armazenada nas bobinas das fases seja devolvida para o link cc na etapa de desmagnetizao,porm, durante a operao de gerao, o caminho desviado para a carga resistiva. Resultados de simulao de uma mquina 6x4,

trifsica so apresentados e discutidos. Experimentalmente, o sistema foi montado utilizando DSP e os resultados so mostrados nestetrabalho, dando sustento a aplicabilidade da mquina a relutncia varivel como motor/gerador para aplicaes industriais diversas.

Palavras-chave Motor/gerador a relutncia varivel, conversor de meia ponte, processador digital de sinais.

1 Introduo

A crescente necessidade de otimizar processos, tor-nando-os mais econmicos, tem levado ao desenvol-vimento de acionamentos eletrnicos para mquinaseltricas capazes de control-las como mo-tor/gerador.

Na indstria automobilstica o motor de partidae o alternador podem ser substitudos por uma nicamquina eltrica, o que economizaria materiais ereduziria o peso e o custo do sistema (Fahimi, 2004).Essas vantagens tambm se aplicam industria ae-ronutica, onde tambm so usadas mquinas eltri-cas para partir turbinas e gerar eletricidade (Mac-Minn, 1989). Alm de permitirem economia no pro-cesso de fabricao, o desenvolvimento de moto-res/geradores para aplicao automotiva permitem aimplementao de novas tecnologias que visam reduo da poluio emitida pelos veculos, tais co-mo (Fahimi, 2004), (Kassakian, 1996), (Miller,

1999): Desligar o motor a combusto toda vs que

o veculo estiver parado em sinaleiros oucongestionamentos, partindo o mesmoquando for acelerado.

Desenvolvimento de veculos hbridos le-ves.

Aumentar a capacidade de gerao, suprin-do a crescente demanda por potncia eltri-ca dos veculos mais modernos.

Visando desenvolver a tecnologia dos moto-res/geradores algumas mquinas eltricas tm sidoexploradas atravs de experimentos. Em (Cai, 2004),um estudo comparativo entre as principais mquinascandidatas aplicaes como motor/gerador apre-sentado. Neste estudo a mquina a relutncia vari-vel (MRV) se mostrou uma forte candidata pelassuas caractersticas construtivas, que permitem, amesma, operar em altas velocidades (de Andrade,2007), com uma ampla faixa de variao de veloci-dade e com um controle simples, quando comparada mquina de induo. Alm disso, uma mquinarobusta e sua confeco simples e barata.

O trabalho apresentado em (Fleury, 2008), mos-trou que a MRV, projetada para este estudo, operan-do como gerador, apresenta a maior potncia entre-gue a carga com a mquina operando a 1300 rpm, eque aps atingir este pico, o valor da potncia entre-gue a carga, diminuiu lentamente com o aumento davelocidade. Esta caracterstica importante paraaplicaes automotivas j que o motor a combustoopera em regime de velocidade varivel, oscilando

entre 600 rpm a 6000 rpm (1:10).Dentro deste contexto, este artigo apresenta um

estudo de uma MRV com seis plos no estator e qua-tro no rotor (6x4), sendo acionada por um conversorde meia ponte acrescido de um rel para modificaodo circuito de desmagnetizao. O controle do mo-tor/gerador a relutncia varivel (MGRV) foi simu-lado utilizando o software MATLAB/SIMULINK etestado experimentalmente utilizando uma platafor-ma DSP. Os resultados obtidos sero apresentados ediscutidos no decorrer do artigo.

4898

XVIII Congresso Brasileiro de Automtica / 12 a 16-setembro-2010, Bonito-MS


2/24

2 Motor/Gerador a Relutncia VarivelA mquina a relutncia possui enrolamentos das

fases nas salincias do estator. A ausncia de enro-lamento nas salincias do rotor permite que altasvelocidades sejam alcanadas (Henriques, 2003). Afigura 1 mostra uma representao de uma MRVcom um dos enrolamentos de fase presente.

Com relao ao funcionamento da mquina, seum plo do rotor se alinha com o plo energizado doestator, a posio de equilbrio estvel. Assim, namquina a relutncia existe uma tendncia naturalde a parte mvel permanecer na posio de indutn-cia mxima da bobina excitada. Se o rotor encontra-se em posio de equilbrio instvel em relao auma determinada fase, e esta energizada, o rotortender a girar para a posio de equilbrio, caracte-rizando uma operao motora. Agora, se da posiode equilbrio estvel, o rotor forado a girar por umagente mecnico, o torque produzido restaurador eresulta em fora contra-eletromotriz aditiva tenso

aplicada, e a mquina gera energia eltrica. Em umamquina a relutncia varivel, a energia mecnicarecebida de uma mquina primria transformadaem energia eltrica forando o desalinho entre oplo do rotor e o plo energizado do estator. Pelafigura 2 possvel observar as regies em relao variao da indutncia, de uma das fases, em que aMGRV opera como motor ou gerador.

Fig.1. Mquina a relutncia varivel 6/4.

Fig.2. Variao da indutncia de uma fase do MGRV.A. Modelagem matemtica

O circuito de uma fase do MGRV pode ser equa-cionado como:

d

dLi

dt

diLRiv ++= (1)

onde v a tenso aplicada, i a corrente da fase,R a resistncia da fase, L a indutncia da fase e aposio do rotor. O terceiro termo do lado direito da

igualdade a fora contra-eletromotriz e, que isola-damente pode ser escrita como:

d

dLie = (2)

onde =d/dt a velocidade angular do rotor.O conjugado mecnico produzido pela MGRV,

desconsiderando as perdas para efeito de anlise,pode ser expresso por (3).

( )

ddLiiT 2

21, = (3)

Algumas concluses podem ser feitas a partir daequao acima: O conjugado mecnico produzidopela mquina independente do sinal da correnteque circula na fase, ento a corrente aplicada na fasepode ser unidirecional. Para se obter o conjugado necessrio o conhecimento da corrente e da variaoda indutncia em relao posio do rotor dL/d.

Para realizao da modelagem matemtica usadano programa de simulao, o conjugado mecnicoproduzido pela mquina foi calculado levando emconsiderao as perdas por atrito viscoso D e mo-

mento de inrciaJ, conforme apresentado pela equa-o (4).

Ddt

dJTT emag = (4)

Considerando trs fases com indutncias e corren-tes instantneas diferentes, o conjugado eletromag-ntico dado por:

++=

d

dLi

d

dLi

d

dLiT cc

bb

aaemag

222

2

1 (5)

A equao de velocidade do rotor (6) completa adescrio dinmica da mquina.

dt

d = (6)

O modelo matemtico do MGRV, considerandoas trs fases, apresentado por (7).

1 2 3

0 0 0 0

0 0 0 0

0 0 0 0

0

0 0 0 0 1 0

0 0 0

0 0 0

0 0 0

0 0 0 0

0 0 0 0 1

a a a

b b b

c c c

m a b c

aa a a

b bb b

ccc c

v R i

v R i

v R i

C i r i r i r D

dLL i id

dL iL id

idLL i

dJ

= +

+

(7)

onde:

d

dLr

d

dLr

d

dLr cba

2

1;

2

1;

2

1321 ===

(8)

Designando por [V], [R], [I], [L] e [

I] as matri-zes na ordem em que aparecem em (6), a matriz deestados do MGRV tem a seguinte forma:

]][[][][][][ 11 IRLVLI

= (9)

4899



3/24


4/24

durante toda a simulao. A velocidade em que amquina passou a gerar energia foi de 1350 rpm, oque ocorreu, aproximadamente com 0.54 s de temposimulado. Este valor da velocidade, onde ocorreu acomutao do modo de operao, foi estipulado ba-seado no estudo desenvolvido em (Fleury, 2008), quemostrou que em torno desta velocidade o GRV en-trega uma maior potncia carga. O comportamentodas correntes da mquina durante o momento detransio pode ser observado na figura 6-b, onde possvel perceber que no incio da operao comogerador as correntes apresentam amplitudes maiores,que diminuem at se estabilizar com valor prximo a9 A. Isso ocorre devido corrente inrush com o ca-pacitor descarregado, usado para filtrar a tenso queser entregue carga resistiva (20 ).

Para evitar uma eventual queima de chaves nomomento da transio de motor para gerador, devido corrente inrush com o capacitor, pode ser adotadaa estratgia de iniciar o funcionamento da mquinacomo gerador com o valor do offreduzido. Pela figu-

ra 7 possvel perceber o efeito da variao do valordo offna amplitude da corrente gerada.A curva de tenso gerada, e entregue a carga re-

sistiva durante o perodo de gerao, pode ser vistaatravs da figura 6-c; e pela figura 6-d, a curva detenso em uma das fases apresentada, permitindoobservar o comportamento, da mesma, durante otransitrio de modo de operao.

A figura 6-e mostra a curva de fluxo em funoda corrente, sendo possvel observar o comportamen-to desta curva durante toda a simulao includo operodo de transio de motor para gerador. A po-tncia consumida pela mquina e gerada podem servisualizadas na curva 6-f.

0 0.5 1 1.50

500

1000

1500

Tempo (s)

Velocidade(rpm)

0.52 0.54 0.56 0.58

-5

0

5

10

Tempo (s) Fig. 6-a. Velocidade do MGRV. Fig. 6-b. Corrente nas fases.

0 0.5 1 1.50

20

40

60

Tempo (s)

Tenso(V)

0 .5 0 .52 0 .54 0 .56 0 .58 0 .6

-40

-20

0

20

Tempo (s)

Tensoemumafase(V)

Fig. 6-c. Tenso gerada pelaMRV. Fig. 6-d. Tenso em uma das fases.

0 5 10 150

0.05

0.1

0.15

0.2

0.25

Corrente (A)

Fluxo(Wb)

0 0.5 1 1.5

0

50

100

150

Tempo (s)

Potncia(W)

Fig. 6-e. Fluxo v.s. corrente. Fig. 6-f. Potncia de entrada e

potncia de sada.

0. 022 0. 023 0. 024 0.025 0. 026 0. 027 0. 028 0.029 0. 030

2

4

6

8

10

12

14

16

Tempo (s)

corrente(A)

Fig. 7. Variao da amplitude da corrente de uma fase em relao ao

valor do ngulo de abertura das chaves (off).

3 Resultados ExperimentaisA MRV, 6x4, trifsica de 1 cv, descrita na tabela 1,foi acoplada a um motor de induo trifsico de 4plos, 2 cv, acionado por um inversor comercial,para a realizao dos testes experimentais. O con-versor de meia ponte apresentado na Fig 3 foi mon-tado para a realizao dos testes e um DSP modeloTMS320F2812 foi utilizado para controlar a MRVcomo motor/gerador. Para obteno da posio rot-rica, necessria para o acionamento do MGRV, fo-ram usados sensores pticos associados a dois discosranhurados (Fig. 10), um para motor (S1) e um paragerador (S2), que indicam o momento certo de mag-netizar cada uma das fases na etapa motora e gera-dora. A Fig. 8 mostra o diagrama de blocos da ban-cada de experimentos e a Fig. 9 apresenta a foto dabancada de testes.

Os testes experimentais foram efetuados com a

mquina primria (MIT) girando no mesmo sentidodo MGRV, operando como motor. Esta situao semelhante a que ocorre quando o motor/gerador deum automvel parte o motor a combusto e continuasendo acionado como motor momentos antes de seumodo de operao ser comutado para gerador.

Fig. 8. Diagrama de blocos do sistema montado para experimentos.

Fig. 9. Foto da bancada de testes montada no laboratrio.

4901



5/24

Os testes foram realizados com o MGRV ope-rando a 1350 rpm. A comutao de motor para ge-rador ou vice-versa controlada, pelo usurio queutiliza computador atravs do software Code Com-poser, utilizado na programao do DSP. Conformefoi feito em simulao, o link cc foi configurado coma tenso de 25 V e a resistncia de carga com valorde 20 .

A Fig. 11 mostra o sinal de corrente em umadas fases da mquina durante a transio de motorpara gerador. Pode ser observado que a corrente pos-sui pequena amplitude durante o funcionamento damquina como motor. Isso se deve ao fato de a m-quina estar operando como motor no mesmo sentidoda mquina primria. Quando a transio ocorre,aps o comando via PC do usurio, o circuito dedesmagnetizao das bobinas modificado com acomutao do rel, e a energia armazenada nas bo-binas na forma de campo, somada a energia geradapassa a ser entregue carga do MGRV, operandocomo gerador. Somado a esta modificao do cami-

nho de desmagnetizao, o programa desenvolvidopara acionar o MGRV passa a magnetizar as bobinasdas fases baseado nos sinas provenientes do grupo desensores usados para gerao, S2 na Fig. 10. Noinicio do funcionamento como gerador a amplitudeda corrente na fase maior por causa que o capacitorde filtro da carga encontra-se descarregado.

Um perodo de 20 ms, durante o qual as chavesdo conversor (MOSFET) ficam todas abertas, foiadicionado ao momento de transio. Isso foi feitopara proteger as chaves eletrnicas de grandes varia-es de tenso, devido ausncia de circuito dedesmagnetizao das bobinas das fases, durante ochaveamento do rel. Este perodo de proteo, du-rante a comutao, pode ser observado nas figuras decorrente e tenso em uma das fases da mquina.

Fig. 10. MRV com os sensores de posio instalados.

1 >1 >1 >1 >

1) Ch 1: 1 V 20 ms

Fig. 11. Corrente em uma das fases durante a transio de motorpara gerador (escala: 1 V - 4 A).

A Fig. 12 apresenta o sinal de tenso em umadas fases do MGRV durante a comutao de motorpara gerador. No incio da etapa geradora a tensoaplicada carga, parte negativa do sinal de tenso,possui menor amplitude devido ao capacitor de filtroda carga estar descarregado. Aps 60 ms a tenso seestabiliza com uma amplitude fixa. As figuras 13 e14 mostram a transio de gerador para motor, sen-do que na figura 13 apresentado o sinal de correnteem uma fase, e na figura 14 mostrado o sinal detenso na fase. Portanto o acionamento desenvolvidopermite a comutao de modo de operao doMGRV nos dois sentidos e pode ser modificado paraefetuar a comutao baseado na aplicao em que oMGRV for utilizado.

T

2 >2 >2 >2 >

2) Ch 2: 20 V 20 ms

Fig. 12. Tenso em uma das fases durante a transio de motor paragerador.

T

1 >1 >1 >1 >

1) Ch 1: 1 V 20 ms

Fig. 13. Corrente em uma das fases durante a transio de geradorpara motor (escala:1 V - 4 A).

T

2 >2 >2 >2 >

2) Ch 2: 20 V 20 ms

Fig. 14. Tenso em uma das fases durante a transio de geradorpara motor.

Pela Fig. 15 pode ser visualizado o sinal de ten-so na carga durante a transio de motor para gera-dor, onde pode ser observada a presena de uma

4902



6/24

oscilao no sinal de tenso, que caractersticodeste tipo de mquina. A figura 16 apresenta o sinalde tenso na carga durante a gerao em uma escaladiferente, com intuito de mostrar com mais detalhesa oscilao presente no sinal. Esta oscilao pode serdiminuda aumentando o tamanho do capacitor defiltro ligado em paralelo carga. Porm, necess-rio observar que o aumento do capacitor de filtroacarretar no aumento da corrente inrush com o ca-pacitor inicialmente descarregado, podendo desper-tar a necessidade de aprimorar o controle durante acomutao, magnetizando gradativamente a mqui-na quando operando como gerador, com intuito deproteger o sistema de grandes picos de correntes.

1 >1 >1 >1 >

1) Ch 2: 10 V 500 ms

Fig. 15. Tenso na carga durante a transio de motor para gerador.

1 >1 >1 >1 >

1) Ch 2: 10 V 10 ms

Fig. 16. Tenso aplicada na carga com a mquina operando comogerador em regime permanente.

4 Concluso

Este artigo apresentou um acionamento capaz depermitir que a mquina a relutncia varivel operecomo motor ou como gerador, possibilitando que a

comutao entre os modos de operao ocorra nosdois sentidos e com o sistema em funcionamento.Um prottipo de uma MRV trifsica, 6x4 de 1 cv foisimulado como motor/gerador e montado em umabancada de testes experimentais, utilizando comomquina primaria um motor de induo trifsico.Um DSP, onde foi programado o algoritmo de con-trole, foi usado no controle do MGRV. Para que atransio de modo de operao ocorra o conversor demeia ponte foi equipado com um rel para permitir odesvio da energia para a carga, quando a mquinaopera como gerador. Associado modificao do

caminho de desmagnetizao, os ngulos de magne-tizao das fases so alterados para que a mudanade modo de operao se complete. Resultados expe-rimentais mostraram a transio de modo de opera-o e comprovaram que a mquina a relutncia vari-vel pode ser aplicada em quaisquer processos quenecessitam de um motor e um gerador em momentosdistintos.

Agradecimentos

Agradecemos FAPEMIG e ao CNPq pelo apoiofinanceiro, e Universidade Federal de Uberlndiapela infra-estrutura disponibilizada. Agradecemostambm PUC-GO e UEG pelo apoio dado aotrabalho.

Referncias Bibliogrficas

Fahimi, B., et. al. A switched reluctance machine-

based starter/alternator for more electric carsTrans. Energ. Conver., vol. 19, no. 1., March2004.

MacMinn, S. R. and Jones, W. D., A very highspeed switched-reluctance starter-generator foraircraft engine applications in Proc. IEEEAerosp. And Electron. Conf., 1989, vol. 4, pp.1758-1764.

Kassakian, J. G., Caliskan, V., Automotiveelectrical systems circa 2005 Spectrum IEEE,Volume: 33, page(s): 22-27, Aug. 1996.

Miller, J. M., Rajarathnam, A. V., and Ehsani, M.,Current status and future trends in moreelectric car power systems Proc. IEEE Veh.Technol. Conf., Houston, TX, Maio 1999.

Cai, W., Comparison and review of electricmachines for integrated starter alternatorapplications, IAS - IEEE, 2004.

Fleury, A. V. S., Silva, F. S., Arajo, W. R. H.,Andrade, D. A., Silveira, A. W. F. V., ReducedSwitch count converter for switched reluctancegenerators Eletrnica de Potncia, vol. 13, no.3, August 2008.

Henriques, L. O. A. P., Rolim, L. G. B., Suemitsu,W. I., Branco, P. J. C., Uma reviso dasestratgias de reduo de ondulaes deconjugado no motor de relutncia chaveado

Eletrnica de Potncia, Vol. 8, no. 1, 2003.de Andrade, R., Sotelo, G. G., Ferreira, A. C.,Rolim, L. G. B. S., Neto, J. L., Stephan, R. M.,Suemitsu, W. I., Nicolsky, R., Flywheel energystorage system description and tests Transactions on applied superconductivity,IEEE, Vol. 17, P. 2, 2007.

4903



7/24

ESTUDO DO GRV OPERANDO EM MALHA FECHADA UTILIZANDO DSP

SILVEIRA,A.W.F.V.,ANDRADE,D.A.,GOMES,L.C.,BISSOCHI,C.A.,FLEURY,A.

Laboratrio de Acionamentos Eltricos, FEELT, Universidade Federal de UberlndiaAv. Joo Naves de vila, 2121, 3N, Santa Mnica, Uberlndia-MG

E-mails: [email protected], [email protected]

Abstract The subject of this paper is to present and test a three-phase 6x4 switched reluctance generator load voltage control. Thedemonstrated strategy uses a PI controller to vary the magnetization level of the phases during the magnetization period using a PWMsignal. This strategy was implemented throw simulation and experimentally using a fixed-point DSP. The results suggest that thisstrategy successfully control the generated voltage applied to the load.

Keywords Switched reluctance generator, half-bridge converter, digital signal processor.

Resumo Este artigo tem como objetivo apresentar e testar uma estratgia de controle de tenso aplicada carga para um geradora relutncia varivel trifsico 6x4. A estratgia demonstrada baseada na utilizao de um controlador PI que varia o nvel de mag-netizao do gerador atravs da atuao no valor mdio da tenso aplicada s fases durante o perodo de magnetizao, utilizando pa-ra isso modulao por largura de pulso (PWM). Esta estratgia foi implementada e testada atravs de simulao computacional e ex-perimentalmente utilizando plataforma DSP. Os resultados so apresentados no decorrer do artigo e mostram que o GRV pode operarem malha fechada de tenso na carga com sucesso.

Palavras-chave Gerador a relutncia varivel, conversor de meia ponte, processador digital de sinais.

1 Introduction

A indstria automobilstica vem incorporando no-vas tecnologias aos automveis visando segurana,desempenho e conforto. Como exemplos citam-se:controle de direo, de frenagem e de trao, acele-rador eletrnico, suspenso ativa, catalisador ele-trosttico e funo de espera para diminuir a polui-o e o consumo. Estes novos avanos tm colabo-rado com o aumento da potncia eltrica requerida

pelos automveis para suprir todos os equipamen-tos eletro-eletrnicos embarcados (Fahimi, 2004).

Atualmente a maioria dos automveis usa o bar-ramento cc, onde so ligadas as cargas e a bateriado automvel, com tenso de 14 V, e apresentamconsumo mdio de potncia de 1.2 kW. Algunsestudos prevem que a potncia eltrica mdia re-querida pelas prximas geraes de automveisser em torno de 3 kW, o que abrir um novo cam-po de pesquisa buscando melhorar a gerao, ar-mazenamento e consequentemente a eletrificaoadequada esta crescente demanda (Miller, 1999).

Os estudos apontam para a substituio do bar-ramento cc de 14 V por um barramento de 42 V,permitindo assim reduzir a corrente eltrica neces-sria para suprir a demanda crescente de potncia.Com isso a bitola dos fios que conduzem eletrici-dade diminuda, o que leva a uma economia decobre e a uma reduo de peso e custo da instala-o (Fahimi, 2004), (Miller, 1999), (Cai, 2004).

Esta crescente demanda por potncia geradanos automveis tem apontado que a tradicionalmquina de Lundell, utilizada como gerador, terque ser otimizada, ou substituda por outro tipo demquina eltrica. Em (Perreaul, 2004) apresen-

tada uma nova tecnologia que promete otimizar ouso da mquina de Lundell, permitindo que a in-fra-estrutura montada para confeco desta mqui-na continue sendo utilizada. Porm, diversos traba-lhos tem sugerido a utilizao de outros tipos demquinas para gerar eletricidade em veculos e-quipados com barramento de 42 V (Cai, 2004),(Chdot, 2007), (Fahimi 2004), (Schofield, 2005).Dentre estes autores, (Vries, 2001), (Fahimi,2004), (Schofield, 2005), (Radun, 1998), indicamque a mquina a relutncia varivel uma fortecandidata a ocupar este importante papel, devido

s suas caractersticas intrnsecas como, simplici-dade, robustez, capacidade de operar com falta defases e em larga faixa de velocidade de operao,ausncia de ims permanentes e de enrolamento norotor e simplicidade de controle.

O trabalho apresentado em (Fleury, 2008),mostrou que o gerador a relutncia varivel (GRV)apresenta melhor desempenho em velocidades a-cima de 1000 rpm, e aps atingir o pico de desem-penho, em torno de 1300 rpm, a potncia geradadecresce lentamente com aumento da velocidadeat 5000 rpm. Essa caracterstica importante emaplicaes automotivas j que o motor a combusto

opera com velocidade varivel e em torno de 600-6000 rpm.Dentro deste contexto, este artigo apresenta

um estudo feito atravs de simulao computacio-nal e experimentos de uma mquina a relutnciavarivel operando como gerador, sendo controladaem malha fechada e acionada por conversor half-bridge (HB). Resultados de simulao e experi-mentais sero apresentados. A figura 1 mostra umdiagrama de blocos de um GRV interligado aosistema de eletrificao automotivo.

2614



8/24

Fig.1. Diagrama de blocos de um GRV interligado a um veculo.

2 GRV Caractersticas

A mquina a relutncia possui enrolamentos dasfases nas salincias do estator. A ausncia de enro-lamento nas salincias do rotor permite que altasvelocidades sejam alcanadas. A figura 2 mostrauma representao de um GRV com um dos enro-lamentos de fase presente (Fleury, 2008).

Com relao ao funcionamento da mquina, se

um plo do rotor se alinha com o plo energizadodo estator, a posio de equilbrio estvel. Assim,na mquina a relutncia existe uma tendncia na-tural de a parte mvel permanecer na posio deindutncia mxima da bobina excitada. Se o rotorencontra-se em posio de equilbrio instvel emrelao a uma determinada fase, e esta energiza-da, o rotor tender a girar para a posio de equil-brio, caracterizando uma operao motora. Agora,se da posio de equilbrio estvel, o rotor fora-do a girar por um agente mecnico, o torque pro-duzido restaurador e resulta em fora contra-eletromotriz aditiva tenso aplicada, e a mquinagera energia eltrica. Em uma mquina a relutn-cia varivel, a energia mecnica recebida de umamquina primria transformada em energia el-trica forando o desalinho entre o plo do rotor e oplo energizado do estator. Pela figura 3 possvelobservar as regies em relao variao da indu-tncia de uma das fases em que a mquina a relu-tncia varivel opera como motor ou gerador.

Fig.2. Mquina a relutncia varivel 6/4.

Fig.3. Variao da indutncia de uma fase de uma mquina arelutncia varivel.

2.1 Modelagem matemtica

O circuito de uma fase do GRV pode ser equa-cionado como:

d

dLi

dt

diLRiv ++= (1)

onde v a tenso aplicada, i a corrente da fase,R a resistncia da fase,L a indutncia da fase e a posio do rotor. O terceiro termo do lado di-

reito da igualdade a fora contra-eletromotrize,que isoladamente pode ser escrita como:

d

dLie = (2)

onde =d/dt a velocidade angular do rotor.O conjugado mecnico produzido pela GRV,

desconsiderando as perdas para efeito de anlise,pode ser expresso por (3).

( )

d

dLiiT 2

2

1, = (3)

Algumas concluses podem ser feitas a partir daequao acima: O conjugado mecnico produzidopela mquina independente do sinal da correnteque circula na fase, ento a corrente aplicada nafase pode ser unidirecional. O sinal do conjugado determinado pela fase da corrente em relao variao da indutncia dL/d.

Para realizao da modelagem matemtica usa-da no programa de simulao, o conjugado mec-nico produzido pela mquina foi calculado levandoem considerao as perdas por atrito viscoso D emomento de inrcia J, conforme apresentado pelaequao (4).

Ddt

dJTT emag = (4)

Considerando trs fases com indutncias e cor-rentes instantneas diferentes, o conjugado eletro-

magntico dado por:

++=

d

dLi

d

dLi

d

dLiT cc

bb

aaemag

222

21 (5)

A equao de velocidade do rotor (6) completa adescrio dinmica da mquina.

dt

d = (6)

O modelo matemtico do GRV, considerando astrs fases, apresentado por (7).

2615



9/24

1 2 3

0 0 0 0

0 0 0 0

0 0 0 0

0

0 0 0 0 1 0

0 0 0

0 0 0

0 0 0

0 0 0 0

0 0 0 0 1

a a a

b b b

c c c

m a b c

aa a a

b

bb b

cc

c c

v R i

v R i

v R i

C i r i r i r D

dLL i id

dL iL i d

idLL i

dJ

= +

+

(7)

onde:

d

dLr

d

dLr

d

dLr cba

2

1;

2

1;

2

1321 ===

(8)

Designando por [V], [R], [I], [L] e [

I] as ma-trizes na ordem em que aparecem em (6), a matrizde estados do GRV tem a seguinte forma:

]][[][][][][ 11 IRLVLI

= (9)

2.2 Modelagem Computacional

O programa Matlab/Simulink foi usado paradesenvolver a simulao de uma mquina a relu-tncia 6/4 operando como gerador. Os dados rela-cionados ao dimensionamento da mquina simula-da esto na tabela 1 e so de uma mquina projeta-da para os ensaios experimentais (Fig. 6). Maioresdetalhes relacionados a modelagem podem ser en-contrados em (Fleury 2008).

O conversor usado para acionar o GRV do tipohalf-bridge (Fig. 4), comumente utilizado para

acionar a mquina relutncia varivel. A figura 5mostra o circuito de magnetizao de desmagneti-zao das bobinas.

Fig.4. Diagrama esquemtico do conversor simulado.

Fig. 5. Circuitos de magnetizao e de desmagnetizao das bobi-nas.

Fig. 6. Mquina a relutncia varivel usada para obteno dosparmetros para a simulao.

Tabela ICaractersticas da MRV

Parmetros Valor

ngulo de Conduo 30 graus

Atrito Viscoso 0.026 N.m.s

Culatra do Estator 12 mmCulatra Rotor 12,4 mm

Comprimento da pilha laminada 107 mm

Dentes do Estator 22,5 mm

Dentes do Rotor 11,7 mm

Dimetro do Estator 140 mm

Dimetro do Rotor 70 mm

Gap de Ar 0,4 mm

Indutncia (posio alinhada) 36 mH

Indutncia (posio desalinhada) 3 mH

Largura dos dentes do Estator 19 mm

Largura dos dentes do Rotor 20 mm

Momento de Inrcia 0,0028 kg.m2Nmero de espiras por fase 100 volta/fase

2.3 Controle do GRV

O gerador a relutncia varivel pode ser controladopara produzir uma potncia desejada na carga oupara produzir na carga uma tenso constante, vari-ando a potncia com a variao da resistncia dacarga. Em aplicaes embarcadas em geral, inclu-do a automotiva, necessrio que a tenso no bar-ramento cc no sofra grandes variaes, mesmocom o gerador operando em velocidade varivel ecom transitrio na impedncia equivalente dascargas acopladas ao sistema de eletrificao.

Diante destas informaes e com intuito deaveriguar a operacionalidade do GRV operando emmalha fechada de tenso gerada na carga, umaestratgia para este tipo de controle ser apresenta-da, simulada e testada experimentalmente.

Esta estratgia utiliza um controlador PI queproduz um sinal proporcional ao erro entre a refe-rncia de tenso na carga desejada e a tenso queest sendo aplicada na mesma. Este sinal intro-duzido a um mdulo PWM que produzir o sinalde gatilho com largura varivel para acionar a

2616



10/24

chave superior do conversor, relacionada faseque est em etapa de magnetizao no momento isso depende da posio do rotor. Por exemplo, se afase A da figura 4 estiver com seu valor de indu-tncia no mximo, caminhando para a diminuiode seu valor, devido a entrada de energia mecnicaadvinda da mquina primria, o sinal PWM seraplicado a chave Q1, enquanto a chave Q2 perma-necer fechada at que o perodo de magnetizaotermine (off). Esta estratgia representada pelafigura 7.

3 Resultados de Simulao

Com intuito de validar a modelagem desen-volvida testes de simulao foram realizados comos seguintes critrios: o gerador a relutncia ope-rou em malha fechada, sendo controlado utilizandoa estratgia descrita neste artigo, a tenso no bar-ramento cc que alimenta o conversor HB foi confi-

gurada com 42 V, a velocidade de operao damquina foi configurada para ser constante e iguala 1350 rpm. A mquina foi simulada durante oitosegundos e foi submetida a um transitrio de resis-tncia da carga acoplada ao GRV, onde a resistn-cia da mesma foi reduzida de 20 para 15 com3 s de simulao e, quando o tempo atingiu 6 s, aresistncia de carga retornou para seu valor inicial.

A figura 8 mostra o sinal de corrente em umadas trs fases da mquina e o sinal de gatilho apli-cado chave superior do conversor relacionado aesta fase, durante o perodo de magnetizao damesma. Vale ressaltar que o mesmo sinal PWM aplicado s trs fases da mquina, j que elas so

magnetizadas sequencialmente no existindo inter-cesso deste perodo entre elas. Por este motivoapenas um controlador PI e um mdulo PWM necessrio para implementao desta estratgia decontrole.

Pela figura 9, pode ser observado o comporta-mento da corrente durante o transitrio de carga.Quando a resistncia da carga reduzida, o contro-lador impe corrente para que a tenso na mesmano reduza, j no momento em que a carga retornaao valor inicial, o controlador atua para que a am-plitude da corrente volte ao valor do inicio da si-mulao. A curva de tenso em uma das fases do

GRV pode ser observada pela figura 10, mostrandoa etapa de magnetizao, parte chaveada e positivada curva, e a etapa de desmagnetizao, parte ne-gativa, que ocorre quando os diodos que constitu-em o conversor HB entram em conduo, entre-gando a energia de magnetizao adicionada aenergia convertida de mecnica em eltrica cargaresistiva.

A figura 11, apresenta a curva de tenso nacarga do gerador, onde pode ser observado nosinstantes de 3 s e 6 s pequenas oscilaes no sinal

de tenso devido aos transitrios de carga efetua-dos nesta simulao. Tambm pode ser visto a pre-sena de uma oscilao no sinal de tenso, sem sera do transitrio. Esta oscilao caracterstica des-te tipo de mquina pode ser reduzida com o au-mento do capacitor utilizado como filtro da tensoentregue a carga.

Fig. 7. Diagrama de blocos do controle de tenso na carga.

0.442 0.443 0.444 0.445 0.446 0.4470

1

2

3

4

5

6

Tempo (s)

Correntede

fase(A),sinalde

gatilho

Fig. 8. Corrente em uma das fases e sinal da gatilho.

0 2 4 6 80

2

4

6

8

10

Tempo (s)

Corrente

(A)

Fig. 9. Corrente em uma das fases.

0.245 0.246 0.247 0.248 0.249 0.25 0.251

-40

-30

-20

-10

0

10

20

30

40

Tempo (s)

Tensonafase(V)

Fig. 10. Tenso em uma das fases.

1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

Tempo (s)

Tenso(V)

Fig. 11. Curva de tenso na carga durante o teste de transitrio de

carga.

2617



11/24

4 Resultados Experimentais

Fig. 12. Foto da bancada de testes montada no laboratrio.Com intuito de validar experimentalmente a estra-tgia de controle apresentada, o GRV descrito an-teriormente foi acoplado a um motor de induotrifsico de 2 cv, 4 plos, acionado por um conver-sor de freqncia comercial. O conversor HB foiconstrudo para acionar o GRV e a estratgia decontrole foi programada para ser executada em umDSP TMS320F2812, utilizado no sistema. A posi-o do rotor, necessria para a aplicao dos sinaisde gatilho durante o perodo de magnetizao dasfases, foi obtida utilizando sensores pticos associ-ados a um disco, que representa o exato instante

em que cada fase deve ser magnetizada. A figura12 apresenta uma foto da bancada de testes monta-da no laboratrio.

O controlador PI, utilizado na estratgia de-senvolvida, foi sintonizado com facilidade por ten-tativa e erro, e os coeficientes empregados foram:Kp= 2 e Ki = 0.8.

Um teste de transitrio de carga foi realizado,onde a resistncia de carga foi reduzida de 20 para 15 , conforme foi realizado em simulao. Areferncia de tenso na carga foi configurada comosendo de 42 V. Neste teste o GRV operou a 1350rpm e pela figura 13 pode ser observado o sinal decorrente, que aumenta de amplitude aps a reduoda carga, e o sinal de tenso, que apresenta umarpida depresso em seu valor logo aps o transit-rio, voltando ao valor de referncia instantes de-pois.

1 >1 >1 >1 >

2 >2 >2 >2 >1) Ch 1: 2 V 500 ms

2) Ch 2: 20 V 500 ms

Fig. 13. Corrente em uma fase (escala: 1 V - 4 A) e tenso na

carga para transitrio de resistncia de carga.

1 >1 >1 >1 >

2 >2 >2 >2 >

1) Ch 1: 10 V 500 us

2) Ch 2: 500 mV 500 us

Fig. 14. Curva de corrente (escala: 1 V - 4 A) e sinal de gatilho.

O sinal de corrente em uma das fases e o respec-tivo sinal de gatilho aplicado chave superior doconversor referente a esta fase, podem ser observa-dos pela figura 14, j a figura 15, mostra o sinal detenso e gatilho de uma das fases para a mesmasituao.

Foi realizado um teste de transitrio de refern-cia para o controlador. Inicialmente a refernciafoi configurada com 42 V e depois modificada ins-tantaneamente para 30 V. A figura 15 mostra oresultado deste teste, onde possvel verificar ocomportamento da corrente, que reduz sua ampli-tude devido ao transitrio, e o sinal de tenso nacarga, que converge para o valor de referncia a-plicado ao controlador.

Um outro teste foi realizado, agora com transi-trio de velocidade. O GRV controlado em malhafechada com referencia de 42 V foi acelerado de800 rpm para 1800 rpm. A figura 16 apresenta oresultado, por onde pode-se observar o sinal detenso, que permaneceu com valor em torno da

referncia, e o sinal de corrente, que reduz de am-plitude na medida que a mquina ganha velocida-de. Note que a amplitude da oscilao presente nosinal de tenso na carga reduz com o aumento davelocidade, o que caracterstico deste tipo de m-quina.

1 >1 >1 >1 >

2 >2 >2 >2 >

1) Ch 1: 10 V 1 ms

2) Ch 2: 20 V 1 ms

Fig. 15. Tenso em uma fase e sinal de gatilho.

T

T

1 >1 >1 >1 >

2 >2 >2 >2 >

1) Ch 1: 2 V 500 ms

2) Ch 2: 20 V 500 ms

Fig. 16. Corrente em uma fase (escala: 1 V - 4 A) e tenso nacarga para transitrio de referncia.

T

T

1 >1 >1 >1 >

2 >2 >2 >2 >

1) Ch 1: 2 V 5 s

2) Ch 2: 10 V 5 s

Fig. 17. Curva de tenso na carga e corrente nafase (escala:1 V - 4 A).

2618



12/24

Visando verificar o perfil da eficincia do GRVoperando com a estratgia de controle apresentada,que visa manter constante a tenso na carga, testesforam realizados com a mquina operando em di-ferentes velocidades. A figura 18 mostra que apotncia gerada, ou seja, a potncia eltrica desada (potncia dissipada na carga) diminuda dapotncia eltrica de entrada no conversor HB, au-menta com o aumento da velocidade.

800 1000 1200 1400 1600 1800 2000 2200

85

90

95

100

105

110

Velocidade (rpm)

PotnciaGerada

Fig. 18. Curva de potncia gerada pelo GRV em funo da veloci-

dade.

5 Concluses

O funcionamento de uma mquina a relutnciavarivel 6x4 operando como gerador controladoem malha fechada de tenso na carga foi estudadoneste trabalho. A estratgia de controle apresenta-da baseada na utilizao de um controlador PIpara variar a mdia da tenso aplicada nas fases

durante o perodo de magnetizao, utilizandosinal PWM. Esta estratgia foi testada atravs desimulao do prottipo montado e experimental-mente utilizando um DSP de ponto fixo. Os resul-tados demonstraram que a tcnica de controle mos-trada no artigo controla bem o GRV, permitindooper-lo em malha fechada de tenso na carga emsituaes de transitrio de resistncia da carga,referncia de tenso e de velocidade. Este tipo decontrole interessante para aplicaes embarcadas,como por exemplo, automotiva, aeronutica e em-barcaes.

Agradecimentos

Agradecimentos FAPEMIG e ao CNPq peloapoio financeiro e Universidade Federal de Uber-lndia pela estrutura disponibilizada.

Referncias Bibliogrficas

Fahimi, B., et. al. A switched reluctance machine-based starter/alternator for more electric carsTrans. Energ. Conver., vol. 19, n1., maro 2004.

Miller, J. M., Rajarathnam, A. V. and Ehsani, M.Current status and future trends in more electriccar power systems, Proc. IEEE Veh. Technol.Conf., Houston, TX, Maio 1999.

Cai, W. Comparison and review of electric machinesfor integrated starter alternator applications, IAS-IEEE, 2004.

Chdot, L. Integrated Starter Generator: The Need foran Optimal Dsing and Control Approach.Application to a Permanent Magnet Machine,Transactions on Industry Applications, IEEE, Vol.

43, No. 2, 2007.Perreault, D. J. Automotive Power Generation and

Control Transactions on Power Electronics, Vol.19, N. 3, 2004.

Vries, A., at al. A Switched Reluctance Machine for aStarter-Alternator System IEMDC-IEEE 2001.

Torrey, D. A. Switched reluctance generator and theircontrol, IEEE Trans. Ind. Electron., vol. 49, pp. 3-14, Fev. 2002.

Schofield, N., Long, S. A. Generator Operation of aSwitched Reluctance Starter/generator at ExtendedSpeeds IEEE 2005.

Radun, V., at al. Two-channel switched reluctancestarter/generator results Transactions on IndustryApplications, IEEE, Vol. 34, No. 5, 1998.

Fleury,A., Silva; F. S., Arajo, W. R. H., Andrade, D.A., Silveira, A. W. F. V. Reduced Switch countconverter for switched reluctance generatorsEletrnica de Potncia, Vol. 13, No. 3, August2008.

2619



13/24

Modeling, Simulation and a Comparative Study Between a Single and a Three-

Phase Switched Reluctance Machine

Abstract. The comparative study of electric machines hasbeen in vogue due to the growing demand for electromechanicalconverters with maximum possible efficiency. In this scene, the

switched reluctance machines have proven to be competitive.Comparative studies between these machines and the already

established induction machines can be easily found in the

scientific literature, but studies on various configurations of the

switched reluctance machines are not as widespread. This papershows the modeling, simulation and presents a comparative

study of two Switched Reluctance Machines to a single phase(6x6) and three phase (6x4). Aspects of construction, drive and

efficiency are discussed in order to find advantages and

disadvantages to each of these machines.

Key words

Single phase Switched Reluctance Machine, Three phaseSwitched Reluctance Machine, comparison of efficiency.

1. Introduction

The interest in Switched Reluctance Machines (SRM)

has getting a competitive market space. The industries arestill in majority, induction machines; some synchronous

machines that require a more rigorous maintenance dueto the presence of brushes and rings; and fewer appear

permanent magnet machines, losing competitiveness

because of the high cost of magnets.Several years ago, the obstacle to the interest in SRM

was the high cost of power electronics, nowadays is not a

problem due to the decrease in cost of microprocessorsand semiconductor switches [1].

Because there are no windings, brushes and magnets on

the rotor, the MRV in addition to having a simplestructure and be more robust, have lower cost of

manufacturing compared to other existing

machines[1].Windings concentrated only in the stator,phases considered magnetically independent of one

another, high torque per amp, high power density and

high effiency are other advantages of this machines.These advantages are leading more and more researchers

to study on their application as electric motor cars, small

domestic appliances, pumps, fans and others [2] [3] [4].But there are also unfavorable characteristics for use as

vibration and acoustic noise, yet several studies arealready being taken to reduce these problems [5].

One study, not very rencent,[7] compares SRM with the

indcuction machines.The objective proposed in this paper is the comparasion

of two SRM: a Single Phase Reluctance Motor

(SPSRW) and a Three Phase Reluctance Motor(TPSRW). The comparative study was carried out

through simulations and experimental results.

2. Structure of the machines

A Switched Reluctance Machine (SRM) is composed of a

laminated structure of double salience, simple, in which

the coils are restricted only to the stator teeth. Moreover,in the case of this work, each coil of a pair of teeth

opposite of the stator are a phase, as shown in Fig.1This figure shows a 6x4 SRW, in other words, a SRM

with six stator poles and four poles in the rotor. Because

each pair of poles in the stator form only one phase, thisis a Three-Phase Switched Reluctance Machine to

(TPSRM).

It also can be seen in Fig.1 the connection in series ofcoils of each pair of teeth opposite to form of mentioned

phase. Thus, the current that runs through these coils is

the same. Fig.1 shows the coils of only one phase, phaseA, but this configuration is repeated for the other two

phases. In this case, phase A is in its position of complete

alignment, this position was chosen to be the reference inthis work, ie, everytime the rotor is aligned with the

stator at a certain phase, it is said that the rotor is in zero

degree of that phase.

Fig.1 Cross Section of a TPSRM, showing the winding of the

phase A.

The Fig.2 shows a 6x6 SRM. As can be seen, what

distinguishes the two machines studied is only thenumber of teeth on the rotor and its drives. Again, each

pair of teeth opposite in the stator was connected in

series, but the energization of all coils will be held at thesame time, no delay between pulses, hence this

configuration of SRM , where the number of teeth rotor

is equal to the number of stator teeth, is called a Single-phase Switched Reluctance Machine (SPSRM). The

polarity of the windings of the other teeth are also

represented in Fig.2.

Fig.2 Cross Section of a SPSRM, showing a part winding of

the phase A.


14/24

3.Principles of Drive

For that each phase could be energized in the correct

moment is necessary to know, every moment, the rotor

position. For this, a positioning disc with optical sensorswas placed on the machine shaft as shown in Fig.3.

Fig.3 - Test bench showing SRM.

A-Three Phase Switched Reluctance Machine

To operate the TPSRM, was used a half-bridge converter.

This converter was chosen to be the most applied to drivethese machines [9].

Fig.4 shows a three phase half-bridge converter. In this

converter, the gate of each switch will be controlled bypositioning sensor, insomuch that each phase will be

energized when are completely disaligned (Fig. 5), at

this point the switch S1 and S2 will be closed and thecurrent coming from the source will flow through the coil

Phase A.

This energizing will have a duration of 30 degrees, iewhen is missing 15 degrees to the complete alignment

this phase will be turned off, turning off the switches S1and S2 (Fig. 6). At this point, the energy that was storedin the coil of phase A will be returned to the source,

establishing a freewheel with the diodes d1, d2 and

source.The name Switched Reluctance Machine is due to the

fact that his machine is always varying the reluctance. Inthe case of the 6x4 configuration the profile of reluctance

is 90 degrees. As is known, the reluctance is inversely

proportional to inductance. Figure 7 shows theinductance profile of a TPSRM

Fig.4 Three Phase Half-Bridge converter.

Fig.5 Phase A completely disaligned in a TPSRM.

Fig.6 Phase A missing 15 graus to aligned in a TPSRM.

Fig.7 Inductance profile of a TPSRM

B- Single Phase Switched Reluctance Machine

A Single Phase Switched Reluctance Machine (SPSRM)

is a machine where, typically, the number of teeth on the

rotor and stator are equal. Thus, there is no discrepancybetween the profile of inductance of each stator tooth.

Thus, these machines are seen as having only one phase.

It is common to find projects with 2x2, 4x4, 6x6 and 8x8poles on the stator and rotor, respectively [8]. Here, we

will analyze the machine with 6x6 configuration.

To operate this machine, again used a half-bridgeconverter, however, in this case, it is necessary just a

phase, as shown in Fig.8

Fig.8 Single-phase half-bridge converter.


15/24

Thus, when the rotor is in complete disalignment, 30

degrees of alignment position, the machine will be

energized (Fig. 9). At this point, switches S1 and S2 willbe closed and the current coming from the source will

flow through the coil of phase A.

This energizing will have a period of 15, ie, when ismissing 15 for the complete alignment the phase will be

turned off , turning off the switches S1 and S2 (Fig.10). At

this point, the energy that was stored in the coil of phaseA will be returned to the source. Establishing then a

freewheel with diodes d1, d2 and source.

Fig.9 Phase A completely disaligned in a SPSRM.

In the case of the 6x6 configuration the profile of

reluctance have 60. The Fig.11 shows the inductanceprofile of a SPSRM.

Fig.10 Phase A missing 5 to aligned in a SPSRM.

4. Mathematical Model

In an inductor the flux linkage by the coil () is

proportional to current (i) that runs through the coil andits inductance (L), have:

eRiv (3)

Where:

tRiv

w

w

O(4)

Fig.11 Inductance profile of a SPSRM

In this way, the voltage at the terminal of each phase

voltage have resistive in nature, due to resistance of the

wires; and inductive, due to the coils of each tooth, so:

eRiv (3)

Where:

tRiv

w

w

O(4)

As the flux linkage by the coils is proportional to the

inductance and current the equation solution (4) involvesa partial derivative, where firstlyL is considered constant

and i variable, and then i is consired constant and L

variable. As L is variable in relation to the rotor positionand the time, replacing equation (1) in equation (4) and

solving, have:

dt

dLi

t

iLRiv

T

Tw

w

w

w (5)

Conceptually, as the derivative of rotor angular position(T ) in relation to the time is the angular speed ():

TZ

w

w

w

w

Li

t

iLRiv (6)

Equation (6) describes the SRM electrically, but for a

complete modeling it is necessary other equation thatglimpse the machine mechanically.For this just do the

equalization the powers so that they are balanced. Thus

the energy entering the system will generate a

electromechanical torque ( emgT ). In result of this input

will be generated a mechanic torque ( mecT )on the system

output. Moreover, should be considered that this

machinhe should be able to win the rotational inertia of

the speed variation (dt

dJ

Y), and win the dynamic

friction of the bearings (Y

D ) [9].Thus:

dt

dJDTT mecemg

YY (7)

Where:

D is the coeficient of friction;

J is the moment of inertia.


16/24

The electromechanical torque can be shown

mathematically as :

Td

dLiTemg

2

2

1 (8)

Therefore the equation (6) and the equation (7),

together,describe in a complete ( electrically and

mechanically) a single-phase SRM, so this work willconsist on the comparison between a single-phase

machine and a three-phase machine which should berepresented in a matrix way so that all phases will beconsidered in the model then for the three-phase machine

have:

ww

ww

ww

T

YT

T

T

T

Y

3

2

1

333

222

111

3

2

1

332211

3

2

1

3

2

1

10000

0000000

000

000

01000

0

0000

0000

0000

0

I

I

I

JLiL

LiL

LiL

i

i

i

Dririri

R

R

R

T

v

v

v

mec

(9)

Where:

1r= Tww 1

1

L; 2r = Tw

w 22

L; 3r = Tw

w 33

L

1I is the derivative of the current of the phase 1 in time;



Y is the angular speed variation in time;

T is the variation of rotor position in time.

5. Simulations

The simulation tools have facilitated the development of

projects more accurate and cheaper in electric machines.

Parameters that were previously impossible to consider,are now easily predicted in the design of these machines

by simulation.

The simulations presented in this work were performedusing MATLAB SIMULINK.

Fig.12 Three-phase half-bridge converter.

Fig 12. Three-phase half-bridge converter.

Thus, each machine was fought degree in degree, and its

inductance was measured. The result can be seen in Fig.7

and Fig.11.

A.Simulation of a TPSRM

In the simulation of a MRVT were used some tools ready

of SIMULINK. The converter shown as electrical

diagram in Figure 4 can be seen in Fig.12, but inSIMULINK.

In this converter was used controlled a current source by

a signal in the simulation of the coils.In addition to the converter is another block that

simulates the mechanical and electrical behavior of the

machine. This block can be seen in Figure 13. In thisblock were set as input, the voltage of the three phases

and the load on the motor shaft. The load may have a

quadratic behavior with respect to angular speed (),characteristic of typical loads such as fans for example or

be a constant load.

The control signal from the current source of theconverter is the phase current which is the output from

block Fig.13.

The Fig.13 is simply an S-function that solves theequation of state (9).

Fig.13 - Resolution of equation (9) in SIMULINK.

Input parameters of the Fig.13 are taken from the simulation of

half-bridge converter in Fig.12.

B. Simulation of a SPSRM

The simulation of SPSRM, of course, was conducted the

same way as was done for TPSRM.Thus, Fig.14 shows the half-bridge converter which is

electrically shown in Fig.8, but in the SIMULINK.

Again, the blocks of Fig 14 and Fig.15 form a closedsystem because the output of Fig 15 (currents) are the

input in Fig.14. And the output of Fig 14 (a voltage Va)

is input in Fig 15.Fig.15 is merely the solution of equations (7) and (8) of

the mathematical model.

Fig.14 - Single-phase half-bridge converter.


17/24

Fig.15 - Resolution of equation (7) and (8) in SIMULINK.

5. Results of Simulations

The simulations were done with machines fed with 311V with rated load on their axes, with the aim of analyzing

parameters such as wave form current on the phase,

variations speed in machine and efficiency.

A. Waveforms current on the phase

The waveforms of the currents of the phases in the two

machines can be seen in Fig.16 and Fig.17.Fig. 16 shows the waveform of the current arising from

the three phases of TPSRM.Fig. 17 shows the waveform of current in a SPSRM.

These figures make it clear that the three-phase machine

has a behavior more constant, because the phase arepowered separately and there is always an active phase.

In the SPSRM exists an interval where the machine is

totally turned off, this would provide a more ficklebehavior.

Fig.16 - Waveform of current in a TPSRM

Fig.17 - Waveform of current in a SPRM.

B. Speed of the machines

The SRM are known to have problems in their oscillationparameters, including in the generated torque and in the

speed.

The TPSRM showed a variation of speed sharp less thanpresented on the SPSRM. The range was of 127 rad / s to

119 rad / s with speed around 1200 rpm desired for this

machine.However, SPSRM presented a disastrous change of

speed, getting between 40 rad / s and 200 rad / s. Since

then this characteristic a huge disadvantage for this typeof machine (6x6 MRVM 1 hp) when is driven in the way

it was done in this work.

C. Effiency of the machines

Both machines showed good results regarding theefficiency item. TPSRM showed 91.5% and 81%

SPSRM.

D. Converters

The single-phase converter of the SPSRM is simpler andcheaper than the converter of the MRVT by being

composed of only one arm, and thus need only one

switch to be operated.

6. Experimental Results

To perform comparative tests between the two

configurations of SRM was mounted a bench containingtwo SRM, a three-phase induction machine (MIT) and a

Half-bridge converter, as shown in fig.3. A MIT was

used as a load. For this, a direct current was applied inphases in order to generate a fixed magnetic field and so

when the SRM are operated and make the MIT turning, a

power appears making that this works as a load.In the first test the TPSRM was fed with a voltage of 200

V on the dc bus and the current values was incremented

one to one starting from zero (empty machine) and go upto 7 A (Maximum load by MIT).

The graph in Fig. 18 shows the decrease of speed and

increase of the power when the load on the shaft of theTPSRM increase.

0 1 2 3 4 5 6 7400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

Current in ampre (Load)

Power(W)

andspeed(rpm)

Fig.18 Power (- - - -) and Speed (_____) in a TPSRM.

Then the same test was repeated for SPSRM, the result is

shown in Fig.19.


18/24

0 1 2 3 4 5 6 71000

1200

1400

1600

1800

2000

2200

2400


Power(W)andspeed(rpm)

Fig.19 Power (- - - -) and Speed (_____) in a SPSRM.

These two figures (Fig. 18 and Fig.19) show that TPSRM

when fed with constant voltage of 200 V always keep a

faster speed than SPSRM, despite its derivative of speedin relation to the load to be greater. Moreover, the input

power required by SPSRM is always greater than the

TPSRM.However, the analysis of input power was compromised

in this test, because despite the magnetic power generated

at MIT have relation to the current (x-axis of figures) it isalso related to the speed of the machines which, as has

been shown is different. So this first test reveals only the

behavior of the machines for their speed when there is aincrease in the load and voltage control in the dc bus.

Thus, takes necessary a second test in which speed inSRM were kept constant at 1200 rpm (nominal speed)

and the current MIT (load) was being added. The result

is shown in Fig. 20.

0 1 2 3 4 5 6 70

500

1000

1500

2000

2500


Power(W)

Fig.20 Input Power in a SPSRM (- - - -) and Input Power in a

TPSRM (_____).

In Fig.20 shows that when subjected to the same load, theSPSRM requires a power input more than four times the

input power required by a TPSRM. When these are

operated the way it was done in this work.

8. Conclusion

Both machines have very similar aspects of construction,

so there is no way to elect between the two that is better

in this item.TPSRM machine proved to be a more constant, with

fewer variations in speed. This did not occur with

SPSRM which was very swinging.The converter SPSRM is simpler and inexpensive,

requiring only two switch to operate it, but these switch

must support peak currents greater than those that occur

in TPSRM. In TPSRM is necessary to use six switchs.

In the simulations, the TPSRM showed a yield of around91.5% and SPSRM showed a yield around 81%. The

simulations were performed using nominal values of

input voltage and load.The experiments were performed at various points of

operation where the increase in load forced the machine

to slow down, increasing its power. This test showed thatwith the same dc bus voltage the TPSRM work with

greater speed and requiring less power input.

Furthermore, when subjected to the same load, theTPSRM needed less input power (4 times less).

So for all these factors it is concluded that the TPSRM

when operated in the same way as was done here, and farmore advantageous than SPSRM.

Acknowledgement

The authors thank the Federal University of Uberlandia

and the PUC-GO, for multiple collaborations. And toCAPES for the scholarships.

References

[1] K.A, Joseph, Opportunities for switched reluctancemotor-drives, Pulp and Paper Industry TechnicalConference, 1999. Conference Record of 1999 Annual,1999,pp.42-47.

[2] H. Chen, Y. Guo, Green methodologies and technologiesof switched reluctance motor drive.,Proceedings of the 3World Congress on Intelligent Control and Automation,vol 5,2000, pp.3717-3720.

[3] L. Chang, Switched Reluctance Motors: Small Motors ofthe Next Generations for Automobiles?, VehicularTechnology Conference ,vol 5, 2003, pp.3316-3320.

[4] H. Chen, Implementation of a Three-Phase SwitchedReluctance Generator System for Wind PowerApplications, Electromagnetic Launch Technology,2008

14

th

Symposium on, 2008, pp.1-6.K.[5] C.Yookpakdee, N.H. Fuenqwarodsakul, Variable SpeedSwitched Reluctance Drive for a Low Cost Applications,

Electrical Engineering/Electronic, Computer,Telecommunications and Information Technology,2009,

ECTI-CON,2009.6th International Conference on, vol 1,2009, pp.262-265.

[6] S. Jose, E.S. Antonio, C. Maria Rosario, Design of asystem for analysis and monitoring of vibrations in LinearSwitched Reluctance machines, MELECON 2010-201015th IEEE Mediterranean Electrotechnica Conference,2010, pp.768-773.

[7] M.R. Harris, T.J.E. Miller, Comparison of Design andPerformance Parameters in Switched Reluctance andInduction Motors, Electrical Machines and Drives, 1989.

Fourth International Conference on, 1989, pp.303-307.Y[8] bKRISHNAN, Ramu, Switched Reluctance Motors

Drives. CRC Press, 2001.

[9] S V. F, Augusto, Modelagem, Construo, Testes eAnalise de Desempenho de um Gerador RelutnciaChaveado, Tese de Doutorado, Universidade Federal deUberlndia, Abril,2008.


19/24

Modeling, Simulation and a Comparative study between a Single-phase Switched

Reluctance Machine (6x6) and a Three-phase Switched Reluctance Machine

Dias, R. J., Andrade, D.A., Cabral, L.G., Silveira, A.W.F.V., Silveira, A.F.V., Gomes, L.C., Bissochi, C. A

Laboratrio de acionamentos eltricos, Depto. de Engenharia Eltrica, Universidade Federal de Uberlndia.

E-mails: [email protected], [email protected]

Abstract. The comparative study of electric machines hasbeen in vogue due to the growing demand for electromechanical

converters with maximum possible efficiency. In this scene, theswitched reluctance machines have proven to be competitive.Comparative studies between these machines and the already

established induction machines can be easily found in the

scientific literature, but studies on various configurations of the

switched reluctance machines are not as widespread.This papershows the modeling, simulation and presents a comparativestudy of two Switched Reluctance Machines to a single phase

(6x6) and three phase (6x4).Aspects of construction, drive and

efficiency are discussed in order to find advantages anddisadvantages to each of these machines.

Key words

Single phase Switched Reluctance Machine, Three phase

Switched Reluctance Machine, comparison of efficiency.

1. Introduction

The interest in Switched Reluctance Machines (SRM)

has getting a competitive market space.The industries are

still in majority, induction machines; some synchronousmachines that require a more rigorous maintenance due

to the presence of brushes and rings; and fewer appearpermanent magnet machines, losing competitiveness

because of the high cost of magnets.

Several years ago, the obstacle to the interest in SRMwas the high cost of power electronics, nowadays is not a

problem due to the decrease in cost of microprocessors

and semiconductor switches [1].

Because there are no windings, brushes and magnets on

the rotor, the MRV in addition to having a simple

structure and be more robust, have lower cost of

manufacturing compared to other existing

machines[1].Windings concentrated only in the stator,

phases considered magnetically independent of one

another, high torque per amp, high power density and

high effiency are other advantages of this machines.These advantages are leading more and more researchersto study on their application as electric motor cars, small

domestic appliances, pumps, fans and others [2] [3] [4].

But there are also unfavorable characteristics for use as

vibration and acoustic noise, yet several studies are

already being taken to reduce these problems [5].

One study, not very rencent,[7] compares SRM with the

indcuction machines.

The objective proposed in this paper is the comparasion

of two SRM: a Single Phase Reluctance Motor

(SPSRW) and a Three Phase Reluctance Motor

(TPSRW). The comparative study was carried out

through simulations and experimental results.

2. Structure of the machines

A Switched Reluctance Machine (SRM) is composed of a

laminated structure of double salience, simple, in which

the coils are restricted only to the stator teeth. Moreover,

in the case of this work, each coil of a pair of teeth

opposite of the stator are a phase, as shown in Fig.1

This figure shows a 6x4 SRW, in other words, a SRM

with six stator poles and four poles in the rotor.

Becauseeach pair of poles in the stator form only one phase, this

is a Three-Phase Switched Reluctance Machine to

(TPSRM).

It also can be seen in Fig.1 the connection in series of

coils of each pair of teeth opposite to form of mentioned

phase.Thus, the current that runs through these coils is

the same.Fig.1 shows the coils of only one phase, phase

A, but this configuration is repeated for the other two

phases.In this case, phase A is in its position of completealignment, this position was chosen to be the reference in

this work, ie, everytime the rotor is aligned with the

stator at a certain phase, it is said that the rotor is in zero

degree of that phase.

Fig.1 Cross Section of a TPSRM, showing the winding of thephase A.

The Fig.2 shows a 6x6 SRM. As can be seen, what

distinguishes the two machines studied is only the

number of teeth on the rotor and its drives. Again, each

pair of teeth opposite in the stator was connected inseries, but the energization of all coils will be held at the

same time, no delay between pulses, hence this

configuration of SRM , where the number of teeth rotor

is equal to the number of stator teeth, is called a Single-

phase Switched Reluctance Machine (SPSRM). The

polarity of the windings of the other teeth are also

represented in Fig.2.


20/24

Fig.2 Cross Section of a SPSRM, showing a part winding of

the phase A.

3.Principles of Drive

For that each phase could be energized in the correct

moment is necessary to know, every moment, the rotor

position. For this, a positioning disc with optical sensors

was placed on the machine shaft as shown in Fig.3.

Fig.3 - Test bench showing SRM.

A-Three Phase Switched Reluctance Machine

To operate the TPSRM, was used a half-bridge converter.

This converter was chosen to be the most applied to drive

these machines [9].

Fig.4 shows a three phase half-bridge converter. In this

converter, the gate of each switch will be controlled by

positioning sensor, insomuch that each phase will beenergized when are completely disaligned (Fig. 5), at

this point the switch S1 and S2 will be closed and the

current coming from the source will flow through the coil

Phase A.

This energizing will have a duration of 30 degrees, ie

when is missing 15 degrees to the complete alignmentthis phase will be turned off, turning off the switches S1

and S2 (Fig. 6). At this point, the energy that was stored

in the coil of phase A will be returned to the source,

establishing a freewheel with the diodes d1, d2 and

source.

The name Switched Reluctance Machine is due to the

fact that his machine is always varying the reluctance. In

the case of the 6x4 configuration the profile of reluctance

is 90 degrees. As is known, the reluctance is inverselyproportional to inductance. Figure 7 shows the

inductance profile of a TPSRM

Fig.4 Three Phase Half-Bridge converter.

Fig.5 Phase A completely disaligned in a TPSRM.

Fig.6 Phase A missing 15 graus to aligned in a TPSRM.

Fig.7 Inductance profile of a TPSRM

B- Single Phase Switched Reluctance Machine

A Single Phase Switched Reluctance Machine (SPSRM)

is a machine where, typically, the number of teeth on therotor and stator are equal. Thus, there is no discrepancy

between the profile of inductance of each stator tooth.

Thus, these machines are seen as having only one phase.

It is common to find projects with 2x2, 4x4, 6x6 and 8x8

poles on the stator and rotor, respectively [8]. Here, we

will analyze the machine with 6x6 configuration.

To operate this machine, again used a half-bridge

converter, however, in this case, it is necessary just aphase, as shown in Fig.8


21/24

Fig.8 Single-phase half-bridge converter.

Thus, when the rotor is in complete disalignment, 30

degrees of alignment position, the machine will beenergized (Fig. 9). At this point, switches S1 and S2 will

be closed and the current coming from the source will

flow through the coil of phase A.

This energizing will have a period of 15, ie, when is

missing 15 for the complete alignment the phase will be

turned off , turning off the switches S1 and S2 (Fig.10). At

this point, the energy that was stored in the coil of phase

A will be returned to the source. Establishing then a

freewheel with diodes d1, d2 and source.

Fig.9 Phase A completely disaligned in a SPSRM.

In the case of the 6x6 configuration the profile of

reluctance have 60. The Fig.11 shows the inductance

profile of a SPSRM.

Fig.10 Phase A missing 5 to aligned in a SPSRM.

4. Mathematical Model

In an inductor the flux linkage by the coil () is

proportional to current (i) that runs through the coil and

its inductance (L), have:

eRiv += (3)

Where:

tRiv

+=

(4)

Fig.11 Inductance profile of a SPSRM

In this way, the voltage at the terminal of each phase

voltage have resistive in nature, due to resistance of the

wires; and inductive, due to the coils of each tooth, so:

eRiv += (3)

Where:

tRiv

+=

(4)

As the flux linkage by the coils is proportional to the

inductance and current the equation solution (4) involvesa partial derivative, where firstlyL is considered constant

and i variable, and then i is consired constant and L

variable. As L is variable in relation to the rotor position

and the time, replacing equation (1) in equation (4) and

solving, have:

dt

dLi

t

iLRiv

+

+= (5)

Conceptually, as the derivative of rotor angular position

( ) in relation to the time is the angular speed ():

+

+=

Li

t

iLRiv (6)

Equation (6) describes the SRM electrically, but for a

complete modeling it is necessary other equation that

glimpse the machine mechanically.For this just do the

equalization the powers so that they are balanced. Thus

the energy entering the system will generate a

electromechanical torque ( emgT ). In result of this input

will be generated a mechanic torque ( mecT )on the system

output. Moreover, should be considered that thismachinhe should be able to win the rotational inertia of

the speed variation (dt

dJ

), and win the dynamic

friction of the bearings (

D ) [9].Thus:

dt

dJDTT

mecemg

++= (7)

Where:

Dis the coeficient of friction;

J is the moment of inertia.


22/24

The electromechanical torque can be shown

mathematically as :

d

dLiTemg

2

2

1= (8)

Therefore the equation (6) and the equation (7),

together,describe in a complete ( electrically and

mechanically) a single-phase SRM, so this work will

consist on the comparison between a single-phase

machine and a three-phase machine which should berepresented in a matrix way so that all phases will be

considered in the model then for the three-phase machine

have:

+

=

&

&

&

&

&

3

2

1

333

222

111

3

2

1

332211

3

2

1

3

2

1

10000

0000

000

000

000

01000

0

0000

0000

0000

0

I

I

I

J

LiL

LiL

LiL

i

i

i

Dririri

R

R

R

T

v

v

v

mec

(9)

Where:

1r= 1

1

L; 2r =

22

L; 3r =

33

L

1I& is the derivative of the current of the phase 1 in time;



& is the angular speed variation in time;

& is the variation of rotor position in time.

5. Simulations

The simulation tools have facilitated the development of

projects more accurate and cheaper in electric machines.Parameters that were previously impossible to consider,

are now easily predicted in the design of these machines

by simulation.

The simulations presented in this work were performed

using MATLAB SIMULINK.

Fig.12 Three-phase half-bridge converter.

Fig 12. Three-phase half-bridge converter.

Thus, each machine was fought degree in degree, and its

inductance was measured. The result can be seen in Fig.7

and Fig.11.

A.Simulation of a TPSRM

In the simulation of a MRVT were used some tools ready

of SIMULINK. The converter shown as electrical

diagram in Figure 4 can be seen in Fig.12, but in

SIMULINK.

In this converter was used controlled a current source by

a signal in the simulation of the coils.

In addition to the converter is another block thatsimulates the mechanical and electrical behavior of the

machine. This block can be seen in Figure 13. In thisblock were set as input, the voltage of the three phases

and the load on the motor shaft. The load may have aquadratic behavior with respect to angular speed (),

characteristic of typical loads such as fans for example or

be a constant load.

The control signal from the current source of the

converter is the phase current which is the output from

block Fig.13.

The Fig.13 is simply an S-function that solves the

equation of state (9).

Fig.13 - Resolution of equation (9) in SIMULINK.

Input parameters of the Fig.13 are taken from the simulation of

half-bridge converter in Fig.12.

B. Simulation of a SPSRM

The simulation of SPSRM, of course, was conducted the

same way as was done for TPSRM.

Thus, Fig.14 shows the half-bridge converter which is

electrically shown in Fig.8, but in the SIMULINK.

Again, the blocks of Fig 14 and Fig.15 form a closed

system because the output of Fig 15 (currents) are the

input in Fig.14. And the output of Fig 14 (a voltage Va)

is input in Fig 15.

Fig.15 is merely the solution of equations (7) and (8) ofthe mathematical model.

Fig.14 - Single-phase half-bridge converter.


23/24

Fig.15 - Resolution of equation (7) and (8) in SIMULINK.

5. Results of Simulations

The simulations were done with machines fed with 311

V with rated load on their axes, with the aim of analyzing

parameters such as wave form current on the phase,

variations speed in machine and efficiency.

A. Waveforms current on the phase

The waveforms of the currents of the phases in the two

machines can be seen in Fig.16 and Fig.17.Fig. 16 shows the waveform of the current arising from

the three phases of TPSRM.

Fig. 17 shows the waveform of current in a SPSRM.

These figures make it clear that the three-phase machine

has a behavior more constant, because the phase are

powered separately and there is always an active phase.In the SPSRM exists an interval where the machine istotally turned off, this would provide a more fickle

behavior.

Fig.16 - Waveform of current in a TPSRM

Fig.17 - Waveform of current in a SPRM.

B. Speed of the machines

The SRM are known to have problems in their oscillation

parameters, including in the generated torque and in the

speed.

The TPSRM showed a variation of speed sharp less than

presented on the SPSRM. The range was of 127 rad / s to

119 rad / s with speed around 1200 rpm desired for this

machine.

However, SPSRM presented a disastrous change ofspeed, getting between 40 rad / s and 200 rad / s. Since

then this characteristic a huge disadvantage for this type

of machine (6x6 MRVM 1 hp) when is driven in the way

it was done in this work.

C. Effiency of the machines

Both machines showed good results regarding the

efficiency item. TPSRM showed 91.5% and 81%

SPSRM.

D. Converters

The single-phase converter of the SPSRM is simpler andcheaper than the converter of the MRVT by being

composed of only one arm, and thus need only one

switch to be operated.

6. Experimental Results

To perform comparative tests between the two

configurations of SRM was mounted a bench containing

two SRM, a three-phase induction machine (MIT) and a

Half-bridge converter, as shown in fig.3. A MIT was

used as a load. For this, a direct current was applied in

phases in order to generate a fixed magnetic field and sowhen the SRM are operated and make the MIT turning, a

power appears making that this works as a load.In the first test the TPSRM was fed with a voltage of 200

V on the dc bus and the current values was incremented

one to one starting from zero (empty machine) and go upto 7 A (Maximum load by MIT).

The graph in Fig. 18 shows the decrease of speed and

increase of the power when the load on the shaft of the

TPSRM increase.

0 1 2 3 4 5 6 7400

600

800

1000

1200

1400

1600

1800

2000

2200

2400


Power(W)

andspeed(rpm)

Fig.18 Power (- - - -) and Speed (_____) in a TPSRM.

Then the same test was repeated for SPSRM, the result is

shown in Fig.19.


24/24

0 1 2 3 4 5 6 71000

1200

1400

1600

1800

2000

2200

2400


Power(W)andspeed(rpm)

Fig.19 Power (- - - -) and Speed (_____) in a SPSRM.

These two figures (Fig. 18 and Fig.19) show that TPSRM

when fed with constant voltage of 200 V always keep a

faster speed than SPSRM, despite its derivative of speed

in relation to the load to be greater.Moreover, the inputpower required by SPSRM is always greater than the

TPSRM.

However, the analysis of input power was compromised

in this test, because despite the magnetic power generated

at MIT have relation to the current (x-axis of figures) it isalso related to the speed of the machines which, as has

been shown is different. So this first test reveals only the

behavior of the machines for their speed when there is a

increase in the load and voltage control in the dc bus.

Thus, takes necessary a second test in which speed in

SRM were kept constant at 1200 rpm (nominal speed)

and the current MIT (load) was being added. The result

is shown in Fig. 20.

0 1 2 3 4 5 6 70

500

1000

1500

2000

2500


Power(W)

Fig.20 Input Power in a SPSRM (- - - -) and Input Power in a

TPSRM (_____).

In Fig.20 shows that when subjected to the same load, the

SPSRM requires a power input more than four times theinput power required by a TPSRM. When these are

operated the way it was done in this work.

8. Conclusion

Both machines have very similar aspects of construction,

so there is no way to elect between the two that is better

in this item.

TPSRM machine proved to be a more constant, with

fewer variations in speed. This did not occur with

SPSRM which was very swinging.

The converter SPSRM is simpler and inexpensive,

requiring only two switch to operate it, but these switch

must support peak currents greater than those that occur

in TPSRM. In TPSRM is necessary to use six switchs.

In the simulations, the TPSRM showed a yield of around

91.5% and SPSRM showed a yield around 81%. The

simulations were performed using nominal values of

input voltage and load.

The experiments were performed at various points of

operation where the increase in load forced the machine

to slow down, increasing its power.This test showed thatwith the same dc bus voltage the TPSRM work withgreater speed and requiring less power input.

Furthermore, when subjected to the same load, the

TPSRM needed less input power (4 times less).

So for all these factors it is concluded that the TPSRM

when operated in the same way as was done here, and far

more advantageous than SPSRM.

Acknowledgement

The authors thank the Federal University of Uberlandia

and the PUC-GO, for multiple collaborations. And to

CAPES for the scholarships.

References

[1] K.A, Joseph, Opportunities for switched reluctancemotor-drives, Pulp and Paper Industry TechnicalConference, 1999. Conference Record of 1999 Annual,1999,pp.42-47.

[2] H. Chen, Y. Guo, Green methodologies and technologiesof switched reluctance motor drive., Proceedings of the 3World Congress on Intelligent Control and Automation,vol 5,2000, pp.3717-3720.

[3] L. Chang, Switched Reluctance Motors: Small Motors ofthe Next Generations for Automobiles?, VehicularTechnology Conference ,vol 5, 2003, pp.3316-3320.

[4] H. Chen, Implementation of a Three-Phase SwitchedReluctance Generator System for Wind PowerApplications, Electromagnetic Launch Technology,2008

14

th

Symposium on, 2008, pp.1-6.K.[5] C.Yookpakdee, N.H. Fuenqwarodsakul, Variable SpeedSwitched Reluctance Drive for a Low Cost Applications,

Electrical Engineering/Electronic, Computer,Telecommunications and Information Technology,2009,

ECTI-CON,2009.6th International Conference on, vol 1,2009, pp.262-265.

[6] S. Jose, E.S. Antonio, C. Maria Rosario, Design of asystem for analysis and monitoring of vibrations in LinearSwitched Reluctance machines, MELECON 2010-201015th IEEE Mediterranean Electrotechnica Conference,2010, pp.768-773.

[7] M.R. Harris, T.J.E. Miller, Comparison of Design andPerformance Parameters in Switched Reluctance andInduction Motors, Electrical Machines and Drives, 1989.Fourth International Conference on, 1989, pp.303-307.Y

[8] bKRISHNAN, Ramu, Switched Reluctance Motors

Drives. CRC Press, 2001.

[9] S V. F, Augusto, Modelagem, Construo, Testes eAnalise de Desempenho de um Gerador RelutnciaChaveado, Tese de Doutorado, Universidade Federal deUberlndia, Abril,2008.

Artigo Maquina Relutancia Variavel

Documents

Transcript of Artigo Maquina Relutancia Variavel