3D Numerical Analysis for Impedance Calculation and High Performance Consideration of Linear Induction Motor for Rail-guided Transportation

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1 ADVANCED ELECTROMAGNETICS SYMPOSIUM, AES 13, 19 MARCH 13, SHARJAH UNITED ARAB EMIRATES 3D Numeral Analss for Impedane Calulaton and Hgh Performane Consderaton of Lnear Induton Motor for Ral-guded Transportaton CUONG Nnh Van 1 *, Yuta Yamamoto 1 and Takafum Kosek 1 1 Department of Eletral Engneerng, Shool of Engneerng, The Unverst of Toko, Japan *Correspondng author, E-mal: nnh.uong@kosek.t.u-toko.a.jp Abstrat In ths paper, the authors desrbe the method of alulatng the mpedane of Lnear Induton Motor (LIM) for ralguded transportaton usng magnet vetor potental that an be obtaned from three-dmensonal numeral analss. Based on ths method, hgh performane and power savng for some models of urrent researh trends n LIM onernng the mehanal learane and seondar reaton plate onstruton are dsussed. 1. Introduton In the past few ears, the onstruton of new urban subwa lnes usng Lnear Induton Motor (LIM) has been developed, espeall n Japan and Korea. Sgnfant advantages of LIM are: dret thrust wthout gears and lnks, smple struture, and eas mantenane. In addton, LIM redues the setonal area of tunnel and the large grad-ablt enables the mnmum length of the route. However, dfferent from rotatng motor, LIM has speal haratersts and nherent problems beause of the non-ontnut of the magnet feld. Longtudnal end effet and transverse edge effet are two major eletromagnet phenomena of LIM, whh makes the analss, desgn and ontrol of ths motor dffult. Whle longtudnal end effet s strongl affeted b slp frequen and the length of mehanal learane, transverse edge effet s strongl affeted b the onstruton of seondar reaton plate. Thus, n the transportaton sstem usng LIM, mehanal learane and seondar reaton plate are mportant desgn fators due to ther nfluene on not onl the operaton ost but also the onstruton ost. In LIM, the eperments for analss and desgn are dffult to arr out due to the requrement of onstruton features. The analss researh of longtudnal end effet and transverse edge effet n LIM s generall based on an dealed mathematal model that has some restrtons [1]- [3]. The frst restrton s that the longtudnal end effet s aused b fnte length of prmar that requres LIM the full modelng n analss. The seond restrton s twodmensonal (-D) analss annot epress the nfluene of transverse edge effet whh s aused b the fnte wdths of the prmar and seondar part. Hene, n order to evaluate the haratersts of LIM, the three-dmensonal (3-D) analss wth full-length model s neessar. In ths paper, 3-D numeral analss wth full model of LIM s used to onsder the generated fores and effen of ths motor owng to the mehanal learane and the onstruton of seondar reaton plate. Frstl, the authors desrbe the method for motor's mpedane alulaton from vetor potental whh an be obtaned from numeral analss. Seondl, b applng ths method, haratersts of LIM, nludng generated fore and power generaton, wth dfferent models onernng the nfluene of mehanal learane and seondar reaton plate wll be dsussed. Fnall, mprovng effen and power fator of LIM wll be larfed.. 3-D LIM model and analss ondtons In order to onsder the haratersts of ths motor, LIM model s desrbed n Fg.1, whh nludes front vew of full model, lateral vew and onstruton of the one-phased ol n 3-D. In addton, other parameters and analss ondtons are summared n Table 1. It must also be noted that the end wndng wth omple shape must be taken nto aount. Therefore, the haratersts of LIM n ths model are qute smlar to the atual LIM. However, beause of the requrement of transent analss of the 3-D full modelng, suffent omputer memor and solvng are neessar. The total pole of ths model s 8 whle the pole pth length s 8.8 mm, so the snhronous speed s about 11.8 m/s (4.3 km/h). As shown n Table 1, the analss s taken n a onstant slp frequen of.1 H, so the prmar ore s movng on seondar part wth onstant speed of 1.6 m/s (38. km/h). Furthermore, n ths model, threephased snusodal urrent at onstant frequen s appled to the ols of LIM and eah phase ol s onneted to the others n seres. In our eperments, the smulatons were onduted wth ELF/MAGIC software n three-dmensonal eletromagnet feld analss and the ntegral element method has been used [4]-[5]. In eah model of smulaton, the omputaton has been arred out n eght perods of the urrent wave-form; the eletral angle step wdth at eah tme step s 1 degree. Ths means 88 steps were alulated (36 steps 8 perods = 88 steps).

2 (a) Front vew of the full model () Lateral vew appromate regulatons. Defnng the mpedane value from vetor potental s dffult beause of the number of alulatons; however, we an obtan the hgh aurate values b adjustng the number of meshes n numeral analss. The detals of ths alulaton method an be seen n Fg.. Frstl, wth the LIM model desrbed n seton, magnet vetor potental A wll be obtaned from the eletromagnet feld analss. After that, eletr salar potental s alulated from A b Mawell equatons. Then, the bak eletromagnet fore (EMF) of eah ol sde and the mpedane, nludng absolute value and power fator wll be determned aordngl. As the analss ondton mentoned n seton, t should be noted that hgh resoluton for the voltage and urrent phase an be obtaned thanks to the analss onduted ever 1 eletral angle. In general, the mpedane of the number -th ol s onssted of self-ndutane, mutual ndutane, and ol wngdng resstane and whh an be desrbed as the followng equaton U () Three dmensons of one U-phase ol model (Etrated proess from full model) Fg. 1. Model of LIM for ral-guded transportaton Table 1. The analss ondtons for LIM Smbols Items Normal frequen [H] 1. Slp frequen [H].1 Rated slp frequen [H] 3. Normal speed [km/h] 38. Prmar soure urrent [A] 17 Materal of onduton plate Cu Relatve permeablt n 1 prmar/bak ron Condutvt n prmar/bak ron. 3. LIM mpedane alulaton method In LIM, mpedane alulaton s a hard top beause the nfluene of equvalent rut parameters of LIM strongl depends on the operatonal speed, espeall at hgh-speed operaton. Most of the other researhers have found out that the mpedane of LIM s based on the model of rotar nduton motor wth longtudnal end effet and transverse edge effet oeffents whh an be ounted for as the funton of operatonal speed, goodness fator and seondar struture parameter [3]. Although ths method an demonstrate the nfluene of the mutual ndutane and seondar resstane to the longtudnal end effet and transverse edge effet, t must be taken out at some -U R n R 1 n Z j R Current and voltage appled to the ol number #n are and, so the mpedane matr an be obtaned as followng or n n1 n nn Z Z Z Z Z Z Z Z Z n 1 n n1 n nn V1 Z11 Z1 Z1n I1 V Z1 Z Z n I V Z Z Z I n n1 n nn n V ZI Fg. 3 shows that n numeral analss wth a urrent soure, the ndued prmar termnal voltages n eah ol an be determned b dret ntegraton over the ol sde of the dstrbuton of the magnet vetor potental through Mawell equaton as shown n Eq. (4) and (5) B A (4) B E (5) t where B, A, E represent for magnet flu denst, magnet vetor potental and eletr feld. (1) () (3)

3 Fg.. Flowhart of mpedane alulaton ds A Prelmnar urrent-soure A V 3D numeral analss Magnet vetor potental A Eletr salar potental Bak eletromotve fore E Prmar termnal voltages n eah ol Impedane and power fator ds End wndng E ds slot Reaton plate B ore LIM Fg. 3. Assumpton of ntegral route n lne ntegral of magnet vetor potental Thus, the eletr feld s obtaned from magnet vetor potental as follows: E ( A ) (6) t In addton, the relaton between the termnal voltage n eah ol and the eletr feld s epressed below: V E d S. So from (6) and (7) we an obtan termnal voltage as follows: V j A d S. From the above, the absolute value of the mpedane of the equvalent rut s alulated as: Z and the power fator p.f. s alulated b usng the phase dfferene between the nput urrent and the bak EMF: pf.. os (1) Wth the dfferent operatng pont of LIM, usng the above proess, the mpedane an be determned as the funton of the seondar speed, and these results are sgnfant when onsderng the power savng n LIM operaton. V I V (7) (8) (9) 4. Analss results and dsusson In ths part, the authors desrbe the haratersts of target LIM at the operatng pont near rated slp frequen. The models of LIM are based on the requrement of reduton of longtudnal end effet and transverse edge effet to obtan hgh effen and power fator. For the purpose of omparson, three models have been used, Fg. 4. Standard model (A): s the model based on the reentl used model of LIM for Lnear Metro sstem n Japan (also desrbed n seton ) Short-gap model (B): s the model wth the same parameter as model A but wth reduton of mehanal learane Full-ap model (C): s the model wth full ap for seondar reaton plate and short-gap wth the demand of reduton of transverse edge effet and nrease thrust and effen [7]. B usng the mpedane alulaton method desrbed n seton 3 of ths paper, the performane of three models has been evaluated through the omparson of generated fore and power generaton. Fg. 5 shows the haratersts of two-dmensonal fores of LIM nludng longtudnal and normal fores varatons n tme steps. Wth the ntal urrent nput, n order to suppress the rapd derease of magnet flu nterlnk between prmar and seondar part, edd urrent n the seondar sde beomes larger. Ths proess makes the transent proess bgger and the -D fore at stead state smaller n omparson wth the value of transent proess. In ths model, t s found that we need 15 - step alulatons n order to obtan thrust at the stead state. Fg. 6 demonstrates one le of eletral angle salar potental (orrespondng to the flu lnkage of the ol), whh s obtaned b vetor potental A along ol lne and the appled urrent at the stead state. Assume that eah phase of salar potental n Fg. 6 s sne wave; ts effetve value s used to alulate the ndued sngle phase termnal voltage V ( u, v, w). Prmar ore 1 mm 9 mm Seondar reaton plate Seondar bak ron 3 mm 36 mm (A). Standard model (B). Short-gap model 1mm mehanal learane 9mm mehanal learane 9 mm 3 mm 36 mm Cap for seondar reaton plate (C). Full-ap model 9mm mehanal learane and full-ap Fg. 4. Analss model for hgh performane 5 mm mm 3

4 Salar potental [Wb] Salar potental [Wb] Salar potental [Wb] -D fore [kn] Current [A] Current [A] Current [A] mm Ar gap & No Cap : Longtudnal 9mm Ar gap & Full ap : Longtudnal 1mm Ar gap : Longtudnal Tmestep Fg. 5. -D fore haratersts of 3 models of LIM at motor startng transent Furthermore, as shown n equaton (9) and (1), from the rato of absolute value of to nput urrent we an alulate the absolute value of mpedane, and also from phase dfferene between and we an determne the power fator of ths motor. Consderng longtudnal end effet and transverse edge effet, from 3-D numeral analss, not onl the mpedane value but also other haratersts of three models are obtaned as shown n Table. In ths smulaton, beause of ondutvt n ron ore settng at, edd urrent loss n ron ore an be gnored. So the Joule heat losses n Table replae the edd urrent losses n seondar ondutor (seondar loss) and prmar opper losses. Whle power fator are determned as (1), the effen an be alulated as followng: Fv F v P (11) Beause of the gnorane of the edd urrent loss at the ron ore, t should be noted that the effen n (11) s a lttle hgher than the LIM n atual operaton. From the result n Table we an see that, as the mehanal learane redues, from model A to model B, the relutane and leakage flu of the magnet rut derease and magnetng ndutane nreases. Consequentl, muh less etaton urrent s requred. Even under the same nput urrent, the more effent transfer of magnet energ between the prmar and seondar sde makes thrust and normal fore nrease. The nrease of ndutane not onl makes power fator derease, but wth the derease of etaton urrent t also leads to the reduton of seondar power loss, whh results n nrease of the effen. The results show that, at the mehanal learane 1 mm n model A and 9 mm n model B, the power losses derease b 14% from 38 kw to 3.7 kw, and the effen nreases b % from 75.7% to 79.7%. Wth the reduton of mehanal learane, slp n optmal desgn must also be redued. However, n our smulaton, slp s set up at the same value.1, so t makes the value n model A bgger than n model B. As the epresson n Mawell stress tensor, normal fore s proportonal to the square of the -omponent of loss magnet flu denst at the ar gap. Furthermore, under ertan gap ross-seton, magnet flu denst s nversel proportonal to the gap between the ores g [8]. Therefore, f the mehanal learane s redued from 1mm to 9mm, the gap between the ores s redued from 17mm to 14mm and normal fore nreases nearl 5%, as shown n Eq.1 and Eq.13. However, dfferent from ths theor, due to the sheldng effet of edd urrent n onduton plate, the result from 3-D analss shows that normal fore nreases of 1% from 17.1kN to 18.1kN. 1 F B B B ( B B, B ) (1) ( A) ( A) B F( B) B( B) ga 17 F B g u v w <Meanal learane 1mm> u v w Eletr angle e [deg.] u v w Eletr angle e [deg.] 1-1 u v w <Meanal learane 9mm> u v w <Meanal learane 9mm & Full Cap> - u v w Eletr angle e [deg.] -17 Fg. 6. Absolute value and phase relaton between salar potental and appled urrent n stead state n 3 models (13) 4

5 Magnet feld at the ar gap along -dreton [T] Table. Charatersts of dfferent models of LIM b 3-D numeral analss Model A B C Thrust [kn] Normal fore [kn] Joule heat [kw] Power fator Effen [%] [%] Prmar ore 9mm Ar gap & No Cap 9mm Ar gap & Full Cap dreton [mm] Fg. 7. Dstrbuton of ar gap flu denst along -dreton In the desgn of a LIM havng full ap for seondar reaton plate, wth the dstrbuton of eletr salar potental and appled urrent n Fg. 6, we an sa that t s a sgnfant method to mprove the power fator of LIM. Calulaton n Table shows that power fator nreases of 14% from.43 n model B to.49 n model C. The eplanaton for ths nrease an be: when the full ap s used, magnet flu denst at the ar gap along -dreton s more balaned, the dfferene of magnet flu from the enter to end of the seondar reaton plate s redued as shown n Fg. 7. As a result, the seondar urrent n - dreton nreases whle the nfluene of -omponent edd urrent dereases. Ths means that transverse edge effet s redued due to the usng of full ap for seondar reaton plate. Ths result shows that usng ap for seondar reaton plate s a sgnfant desgn to get hgher thrust and to redue prmar nput. However, t must be noted that n order to nrease appromatel % of thrust and effen, from model B to model C, the amount of opper needed had nreased of 7%. Therefore, ths desgn s a poor desgn n term of ost of buldng. Hene, n order to desgn an effetve motor that an redue both transverse edge effet and materal ost, the desgner must onsder arefull the advantages and dsadvantages of eah model. 5. Conluson In ths paper, the mpedane alulaton method based on the 3-D numeral eletromagnet analss s proposed for desgnng a new LIM for lnear subwa sstems. B usng ths method, t s possble to determne the haratersts of LIM wth hgh aura through a number of tests that annot be realed under normal ondtons. The 3-D numeral analss has proved the sgnfant result for obtanng hgher thrust and redung prmar nput onernng mehanal learane reduton and usng ap for seondar reaton plate. However, redung mehanal learane leads to the derease of power fator, and usng ap requres a great more onstruton ost whle the LIM's qualt has a lttle mprovement. Sne the onstruton of mehanal learane and seondar reaton plate are mportant desgn fators from the vewpont of safet haraterst, ost of buldng and performane, the method proposed n ths paper an be used to fnd the optmal desgn of LIM for lnear subwa sstem. In future work, other desgns of seondar reaton plate as well as saturaton of bak ron wll be onsdered b usng 3-D numeral analss and ths mpedane alulaton method. Aknowledgement The authors gratefull aknowledge the support of Htah, Ltd and Japan Subwa Assoaton (JSA) to ths work. Referenes [1] K. Oberettl, Three-dmensonal theor of lnear nduton motor onsderng end-effet and wndng dstrbuton, Arh. f. Elek, vol. 55, Aprl [] A. Lang, The effet of stra felds on the desgn and performane of lnear nduton motors, PhD. Thess, Tehn. Unv. Braunshweg, German, June [3] W. u, J. G. Zhu, Y. Zhang, Z. L, Y. Y. Wang, Y. Guo, Equvalent rut for sngle-sded lnear nduton motor, IEEE Trans. on ndustr applatons, 1. [4] Y. Yamamoto, N. V. Cuong, T. Kosek, A numeral analss on varaton of fores and mpedane of a sngle-sded lnear nduton motor to lateral dsplaement, Conferene of Ele. Eng., Hroshma, Japan, pp.44-46, Marh 1 (In Japanese) [5] Y. Yamamoto, N. V. Cuong, T. Kosek, Performane mprovement and power-savng of lnear nduton motors for urban ral-guded transport onsderng ther lateral edge effet, Conferene of Ele. Eng., Toko, Japan, Deember 1 (In Japanese) [6] T. Kosek, Flu snthesng Lnear Induton Motor, The Unverst of Toko, PhD. Thess, URL: ?mode=full [7] S. G. Lee, H. W. Lee, S. H. Ham, C. S. Jn, H. J. Park, J. Lee, Influene of the onstruton of seondar reaton plate on the transverse edge effet n lnear nduton motor, IEEE Trans. Mag., Vol. 45, No. 6, June 9. [8] L. Huaj, Z. Yng, D. Yume, Normal fore haratersts analss of sngle sded lnear nduton motor, ICEM 1. 5