USEFUL TECHNIQUES FOR FIELD ANALYSTS IN THE DESIGN AND OPTIMIZATION OF LINEAR INDUCTION MOTORS

Transcription

1 USEFUL TECHNIQUES FOR FIELD ANALYSTS IN THE DESIGN AND OPTIMIZATION OF LINEAR INDUCTION MOTORS By: K.R. Davey R.C. Zowarka Twelfth Biennial IEEE Conference on Electromagnetic Field Comutation (CEFC 006), Miami, Florida, U.S.A., Aril 30-May 3, 006, PN 308 Center for Electromechanic The Univerity of Texa at Autin PRC, Mail Code R7000 Autin, TX 7871 (51)

2 > CEFC 006, bet fit 11 (a) (double-click here) < Recommendation for Field Analyt in the Deign and Otimization of Induction Motor Kent R. Davey, Fellow, IEEE, and Ray C. Zowarka Abtract Induction motor otimization can be time conuming. One of the arameter central to the deign i li, which change greatly a the field analyt modifie the layout of the machine. Two notable contribution of thi aer include (1) a method for comuting ower factor while modeling only 1/3 of one ole itch of the machine, and () a method for minimizing the number of li calculation required during deign otimization by uing equivalent circuit rereentation of voltage, torque, and rotor ower diiation. The firt contribution allow the deigner to analyze the mallet ubortion of the machine oible during otimization. The econd reduce the overhead required by numerou li calculation. The imortance of introducing ower factor into the otimization i alo dicued. A linear induction motor i the rimary focu of thi aer. Index Term linear induction motor, otimization, ower factor, vector otential. I I. INDUCTION MOTOR OPTIMIZATION BACKGROUND n the early year of motor otimization, much work wa aroached through the ue of the equivalent circuit, and tying in certain erformance criteria to that circuit [1]. Mot attemted otimization did not involve detail of lot and back iron dimenion, but rather caacitance and oerating regime to enhance efficiency []. Finite element analyi i becoming increaingly integral to induction motor deign. One of the more thorough examle i that by [3], where objective function uch a cot and teady tate ower were couled with multile contraint involving tarting torque, ull out torque, ower factor, and temerature in the tator winding. Thi aer how how to accomlih the tak uing an uncontrained otimization with 1/6 of a ole itch followed by a contrained otimization. II. THE PROBLEM DEFINED AND DOCUMENT OUTLINE The field analyt tyically begin an induction motor deign with a good finite element analyi tool, a targeted ower and eed, and ome guideline for minimizing cot, ize, or both. Thi information i enough to dictate torque. A motor ize i dictated by the torque demand. In the at, we targeted oeration torque at ½ ull out torque, but the new vector controller have allowed oeration very cloe to eak torque caability. With a wound rotor or ermanent magnet machine, it i trivial to lace the rotor in it eak torque oition and Manucrit received January 15, 006. Thi work wa uorted by the Office of Naval Reearch and American Maglev, Inc. K. R. Davey and R. C. Zowarka are with the Center for Electromechanic, Burnet Rd., Autin, Texa, USA, (hone: ; fax: ; k.davey@mail.utexa.edu, r.zowarka@mail.utexa.edu). analyze about that oint. By contrat, eak torque for an induction motor i determined by li, a li value that i very deendent on the hae and ize of the teeth, and amount of back iron, i.e., all the arameter that vary in the otimization. Comlicated otimization deign involving induction motor are exacerbated by thi roerty, i.e., that one of the key otimization indexe, eak torque, i li deendent. More ecifically, the li where the torque eak change coniderably with deign modification. Mot commercial finite element code oe arametric analyi caability. Even with thee caabilitie, the analyi time i driven u by the neceity of invetigating hyical deign change at a whole range of li value. The long analyi time i raied to another level with linear induction motor becaue angular eriodic boundary condition cannot be ued and the number of unknown become very large. The deign roblem for rotating and linear machine i aggravated a bit more by the fact that the end uer i uually concerned about a range of erformance criteria involving indexe uch a ower/weight, cot, ower factor, and thermal rie. The technique develoed are quite alicable to rotating and linear induction motor, but ecial attention i given to linear induction motor in thi aer. Thi aer i outlined in three diviion. Firt, a arametric otimization i decribed for determining the lot layout and back iron geometry. Sli i necearily a art of thi analyi. In the firt diviion, the two mot notable contribution of thi aer are reented. A method for comuting ower factor while modeling only 1/3 of one ole itch i dicloed. In addition, a method of incororating equivalent circuit relation into the analyi i introduced to reduce the number of li calculation required. Second, a method i hown for tranferring thi firt tage data into a linear embodiment. A hort linear motor i emloyed to redict the effect of a very long one. Third, the otimization of the reaction late cloure hae i dicued involving a three dimenional analyi. A. Thermal Conideration The rimary focu of thi work involved a Maglev alication in which the heating of the reaction late wa of econdary interet, being intermittent. Exerience ha taught u that a current denity of A/m in the coer i a good number to ue for continuou duty tator conductor cooled by air. Thi number hould be increaed to A/m for water cooled coil. Thi number i increaed uward deending on the duty cycle (61% for thi tudy) and the exoure of the end winding. We tyically erform a thermal analyi after the firt magnetic run and then iterate one to two cycle. The current denity i held fixed during the magnetic analyi, decreaed by the exected acking fraction.

3 > CEFC 006, bet fit 11 (a) (double-click here) < Deending on the voltage targeted, thi number can range from 35 to 75% for a form wound coil machine. A reliminary inulation ecification mut be erformed if the magnetic analyi i to be meaningful. III. THE PARAMETRIC SETUP Rotating machine have the advantage of allowing angular eriodic boundary condition to reduce the ize of the roblem. The deign arameter of interet include the tator and rotor lot width and deth, ga radiu, and amount of back iron behind the rotor and tator. For Maglev alication uch a that driving thi work, the reaction rail wa deigned largely by economic to be a 6.35 cm heet of aluminum backed by a 19 cm heet of The air ga i alo dictated by nonelectrical conideration, in thi cae by ractical mechanical tolerance to 10 mm. The firt te i to rereent the linear motor with a rotary counterart. Why i thi done? Linear motor have ignificant entry and exit effect, but thoe effect hould not be made a art of the otimization which will focu on maximizing thrut/weight and ower factor on a er unit length bai. Becaue of the high ole count characterizing thee motor, it i imortant to otimize the central ortion of the motor to the excluion of end effect. The otimization need to be done with a mall a ortion of the machine a oible to minimize analyi time. M-19 Single ided LIM z x J= A/m y Aluminum σ= S/m mm ga Fig. 1. Cro-ection of a one ided linear induction motor rereented a a large radiu rotary counterart. We deire the bet choice of x, y, and z to maximize erformance. The length i to be choen later to meet the criteria of the onor after the right cro-ection i determined. An uncontrained otimization i emloyed to elect the tooth width, deth, and back iron thickne which maximize one of two indexe, torque/weight and torque/weight time ower factor. The quetion of what contitute bet erformance i quite legitimate. To quickly et the tage for the ret of the aer, thee otimization are olved uing a 4-level neted loo of the unknown x, y, and z lu li. A 4-dimenional line i fit to the data, and variable metric method are ued to find the true maximum [4][5][6]. There are two roblem with the reulting olution hown in Fig.. The tructural integrity of the very lender teeth i quetionable. More imortantly, however, the ynchronou reactance commenurate with the long lot deliver a very oor ower factor and a high current demand on the inverter. Bet torque/ weight ratio Dimenion in cm Fig.. Bet torque-to-weight ratio cro-ection reulting from maximizing torque to weight. Incororating ower factor into the otimization i a more rudent aroach. But thi oe a bit of difficulty. Fig. 3 how the geometry to be otimized, which ue a 5/6 itch three hae winding on the tator. Only 1/180 th of the motor i analyzed uing a 60 degree hae eriodic boundary condition. For the two degree ection hown in inet (b), the vector otential at θ = 0 i reeated at θ =, and hifted by 60. An integration of the vector otential over the lot cro-ection i required to extract ower factor. Portion of thi integration mut be hae hifted by 10 and 180 to comlete thi calculation of ower factor. Air ga (a) Volume current hae attern aluminum θ=0 θ= Fig. 3. Single ided induction motor to be otimized. 1 Phae attern < 0 < -60 < -10 < 180 < 10 < 60 aluminum (b) Volume current ued with hae eriodic condition We wih to comute the voltage induced in the coil air 1-3 and -4 in inet (a) of Fig. 3. But the only coil available in the analyi are thoe hown in inet (b). The olution follow by oberving that volume 5 and 6 hold the neceary 6 5

4 > CEFC 006, bet fit 11 (a) (double-click here) < information i their vector otential are delayed by 180 and 10 degree, reectively. The vector otential through thee volume mut be logged through the analyi and an integration erformed, r r r r r r π j r r jπ 3 V + V = A dl + A dl e A dl e A dl V1 V V5 V6. (1) A the geometry i changed ubtantially, it i imortant to cature erformance near eak li. It i deirable to reduce the number of calculation for li. One technique for doing thi i to recognize from the equivalent circuit of an induction motor hown in Fig. 4, that the thrut varie quite cloely with li a Rr ω M I πq πq I k L F = =. λ Rr λ ( ωl + r) + 1 () R( V ) kl= 1+. (7) I Since all three of thee quantitie are eaily comuted through the analyi, they rovide not only an eay etimate of k L and thu eak thrut, but alo erve a a olution integrity check. In theory only two li calculation are required, but thi author ued 4-5 oint to minimize numerical error. When ower factor i added to the otimization index, the lot become much horter a hown in Fig. 5. Otimized deign when ower factor i added Comute the vector otential over thi comlete region Dimenion in cm Fig. 5. Slot deign uing ower factor time torque/weight a the otimization index. Fig. 4. One hae of the equivalent T circuit for an induction motor. Here, i the li at eak thrut, q i the number of hae, and λ i the tator wavelength; k i the couling coefficient between rotor and tator defined a M k =. (3) LL The eak thrut i r π q I k L Feak =. (4) λ The roblem degenerate to determining the right value of k L. With a bit of analyi, it can be hown that thi ecial roduct i linked not only to thrut and the induced tator hae voltage, but alo to ower diiation on the rotor [7]. kl kl π F = 1 +, (5) qλ I P = 1 +. (6) qi A. Linear Motor Analyi Fig. 6 how the linear embodiment of Fig. 5. One central ole Torque / weight ower factor otimization Central ole air Subection containing 3 ide ole and one central ole air. Fig. 6. Linear embodiment of the induction motor. air i oitioned between 3 ide ole. The ide ole rovide the entry and exit effect. Thi geometry i analyzed for force with the number of central unit, n, for the final motor treated a an unknown. F = nf + F. (8) target central ideunit Thi deign wa comlicated by the additional demand that the motor achieve target thrut with zero vertical force. That mean the motor i oerated at a much higher li than it

5 > CEFC 006, bet fit 11 (a) (double-click here) < rotary counterart. IV. RESULTS Fig. 7 how the finihed tator, 3.35 m long. The thrut and lift force are hown for two different oerating ga. The fact that the vertical force go through zero at the ame li frequency i ignificant. The attractive force to the back late and the eddy current ooing thi attraction have the ame ga deendence, i.e., a 1/ga deendence mm aluminum backed by 19 mm of 1.9 cm 17.1 cm Geometry reeat in thi direction Mirror image below not hown Fig. 9. The reaction rail width mut be extended arametrically in 3D. Reult of the Analyi Fig. 7. Picture of the finihed motor. Force (lb) Force at I mid =868 A, 60 mh, Variable Ga Fx (5 mm) Fy (5 mm) Fx (15 mm) Fy (15 mm) Sli Frequency (f e -f m ) Fig. 8. Thrut and lift force for the comleted motor. The force continue to increae a the reaction late width increae. The knee of the curve aear to make the late about 3.8 cm wider than the motor. Fig. 10 how a comarion to a double ided geometry. Although it doe not have the enalty of unwanted vertical force, the geometry force a vertical reaction late. If the working height of that reaction late i 15. cm, the ingled ided deign i favored. Otimizing againt thrut/weight alo exceed deired inverter ecification. V. CONCLUSIONS Incororating equivalent circuit rereentation into induction motor analyi avoid exceive calculation at different li value. Integrating vector otential over lot with aroriate hae change allow ower factor calculation with le than one ole of geometry. Configuration Otimization Length weight (kg) Rail dii kw CuLo kw Stl Lo kw efficiency ower factor V*I I line (A) nturn/half lot 1 ide Fx/weight.13 m 85.7 kw 49.4 kw 1.74 kw 0.74+j1.6 MW 045 A 80.40% 6.7 cm tack ide Fx/weight*f 3.35 m 0.76+j1.187 MW % ide Fx/weight m 3.8 kw 53.6 kw 1.74 kw j1.4 MW 07 A 15. cm tack % 0.49 ide Fx/weight*f.13 m 30.9 KW 61.4 KW 1.3 kw j1. MW 159 A Both thrut/weight ratio exceed ec on I uing thrut/weight for otimization Fig. 10. Comarion with double ided geometry. VI. REFERENCES % [1] W. Jazdzynki, Multicriterial otimiation of quirrel-cage induction motor deign, IEEE Proc B, Electric Power, vol. 136, no. 6, , Nov [] H. Huang,, E. F. Fuch, J. C. White, Otimization of ingle-hae induction motor deign. II. The maximum efficiency and minimum cot of an otimal deign, IEEE Tran. on Energy Conv., vol. 3, no., , June [3] A. Daidone, F. Parailiti, M. Villani, S. Lucidi, A new method for the deign otimization of three-hae induction motor, IEEE Tran. Mag., vol. 34, no. 5, , Set [4] K. R. Davey, Magnet deign otimization uing variable metric, IEEE Tran. on Mag., vol. 31, no. 6, , [5] K. R. Davey, Ue of tenor roduct line in magnet otimization, IEEE Tran. on Mag., vol. 35, no. 3, , May [6] K. R. Davey, Examination of variou technique for the acceleration of multivariable otimization technique, IEEE Tran. on Mag., vol. 39, no. 3, , May 003. [7] K. R. Davey, The equivalent T circuit of the induction motor: it nonuniquene and ue to the magnetic field analyt, ubmitted to the IEEE CEFC 006, Miami, FL, Ar. 30-May 3,