Thrust Control of Traction Linear Induction Motors in Switch Areas

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1 Thut Contol of Taction inea Induction Moto in Switch Aea Cai-Xia Tao,Dan Zhang,Xiao i School of Autoation and Electical engineeing anzhou JiaoTong Unieity 88 Wet Anning Rd.anzhou Ganu China @tu.lzjtu.edu.cn Abtact: Rail tanit yte poweed by linea induction oto hae gained widepead populaity. In ode to ole the poble of no thut in witch aea whee thee ae no eno boad, the oto thut i inceaed pio to enteing the witch aea o that the total thut eain contant. In the two condition,whee include and exclude econday,not only the linea induction oto odel wa etablihed, but alo the iulation odel of the diect thut contol and the contant thut contol wee etablihed. Siulation tudie wee conducted on the diect thut of a ingle oto, and the contant thut contol of the tain.expeiental eult hae alidated the odel. Keywod: ail tanit yte;linea induction; oto;diect thut contol;witch aea;pio;econday 1 Intoduction With the inceaingly eiou poble of uban taffic congetion, China ha enteed a peak peiod of uban ail tanit deelopent.tain with ingle ided linea induction oto hae the adantage of fat acceleation,high clibing ability, and all tuning adiu;equiing all aea of tunnel tuctue and poiding oe flexible choice of ubway line. Theefoe, ail tanpot yte poweed by linea induction oto hae gained widepeed attention[1]. Diect thut contol contol technology ha iple algoith,fat dynaic epone, obutne againt paaete aiation, and i ideal fo contolling taction oto[]. A geat deal of eeach ha been conducted on ingle ided linea induction oto. The ipact of the econd longitudinal edge effect on oto cla electoagnetic foce i analyzed by oling the oto ai gap agnetic field ditibution[3]. No unit dienion of Q i intoduced to aend the econday eitance and utual inductance in the otay induction oto[4]. Slip-fequency cala contol ode i widely ued fo linea induction oto contol in uban ail yte[5].diect thut contol baed on a witch table i iulated in[6]. The diect thut contol of efficiency optiization enegy-aing contol i applied to cued linea induction oto.it i obiouly illutated that linea induction oto tain will loe thut in witch aea.in pite of extenie tudie, no olution ha been found to the poble of lo of thut in witch aea of non induction. Fo the thut lo poble, thi pape ceate a odel of linea induction oto without econday plate ituation in a tationay coodinate yte. The iulation odel of linea induction taction oto and diect thut ae built in Matlab/Siulink. The iulation of peed contol and thut contol i conducted to eify the contol yte. Futheoe, the contant thut contol in witch aea i analyzed and the futue eeach wok i dicued. Matheatical odel of linea induction oto inea induction oto can be conideed a the otay induction oto ectioned axially and E-ISSN: Volue 10, 015

2 expanded hoizontally. The tato on the oto fae becoe the piay on the botto of the tain, and the oto becoe the econday laid in the iddle of the ail. Thi ayety caue the edge effect, and the econd longitudinal edge effect i the ot ignificant. Gien the coection facto of the econd longitudinal edge effect Q[7]. T DR Q (1 T ( + Whee, T i the contant of piay tie, T i the contant of econday tie, eitance, R i econday i the utual inductance, i the econday leakage inductance, D i the piay length, i the peed. Edge effect function i[7]: Q e f ( Q 1 ( Q Eddy-cuent lo i equialent to the aiation of the excitation eitance at the end of the econday. The eied excitation eitance i[7]: R R f ( Q (3 The deagnetization effect of a econday otex i equialent to the aiation of agnetic inductance. The eied agnetic inductance i[7]: Whee, coected, [1 f ( Q] (4 i excitation inductance which R i the excitation eitance which coected. The equialent cicuit of a linea induction oto with the econd longitudinal edge effect i hown in Fig.1, whee R i the piay eitance, i the piay leakage inductance, u i the piay oltage ecto, I i the piay cuent ecto, I i the econday cuent ecto, and I i the utual inductance of the cuent ecto. + u R I I R f(q [1-f(Q] I R / Fig. 1 inea induction oto equialent cicuit Baed on the equialent cicuit of Fig.1, a dynaic atheatical odel of linea inducttion oto in two-phae tationay coodinate yte i built a follow. The oltage equation i: u Ri + R + u Ri + R + (5 0 Ri + R + + ωψ 0 R i R i ωψ Whee, u i the -axi piay oltage, u i the -axi piay oltage, i i the -axi piay cuent, i i the -axi piay cuent, i i the -axi econday cuent, i i the -axi econday cuent, ψ i the -axi piay flux, ψ i the -axi piay flux; ψ i the -axi econday flux, ψ i the -axi econday flux, and ω i the linea induction oto equialent angula elocity. The flux equation i: ψ ψ ψ ψ i i i i (6 The equation of otion i[8]: d (7 Whee, F e i the electoagnetic foce, F load, i the load thut, and i the piay quality. The thut equation i: 3 p ( ψ i ψ i (8 τ 4 Siulink doen t include a linea induction E-ISSN: Volue 10, 015

3 oto odel equied in the iulation. We build a linea induction oto odel uing an -function decibed a follow. In ode to obtain the equation of -fuction, we calculate the cuent baed on the flux equation of the linea induction oto. i i i i [ ψ [ ψ [ ψ [ ψ ( ( ( ( + ψ + ψ + ψ + ψ (9 A ( + ( + (10 The flux linkage tate equation i obtained fo the oltage equation of the linea induction oto. u u R i R i ω ψ + ω ψ (11 The angula elocity tate equation i obtained fo the angula elocity of oeent[8]: dω τ ( (1 inea induction oto don t hae thut in a witch aea whee the econday eno boad cannot be laid. In eality, inetia caie the tain out of the witch aea. In thi cae, othe oto tepoaily inceae the thut to copenate fo the lo of thut of the linea induction oto. In the witch aea of non-induction, the atheatical odel of the linea induction oto need to be odified to exclude the econday. Fit calculate the utual inductance, i calculated a[9]: 41 ( W1k w1 a 1 µ 0 (13 ( p f gk g k µ 4 p 3 k w1 inn( y 1 (14 q1 in( q k g 1 1 t1 (15 b0 / g t1 5 + b / g Whee, 1 i the nube of phae, μ 0 epeent the acuu peeability, W 1 i each eie with the piay winding tun, kw 1 i the winding facto; k g i the gap coefficient, k μ i the agnetic atuation coefficient, y i the elatie pitch of the winding; q 1 i the nube of lot pe pole pe phae, t 1 i the piay pitch, and b 0 i the gooe wih. Fo Equation 13, the utual inductance i ineely popotional to the echanical ai gap of the linea induction oto. In the witch aea of non-induction, the echanical ai gap i gτ[9]. The utual inductance wa 0.64H. Fa le than the utual inductance of linea induction oto with econday 4.36H, o the utual inductance can be ignoed. At the ae tie becaue only contain piay, o econday paaete ae ignoed. The flux linkage tate equation i: u 0 u i Ri The cuent i calculated a: iψ iψ (16 (17 3 Diect Thut Contol Siulation Model Diect Thut Contol and diect toque contol ae actually equialent. The piay and the E-ISSN: Volue 10, 015

4 econday of linea induction oto do a elatie linea otion. At thi point the electoagnetic toque i the electoagnetic foce. They can be coneted between each othe, naely[10]: pτ T e (18 Whee, T e, i electoagnetic toque. The contol block diaga of diect thut baed on the pinciple of witching ecto table i hown in Figue. Thee ae thee coponent including the flux and thut obee, the flux egulato, the thut egulato and the witch table[11]. A gien agnetic chain A gien thu + + Flux egulato Thut egulato Magnetic chain ecto Switching tate table Magnetic chain and thut obee The feedback ignal inete inea induction oto Fig. Diect Thut Contol Block Diaga Copaed with diect toque contol,accuate flux obeation of the linea induction oto i the key to ipoe the diect thut contol pefoance. The tato flux i obtained uing the tato oltage and cuent in the otay induction oto. ψ ψ ] ] (19 The edge effect need to be conideed when thi tato flux odel i applied to linea induction oto. The aboe foula ae odified a: ψ ψ ] ] (0 Take Guangzhou Meto ine FOUR a an exaple. The tain had fou oto tain unit. Each unit had an inete and two linea induction oto. Each inete doe a oto a a iplified iulation odel, totaling fou oto. The aplitude of the piay cuent in the tationay coodinate yte inceae. The aplitude aiation of the cuent i checked to decide when the oto i detached fo the econday eno boad, which i the tiing of inceaing the thut befoe enteing the witch aea. Matlab/Siulink wa ued to build the odel a hown in Fig Udc Continuou powegui Udc 3 i1 4 fcn i Udc1 Udc i3 Udc3 i4 Udc4 Fcn Udc i IM1 Udc Floac i IM Udc i IM3 _total Udc i IM4 Fig.3 Siulation Model of Contant Thut Contol The diect thut contol of a ingle linea induction oto odel i hown in Fig Udc Continuou powegui fun_dtc S-Function1 VSI S-Function F F F1 XY Gaph ψ ψ JS i u i i i u Q f (Q ψ IM ψ ψ u u i i i i Re I R to C Q.f(Q u u C to M Fig.4 Diect thut contol odel of a linea induction oto 4 Siulation Analyi Fit, the diect thut contol of a ingle linea induction oto wa iulated, whee R wa 0.045Ω, R wa 0.16Ω, wa 1.1H, wa 0.35H, wa 4.36H, p wa 6, τ wa 0.88, wa 500kg, and D wa The peed PI egulato paaete K P wa 5000, and K I wa 175. The gien flux alue wa 0.8Wb. The hyteei flux linkage egulato loop wih wa 0.00Wb, and the thut hyteei egulato loop wih wa 0.05N. We ued the iulation algoith ode4, and iulation tep wa /3 /3 i ψ iabc E-ISSN: Volue 10, 015

It i noted that with a contant peed the aplitude of the cuent inceaed a the peed inceaed. Thi i becaue the cuent need to be inceaed to copenate the lo caued by the edge effect.

5 The peed tep iulation condition ae that the peed at the beginning (0 econd wa 8/, the peed at.5econd wa 10/, and the thut load wa 1000N. The peed epone cue of the linea induction oto i hown in Figue 5. The thee-phae cuent cue of the linea induction oto i hown in Figue 6. It i noted that with a contant peed the aplitude of the cuent inceaed a the peed inceaed. Thi i becaue the cuent need to be inceaed to copenate the lo caued by the edge effect. daatically inceaed in the tie peiod fo.5econd to 3.5econd. The -axi thee-phae cuent of the linea induction oto i hown in Fig.9, whee the cuent aplitude oe to 440A which led to a 300% oeload. Thee phae cuent(a Tie( Fig.8 Thee-phae cuent of the fit linea induction oto Speed(/ Tie( -axi cuent aplitude(a Tie( Fig.5 Speed waefo of a linea induction oto Thee phae cuent(a Tie( Fig.6 Tthee-phae cuent of a linea induction oto The thut tep iulation condition ae that the load thut wa 1000N at the beginning and 000N at.5 econd, and the gien peed wa 8/. The wae of electoagnetic wae i hown in Fig.7, which can tack the thut. Thut(N Tie( Fig.7 Electoagnetic thut with edge effect The iulation condition of the linea induction oto without the econday ae that the gien peed wa 8 /, and the load thut wa 1500N. Aue that the econday wa dipatched fo the linea induction oto at.5econd. The utual inductance wa 0.64 H. The thee-phae cuent waefo i hown in Fig.8. It wa noted that the fequency of the thee-phae cuent in the fit linea induction oto Fig.9 -axi cuent aplitude of the fit linea induction oto Next, the contant thut contol of the odel in Figue 3 wa iulated. The -axi cuent of the linea induction oto wa inetigated. When the cuent i 00% highe than noal, we inceaed the thut of the othe thee oto by one thid. The thut of the fit oto i hown in Fig.10. Thee wee no eno boad between.5 econd and 3.5 econd. The thut of the econd oto i hown in Fig.11. The thut inceaed by one thid between.5econd to 3.5 econd. The total thut of the fou oto i hown in Figue 1, which wa a contant of 6000N between.5econd to 3.5econd. The light dop afte.5 econd wa due to the delay of the thut boot of othe thee oto (econd to fouth. Thee wa one econd peed lo when thee wa a thut lo in the fit oto, which caued the light ie of the total thut afte 3.5econd. Afte 3.5 econd, the fit oto opeated noally poducing full thut and the tain egained the gien peed. Thut(N Tie( Fig.10 Thut of the fit linea induction oto E-ISSN: Volue 10, 015

6 Thut(N Tie( Fig.11 Thut of the econd linea induction oto Thut(N Fig.1 5 Concluion Tie( Total thut of fou linea induction oto Thi pape etablihed a atheatical odel of linea induction oto in the two-phae tationay coodinate yte uing -fuction.the diect thut contol tategy of linea induction oto wa tudied and iulated uing Matlab/Siulink oftwae. The iulation eult uggeted the following: The thut of oto in the non-induction aea dopped to zeo. Contant total thut wa achieed by inceaing the thut of othe oto. The tiing fo copenating thut wa deteined by the aiation of the -axi piay cuent aplitude in the coodinate yte. The oeload of the -axipiay cuent aplitude of the oto in a non-induction aea wa aound 300%. The iulation wa conducted of the thut lo of one oto in the witch aea. The tategy hould be odified fo pactical ituation, including the tiing of thut copenation and the oeloading capability of each oto. (econd edition,tokyo:unieity of TokyoPe, 1978,pp [4]Duncan J., Eng C,inea induction oto equial ent-cicuit odel,ieee Tan,On Electic Powe Application, Vol.130,No.1,1983,pp [5] Zheng Qiongling, Zhao Jia, and Fan Jiafen, Rail taction taniion of linea oto, China ScienceandTechnologyPe,Beijing,Vol.15,No. 19,009,pp [6] ai YS, Chen JH,A New Appoach to Diect Toq ue Contol of Induction Moto Die fo Conta nt Inete Switching quency and Toque Ripple Reduction,IEEE Tanaction on Enegy Coneion, Vol.16,No.3,001,pp.0-7. [7] Wang Ke, City ail linea induction oto chaact eitic analyi and diect taction contol tateg y, Beijing: Intitute of Electical Engineeing, 009:44. [8] i Xiao, Tao Caixia, Finite eleent analyi of taction linea induction oto baed on Anoft Softwae,Study of uban ail taffic,vol.17,no.3,014,pp [9] ong Xialing,Theoy of linea induction oto and electoagnetic deign,beijing:science Pe Vol.1,No.6,006,pp [10]Macello Pucci,State pace-ecto odel of linea induction oto,ieee Tan. On Induty Appl ication,vol.50,no.1,014,pp [11]uQingfen, Chaacteitic of linea ynchonou oto,hangzhou:zhejiang Unieity,005. Refeence: [1] Giea JF,inea Induction die,oxfod:claend on Pe,1994,pp.4-8. [] Depenbock M,Diect elf-contol (DSC of ine te-fed induction achine,ieee Tan.On Powe Electonic, Vol.3,No.4,1988,pp [3] Yaaua S,Theoy of linea induction oto E-ISSN: Volue 10, 015

FARADAY'S LAW dt

FARADAY'S LAW dt FAADAY'S LAW 31.1 Faaday's Law of Induction In the peious chapte we leaned that electic cuent poduces agnetic field. Afte this ipotant discoey, scientists wondeed: if electic cuent poduces agnetic field,