Development of Analytical Models for Switched Reluctance Machine and their Validation

Transcription

1 J Eectr Eng Techno.2015; 10(?): ISSN(Prnt) ISSN(Onne) Deveopment of Anaytca Modes for Swtched euctance Machne and ther Vadaton. Jayapragash and C. Cheamuthu* Abstract Ths paper presents anayss of Swtched euctance Machne (SM) usng Geometry Based Anaytca Mode (GBAM), Fnte Eement Anayss (FEA) and Fourer Seres Mode (FSM) wth curve fttng technque. Further a Transent Anayss (TA) technque s proposed to corroborate the anayss. The man am of ths paper s to gve n depth procedure n deveopng a Geometry Based Anaytca Mode of Swtched euctance Machne whch s very accurate and smpe. The GBAM s deveoped for the specfcatons obtaned from the manufacturer and magnetzng characterstc of the matera used for the constructon. Precse vaues of the parameters ke Magneto Motve Force (MMF), fux nkage, nductance and torque are obtaned for varous rotor postons takng nto account the Frngng Effect (FE). The FEA mode s deveoped usng MagNet7.1.1 for the same machne geometry used n GBAM and the resuts are compared wth GBAM. Further another anaytca mode caed Fourer Seres Mode s deveoped to justfy the accuracy of the resuts obtaned by the methods GBAM and FEA mode. A prototype of mcrocontroer based SM drve system s constructed for vadatng the anayss and the resuts are reported. Keywords: Swtched euctance Machne (SM), Geometry Based Anaytc Mode (GBAM), Frngng Effect (FE), Fnte Eement Anayss (FEA), Fourer Seres Mode (FSM) & Transent Anayss (TA) 1. Introducton Besdes beng smpe and robust, the absence of wndngs and magnets on the rotor n a Swtched euctance Machne (SM) makes t sutabe for varabe speed appcatons [1]. The SM s hghy non-near n nature due to ts douby saent structure, magnetc characterstcs and couped reatonshp among rotor poston, phase current and fux nkage [2]. As the near mode of the machne s unsutabe for hgh performance appcatons, varous technques are deveoped to ncorporate the non-neartes n the machne. Snce the fux mode proposed by A. adun [3] coud not be nverted to express stator current as a functon of fux nkage and poston, the mode was found to be of tte use further for rea tme mpementaton. A non-near anaytca mode of SM based on the exstng machne geometry and matera propertes usng fourer seres was presented by Ahmed Kha et a [4, 5]. Ths mode nvoved compex procedure and more nformaton about the matera. Later, Wen Dng and Deang Lang proposed a smpe and rapd non-near mode of ntegrated SS/G to characterze the nherent reatonshp among phase currents, rotor poston, fux nkage and torque [6]. In ths mode, Correspondng Author: Dept. of Eectrca and Eectroncs Engneerng, St. Joseph s Insttute of Technoogy, Inda. (r.jayapragash@ gma.com) * Dept. of Eectrca and Eectroncs Engneerng,.M.K. Engneerng Coege, Inda. (magud60@hotma.com) eceved: January 5, 2014; Accepted: December 2, 2014 ony the frst fve components of the Fourer Seres descrbng the current n terms of arc tangent functon are consdered to express the whoe fux nkage mode ψ(θ,) of SS/G. Anaytca mode of SM consderng mutua nductance was presented by D.N. Essah et a [7]. Ths mode was deveoped by consderng the mutua nductance between the phases aone. Comparson of dfferent anaytca modes was done by Shoujun Song et a [8]. Non-near modeng of SM usng Artfca Integence (AI) technque was addressed by T. Lachman et a [9]. The accuracy of the mode deveoped usng AI technques many depends on the amount of the gven fux nkagecurrent-poston data and the pror number of fuzzy rues or the expermenta knowedge. Measurement of fux nkage and nductance of SM usng numerca ntegraton technque reported by akesh Saxena et a [10] was proved to be aborous and reatvey dffcut to mpement the contro agorthms. Hujun Zhou, Wen Dng and Zhenmn Yu reported a non-near mode of SM usng fourer seres mode [13]. To deveop ths mode t s mandatory to use the data obtaned ether from FEA or from expermenta set-up. Whe anayss of SM parameters usng dfferent methods have been reported n the past, the performance anayss of SM consderng saturaton and frngng effect have not yet been dscussed. Though many methods were dscussed for obtanng the nductance profe of the SM, those technques nvoved 30 Copyrght c The Korean Insttute of Eectrca Engneers Ths s an Open-Access artce dstrbuted under the terms of the Creatve Commons Attrbuton Non-Commerca Lcense ( censes/by-nc/3.0/)whch permts unrestrcted non-commerca use, dstrbuton, and reproducton n any medum, provded the orgna work s propery cted.

2 . Jayapragash and C. Cheamuthu compex computatona procedures as we as requres data ether from FEA mode or from expermenta set-up. It makes the steps nvoved more cumbersome and consumes more tme for computaton. More assumptons are made for anayss and mode deveopment, therefore accurate resuts may not be obtaned. In vew of ths, a Geometry Based Anaytca Mode (GBAM) s deveoped from machne geometry and magnetzaton characterstc of the matera used by takng the frngng effect nto account. Aso a prototype SM drve mode s fabrcated and the nductance profe s obtaned usng a smpe technque caed Transent Anayss (TA) technque. Ths paper s organzed nto sx sectons. The varous steps nvoved n deveopng the GBAM are dscussed n secton 2. Whe secton 3 brefs the Fnte Eement Anayss (FEA) mode of SM, secton 4 deas wth comparson of both GBAM and FEA modes. FSM deveopment and ts comparson wth FEA mode s dscussed n Secton 5. Secton 6 expans the mpementaton of expermenta mode, resuts and vadaton. 2. Geometry Based Anaytca Mode of SM The detaed procedure for deveopng the GBAM s descrbed beow. 2.1 Cacuaton of agned nductance The nductance n a magnetc crcut s cacuated usng the expresson H s the magnetc fed ntensty. Vaues of B and H at each part of the machne are to be known to cacuate ther reuctances. Accordng to Ampere s crcuta aw, MMF = NI = ( H) (4) Phase wndng of the SM s dvded nto two cos, wth each co havng N turns paced on the dametrcay opposte poes and carryng a current of I Amperes. Therefore the tota MMF of the magnetc crcut s expressed as MMF = 2NI (5) The fux path of the machne at the agned poston s shown n Fg. 1. The path foowed by the fux nes shown n Fg. 1 s consdered for deveopng the equvaent magnetc crcut at the agned poston and t s shown n Fg. 2 Fux nes are cosed nes and compete ts path through stator yoke, stator poe, ar gap, rotor poe and rotor yoke. Fux nes cross the stator poe, ar gap and rotor poe twce. The equaton to obtan tota mmf n terms of magnetc fed ntensty (H) and ength of the fux path () s expressed as 2NI = H + 2H + 2H + 2H + H (6) sy sy sp sp g g rp rp ry ry where H sy, H sp, H g, H rp, H ry are the magnetc fed ntenstes at 2 N L = (1) where N s the number of turns/poe s the summaton of reuctances of dfferent parts of the magnetc crcut. euctance s expressed as = (2) ( μ A) where s the ength of the magnetc path µ s the permeabty of the medum A s the cross sectona area of the fux path. Fg. 1. Fux pattern at the agned poston For ar µ = 1.256e -6, but for magnetc matera t s not constant and depends on B and H. Therefore expresson for reuctance s expressed as H = (3) BA where B s the fux densty Fg. 2. Equvaent magnetc crcut at the agned poston 31

3 Deveopment of Anaytca Modes for Swtched euctance Machne and ther Vadaton stator yoke, stator poe, ar gap, rotor poe and rotor yoke respectvey. sy, sp, g, rp, ry are ther correspondng engths. sy S =Π yr + S 2 yor (7) Fux densty at stator poe s expressed as B sp φ = A sp where A sp = Area of stator poe and t s gven as (15) where S yr =Inner radus of stator yoke S yor =Outer radus of stator yoke = S ; Stator poe heght (8) sp ph ry =Π yr + 2 yor where yr =Inner radus of rotor yoke yor =Outer radus of rotor yoke rp ph (9) = ; otor poe heght (10) The path of the ar gap through whch fux competes ts path s a compex one and determnng ength of the ar gap s dffcut. As H g g = Φ g g, nstead of usng H g g n the Eq. (6) Φ g g s used where Φ g s the fux through the ar gap and g s the reuctance of the ar gap. Procedure to obtan g s expaned n secton 2.2. For ar µ = 1.256e -6 s a constant. Therefore reuctance, = s found wthout the knowedge of B and H. ( μ A) The new equaton to cacuate tota mmf s expressed as 2NI = H + 2H + 2φ + 2H + H (11) sy sy sp sp g g rp rp ry ry Intay the net fux set up n the machne s assumed as ow as 1e -8 and as ths s the fux crossng the ar gap, Φ g =Φ. The fux carred by the dfferent parts of the machne vares. Based on the amount of fux, the fux densty at that part s cacuated usng the formua Asp = Spw * L (16) where S pw =Stator poe wdth otor yoke carres ony haf the fux. Therefore fux densty at rotor yoke (B ry ) s represented as B ry φ = 2A ry Fux densty at rotor poe s expressed as B rp φ = A rp where A rp = Area of rotor poe and t s gven as (17) (18) Arp = pw * L (19) where pw =otor poe wdth For the known B, correspondng H s obtaned by reverse mappng from the B-H data of M19 and t s shown n Fg. 3. If the obtaned B s greater than the data wth us, t s mted to the maxmum B. Thus H and for dfferent parts are obtaned and Φ g g s aso known. Substtutng these vaues n Eq. (11), eft hand sde vaue s compared wth rght hand sde vaue. The fux s graduay ncreased t the error s ess than 1%. B = φ / A (12) Stator yoke carres ony haf the fux. Therefore fux densty at stator yoke (B sy ) s represented as B sy φ = 2A sy where A sy = Area of stator yoke and t s gven as where S yt =Stator yoke thckness L=Stack ength (13) A = S * L (14) sy yt Fg. 3. B-H curve of M-19 stee 2.2 Ar gap reuctance at the agned poston The fux buges n the ar gap causng frngng effect and as the dfference n the wdth of stator and rotor poe wdth s very sma the boundary can be consdered as crcuar wth dameter equa to the ar gap. Top vew of the agned poston of stator and rotor poe s as shown n the Fg J Eectr Eng Techno.2015;10(1): 30-40

4 . Jayapragash and C. Cheamuthu euctance of rotor poe s wrtten as Fg. 4. Top vew of the agned poston rp euctance of rotor yoke s ry Hrprp = B rp A rp Hryry = B ry A ry (23) (24) Fg. 5. Increment n the wdth To cacuate the ar gap reuctance, the ar gap s spt nto 100 vertca ayers. The area of each ayer graduay ncreases due to ncrease n the wdth and heght of the ar gap. As shown n the Fg. 5, the ncrement n the wdth for any ange Φ w be ( g /2) snφ. But two hemspherca regons are present so the tota ncrement aong the wdth or heght of the ar gap s g snφ. The tota ange s spt nto 100 parttons of each. Substtutng the reuctance of varous parts n the fundamenta expresson (1), the resutant expresson to obtan reuctance as a functon of current s gven by 4NN La () = 2 sp 2g 2rp ry sy (25) The resut obtaned by sovng the Eq. (25) s shown n Fg. 6. The phase nductance s droopng when the current through the wndng ncreases. g Length of ndvdua ayer = 100 Wdth of each ayer = wm + g snφ, where w m s mean of stator and rotor poe wdth. Heght of each ayer = L+ snφ (20) Area of the ndvdua ayer s the product of ts wdth and heght. euctance of the ndvdua ayer s obtaned usng the Eq. (2). Tota reuctance of the ar gap g s summaton of the reuctance of ndvdua ayer. g Fg. 6. Inductance Vs Current at agned poston 2.4 Cacuaton of unagned nductance The fux path of the machne n the unagned poston s shown n the Fg euctance cacuaton of ron parts euctance of the Iron parts s cacuated as foows. euctance of stator yoke s gven by sy H sysy = B sya sy (21) euctance of stator poe s expressed as sp Hspsp = B spa sp (22) Fg. 7. Fux pattern at the unagned poston 33

5 Deveopment of Anaytca Modes for Swtched euctance Machne and ther Vadaton where pr =otor poe radus S arc =Stator poe arc Area of the ar gap s expressed as where A = W* L (28) Fg. 8. Equvaent magnetc crcut at the un-agned poston The path foowed by the fux nes shown n Fg. 7 s consdered for deveopng the equvaent magnetc crcut at the unagned poston and t s shown n Fg. 8. Equaton to obtan tota mmf of the magnetc path shown n the equvaent crcut s gven as 2NI = 2Hspsp+ φgg + 2Hrprp + Hryry + 2Hrptrpt + Hsysy (26) where H rpt =Magnetc fed ntensty at the rotor poe tp rpt =Length of the rotor poe tp 2.5 Ar gap reuctance at the un-agned poston The fux nes crossng the ar gap at unagned poston s gven n deta n the Fg. 9. Based on symmetry ony haf of the tota fux s consdered for anayss. The ar gap s treated as combnaton of three sectons as shown n the Fg. 9. The sectons can be treated as dea geometrca fgures wthout much oss n accuracy. Fg. 9. Dfferent sectons of the ar gap at unagned poston Secton 1 It s modeed as a rectange, wth ength equa to the dstance between the stator poe tp and the centre of the rotor poe. The centre of rotor poe s at an ange 30 deg from the horzonta and the stator poe tp s at an ange haf of the stator poe arc. Consderng rotor poe radus as a common radus the ength s found usng the formua, Arc ength = adus * Arc ange. Dvergence of fux nes at the stator poe tp s generay mted to 2mm. Therefore the wdth s ( g +2mm). euctance of the secton 1 s computed as foows. Length of the ar gap s gven as Π = pr (30 Sarc / 2) (27) 180 W= wdth of the ar gap= + 2mm (29) euctance of secton 1 s descrbed as g 1 = 7 (4 π e (30) * A) The sdes of the Fg. 9 are a, b, c and d whch are gven as a - dstance from centre of stator poe to rotor poe tp, t s expressed as Π a = pr (30 arc / 2) (31) 180 b and d - dstance between rotor yoke and stator poe tp, t s wrtten as b= d = + (32) ph where ph =otor poe heght c - haf the dstance between two rotor poes, t s gven as c = 2Π 6 /12 (33) ( yor pw ) Secton 2 It has 3 sdes, whch are a-c, b and d. Secton 2 s separated n to 100 horzonta ayers of unform area and varyng ength. Length of each ayer= nb /100, where n=1 to 100 Area of each ayer = ( a c) L/100 euctance of each ayer s cacuated and the reuctance of secton 2 ( 2 ) s parae combnaton of hundred ayers. Secton 3 It has sdes b and c and reuctance of ths secton s descrbed as b 3 = 7 {4 Πe [ c* L]} g (34) euctance of 3 sectons s n parae and the tota ar gap reuctance s gven as g 1 = (35) 34 J Eectr Eng Techno.2015;10(1): 30-40

6 . Jayapragash and C. Cheamuthu Fg.10. Inductance Vs Current at un-agned poston The varaton of unagned nductance for the change n current vaue s very mnmum. Therefore t s consdered as constant vaue for partcuar SG and t s expressed as L u 4NN = ( 2sp + 2g + 2rp + ry + 2rpt + sy) (36) The resut obtaned by sovng Eq. (36) s gven n Fg Inductance profe of SM The phase nductance s droopng when the rotor eaves the agned poston. Durng fang nductance perod, varaton of nductance wth respect to rotor poston s negatve. Therefore torque generated s aso negatve [11]. If the phase s excted n ths perod, rotor experences torque whch opposes rotaton and extracts energy from the turbne. Inductance varaton as a functon of current and poston s gven as Fg. 12. ψ- characterstcs of SM Compete cyce of nductance varaton as a functon of current and poston s shown n Fg Fux nkage cacuaton Fux nkage as a functon of current and poston s expressed as ψ (, I θ) = LI (, θ) I (40) Fg. 12 shows ψ- characterstcs of SM where t s evdent that a nonnearty exsts at the agned poston and s consdered by makng the fourer seres coeffcents a o () and a 1 () dependent on the phase current. 2.8 Torque cacuaton The nstantaneous torque as a functon of current and poston s cacuated usng the formua where LI = a + a Nθ (37) (, θ ) 0() 1()cos r 1 a0 () = ( La() + Lu) 2 (38) 1 a1 () = ( La() Lu) 2 (39) 1 2 dl( I, θ ) T(, I θ ) = I (41) 2 dθ The response obtaned by sovng the Eq. (41) s gven n Fg. 13. Durng fang nductance perod, varaton of nductance wth respect to rotor poston s negatve. Therefore torque generated s aso negatve. Fg. 11. Inductance varaton as a functon of current and poston Fg. 13. Torque Characterstcs 35

7 Deveopment of Anaytca Modes for Swtched euctance Machne and ther Vadaton 3. FEA Mode Among varous numerca methods FEA s most frequenty used. There are many types of software avaabe to anayze and compute the eectromagnetc fed of the machne accuratey n two-dmenson (2-D). In ths paper MagNet s used to bud the mode. The FEA mode of 4 Phase 8/6 SM s shown n Fg. 14 (a) for the specfcatons n Tabe 4. The mesh pattern of the probem regon at the agned and unagned postons s shown n Fg. 14 (b) and Fg. 14 (c) respectvey. FEA Mode shown n Fg.14 s soved to obtan the data ke fux nkage, nductance and torque. The varaton of fux nkage wth respect to current s shown n Fg. 15. Fg.16. Inductance Profe Fg.17. Torque characterstcs (a) It s evdent from Fg. 16 that nductance s maxmum at the agned poston. When the rotor eaves the agned poston nductance decreases and t s mnmum at the unagned poston. The nductance profe of the machne s perodc functon of rotor poston as seen n Fg. 16. Torque obtaned from FEA mode for varous vaues of current and poston s shown n Fg. 17. It s negatve from 0-30 degrees and postve from degrees. 4. Comparson of Anaytca Mode wth FEA Mode (b) Fg. 14. (a) FEA Mode of 4 Phase 8/6 SG; (b) and (c) Mesh pattern at agned and un- agned postons (c) The response of fux mode s compared wth ψ- characterstcs of FEA mode and s shown n Fg. 18. The comparson s done at agned and unagned postons. The resuts ndcate there exsts a cose match between anaytca mode and FEA mode. Fg.15. Fux Lnkage vs Current Fg.18. Fux nkage comparson wth FEA 36 J Eectr Eng Techno.2015;10(1): 30-40

8 . Jayapragash and C. Cheamuthu The nductance profe obtaned from anaytca mode s compared wth FEA mode for a fxed vaue of current and s shown n Fg. 19. Ths resut aso reveas that the Anaytca Mode and FEA mode are ake. L a () = L(0,) - agned nductance L () = L(10,) one thrd way nductance L m () = L(15,) md way nductance L j () = L(20,) two thrd way nductance L u () = L(30,) un-agned nductance The genera expresson of nductance consderng the fve dfferent postons as stated above s approxmated as where 0 4 L( θ, ) = L ( ) + L ( )cos( nn θ ) (43) n= 1 n r Fg.19. Inductance comparson wth FEA Comparson of the torque obtaned from Anaytca mode s performed wth FEA and s shown n Fg. 20. Fg.20. Torque comparson wth FEA L0 () = La() + L() + Lj() + Lu() (44) L1 () = La() + L() Lj() Lu() (45) L2 () = La() Lm() + Lu() (46) L3 () = La() L() + Lj() Lu() (47) L4 () = La() L() + Lm() Lj() + Lu() 3 12 (48) For dfferent vaues of current, L a (), L (), L m (), L j () and L u () are cacuated usng the data obtaned from ether FEA method or expermenta measurement and t s shown n Fg Fourer Seres Mode of SM The nonnear mode to SM n terms of fourer seres expresson of phase sef-nductance s cacuated anaytcay, under the assumpton of neggbe mutua effect between the ndvdua SM phases and varous osses. A fourer seres representaton s used to express the phase nductance wth respect to the rotor poston as [13] Phase Inductance (H) La() L() Lm() Lj() O - data measured fttng curve L( θ, ) = L ( ) + L ( )cos( nn θ ) (42) 0 n= 1 where L(θ,) phase nductance L 0 () & L n () fourer seres co-effcents N r number of rotor poes θ anguar poston of the rotor To determne the coeffcents n the Fourer seres, t s necessary to know the nductance at severa specfc postons. The foowng reevant assumptons are further made for an 8/6 SM: n r Lu() Phase Current (A) Fg. 21. Inductance and fttng curve The generazed equaton for L a (), L (), L m (), L j () and L u () are obtaned usng curve fttng technque. Whch are expressed as foows L a () = e-005x x x x x (49) L () = e-005x x x x x (50) 37

9 Deveopment of Anaytca Modes for Swtched euctance Machne and ther Vadaton L m () = e-006x x x x x (51) L j () = e-006x e-005x x x x (52) L j () = e-021x e-019x e-018x e-018x e-017x (53) The nductance profe obtaned usng curve fttng technque for varous vaues of current s compared wth FEA mode and t s shown n Fg. 22. Phase Inductance (H) FSM FEA 4A 6A 8A 1A 3A 5A 2A 7A 6. Expermenta esuts The Parameters ke nductance, fux nkage and torque obtaned from AM s confrmed wth FEA mode and found that there s a cose match between the parameters. Hardware mode [12] s deveoped to vadate the nductance at the agned and un agned postons The compete bock dagram of the expermenta set up s shown n Fg. 24. For vadaton of the nductance vaues, mcrocontroer based expermenta set up s deveoped and t s shown n Fg. 25. The stator wndng of the SM s excted by DC suppy obtaned from a fu brdge dode rectfer powered by an Auto-Transformer. MOSFET IF540 and 1 ohm resstor are connected n seres wth the phase wndng. Trggerng sgna requred for the MOSFET s generated by ATMEGA16 mcrocontroer and t s supped to the gate termna of the MOSFET through Opto-soator MCT2E otor Poston Fg.22. Inductance comparson As per non-near nductance mode, the torque s descrbed as 4 T( θ, ) = ( Nr) n.sn( nnrθ). L. nd n= 1 0 (54) Fg.24. Bock dagram of the expermenta set up The above equaton s soved to obtan the torque response of the SM and t s gven n Fg FSM FEA Torque (N-m) A 8A otor Poston Fg. 23. Torque comparson Fg. 25. Expermenta set up Power crcut for energzng one of the phase wndng through MOSFET IF540 s shown n Fg. 26. From the resuts t s cear that the fourer seres mode s accurate but t cannot be deveoped wthout usng the data obtaned ether from FEA mode or from experments measurement. Many number of data are assumed for anayss and mode deveopment. Therefore, GBAM s deveoped and dscussed n detaed manner. Fg. 26. Power Crcut 38 J Eectr Eng Techno.2015;10(1): 30-40

10 . Jayapragash and C. Cheamuthu Gate sgna s obtaned from mcrocontroer and t s supped to the gate termna of the MOSFET through drver crcut. The compete crcut dagram of the drver crcut s shown n Fg. 27. One of the phase wndng s excted to brng the rotor to agned poston. Votage apped to the stator wndng s vared to adjust the current fow through the wndng and transent response s captured usng Dgta Storage Oscoscope (DSO). From the rse tme of the transent response, nductance s obtaned at agned poston for varous vaues of current. Eectrca equvaent crcut of the phase wndng s shown n Fg. 28. The votage equaton correspondng to eectrca equvaent of the phase wndng for zero nta current [(0)=0] s expressed as V = L(, θ ) d + (55) dt Sovng the non-near Eq. (42) gves the resut as nductance s obtaned for the varous vaues of current and t s compared wth the FEA mode and Anaytca mode. The resuts are tabuated n Tabe 1. Fux nkage at the agned poston for dfferent vaues of current s cacuated from nductance obtaned from expermenta set up and t s compared wth the FEA mode and Anaytca mode. The resuts are tabuated n Tabe 2. Fg. 29. Transent current characterstc at 1A where t V t () = (1 eτ ) (56) L τ = (57) When t=5τ, system reaches steady state and nductance vaue s obtaned from the rse tme of the transent response. Transent response of the drve system when the wndng carres 1A and 2A are shown n Fg. 29 and Fg. 30 respectvey. From the transent characterstc of the rea tme system Fg. 30. Transent current characterstc at 2A Tabe 1. Inductance vaue comparson at agned poston Current (A) GBAM Mode (H) FEA Mode (H) Expermenta esut (H) Tabe 2. Fux nkage comparson at agned poston Fg. 27. Drver Crcut Current (A) GBAM Mode FEA Mode Expermenta esut Tabe 3. Inductance vaue comparson at un-agned poston Fg. 28. Eectrca equvaent of phase wndng GBAM Mode (H) FEA Mode (H) Expermenta esut (H)

11 Deveopment of Anaytca Modes for Swtched euctance Machne and ther Vadaton Un-agned poston s obtaned by exctng two phase wndngs smutaneousy and un-agned nductance s obtaned for varous vaues of current. It s found that unagned nductance s constant rrespectve of the current magntude and t s shown n Tabe Concuson The Geometry Based Anaytca Mode of SM consderng frngng effect s dscussed brefy and the resuts are compared wth the FEA mode of a SM. The resuts show that a cose matches between anaytca and FEA modes exst. The anaytca mode presented s very accurate, smpe and t consumes ess tme than the other methods and aso gves resuts cose to FEA. Further for justfyng the resuts obtaned from GBAM another anaytca method caed Fourer Seres Mode s deveoped wth curve fttng technque. The resuts obtaned from FSM s verfed wth the FEA and found satsfactory but t s mandatory to use the data obtaned ether from FEA mode or from expermenta measurements. Many numbers of data are assumed for anayss and mode deveopment. Therefore, GBAM s deveoped and t does not requre any data from FEA mode/expermenta measurements. Impemented mcrocontroer based SM drve system comprses of SM has the same machne geometry whch s consdered for anaytca mode. Inductance profe of the machne s obtaned for varous vaues of current usng Transent Anayss Technque and t s vadated wth the anaytca and FEA modes. Annexure Tabe 4. Eectrca specfcatons of SM ated Power ated Speed ated Votage ated Current Constructon and mechanca specfcatons 1Hp (746w) 3000 PM 330 V,DC 5 A Wndng gauge 24 SWG No. of turns per poe 100 turns Stator core stampng thckness 0.5 mm otor core stampng thckness 0.5 mm Shaft dameter 14 mm Thckness of rotor yoke 5.8 mm Heght of rotor poe 10 mm Ar gap ength 0.2 mm Heght of stator poe 9 mm Thckness of stator yoke 11.5 mm Stack ength 80 mm Stator poe arc 22 deg otor poe arc 25 deg Matera used CNGO grade M-19 eferences [1] T.J.E. Mer, Swtched reuctance motors and ther contro, Oxford Unversty Press, [2]. Krshnan, Swtched reuctance motor drves, modeng, smuaton, anayss, desgn and appcatons, CC Press, [3] A. adun, Anaytca cacuaton of swtched reuctance motor s unagned nductance, IEEE Trans. Magn., vo. 35, No. 6, pp , Nov [4] S. A. Hossan and I. Husan, A geometry based smpfed anaytca mode of swtched reuctance machnes for rea-tme controer mpementaton, IEEE Trans. Power Eectron., vo. 18, No. 6, pp , Nov [5] Ahmed Kha and I. Husan, A Fourer Seres Generazed Geometry-Based Anaytca Mode of Swtched euctance Machnes, IEEE Trans. Ind. Appcatons, vo. 43, No. 3, pp , June [6] Wen Dng and Deang Lang, A Fast Anaytca Mode for an Integrated Swtched euctance Starter/ Generator, IEEE Trans. Energy Converson, vo. 25, No. 4, pp , Dec [7] D.N. Essah and S.D. Sudhoff, An Improved Anaytca Mode for the Swtched euctance Motor, IEEE Trans. Energy Converson, vo. 18, No.3, pp , Sep [8] Shoujun Song and Weguo Lu, A Comparatve Study on Modeng Methods for Swtched euctance Machnes, Computer and Informaton Scence, vo. 03, No.02, pp , May [9] T. Lachman, T.. Mohamad, and C. H. Fong, Nonnear modeng of swtched reuctance motors usng artfca ntegence technques, IEE Procs-Eec Power App, vo. 151, no. 1, pp , Jan [10] akesh Saxena, Bhm Sngh and Yogesh Paharya, Measurement of fux nkage and nductance profe of SM Internatona Journa of Computer and Eectrca Engneerng, Vo. 2, No. 2, Apr [11] Davd A. Torrey, Swtched reuctance generators and ther contro, IEEE Transactons on Industra Eectroncs, Vo.49, No.1, Feb [12] Yuan-Chh, Chang-Mng Law, On the desgn of power crcut and contro scheme for swtched reuctance generator, IEEE Transactons on Power Eectroncs, Vo. 23, No.1, January [13] Hujun Zhou, Wen Dng and Zhenmn Yu, A nonnear mode for the swtched reuctance motor, Schoo of Eectrca Engneerng, X an , Chna, [14] Hep Browser of MagNet7.1.1, Infoytca Corporaton 40 J Eectr Eng Techno.2015;10(1): 30-40

12 . Jayapragash and C. Cheamuthu. Jayapragash He receved the A.M.I.E. degree n Eectrca Engneerng from Insttuton of Engneers (Inda), Kokatta n 2004 and M.E. degree n Power Eectroncs and Drves from A.C. Coege of Engneerng and Technoogy, Anna Unversty, Tam Nadu n He s presenty pursung Ph.D n Anna Unversty, Chenna, Inda. He s currenty an Assocate Professor n the Department of Eectrca and Eectroncs Engneerng, St. Joseph s Insttute of Technoogy, Chenna, Inda. Hs research nterests are Anaytca Mode Deveopment, Contro of Eectrca Drves and enewabe Energy Systems. C. Cheamuthu He receved Ph.D degree n Power Eectroncs from IIT Chenna, Inda. He s currenty workng as a Professor n the department of Eectrca and Eectroncs Engneerng,.M.K. Engneerng Coege, chenna, Inda. Hs area of nterests are Power Eectroncs, Eectrca Drves and Contro, Mcroprocessor based System Desgn, Networkng and Image Processng. 41