Synchronous Motor Design using Particle Swarm Optimization Technique

Transcription

1 Proceedings o the 4 th Interntionl Middle Est Power Systems Conerence (MEPCON ), Ciro University, Egypt, December 9-,, Pper ID 87. Synchronous Motor Design using Prticle Swrm Optimiztion Technique R. A. El-Sehiemy nd M. I. Abd-Elwnis A. B. otb nd M. Elwny Deprtment o Electricl Engineering Deprtment o Electricl Engineering University o Krelsheih University o Al-Azhr Krelsheih, Egypt Ciro, Egypt {elsehiemy&mohmed.solimn4}@eng.s.edu.eg elwny6@hotmil.com Abstrct- This pper investigtes n optimiztion procedure or the design o synchronous motor (SM) using prticle swrm optimiztion (PSO) procedure. The PSO is proposed to minimize the motor volume nd to mximize the motor output power. The proposed procedure hs two stges or motor design. In the irst stge, the sttor prmeters re optimized while in the second stge, the ield nd dmper winding re designed. The proposed lgorithm is eiciently compred with the prcticl experience-bsed method. The proposed procedure is eiciently design the SM bsed on the 4- pole proto-type synchronous mchine which is produced t 7 militry production ctories. The proposed procedure leds to more economicl motor compred to the prcticl experience bsed method. Also, the proposed procedure mximizes the SM developed pprent power nd reduces the ield/dmper windings in terms o their conductors' dimeters nd number o conductor per slot. Keywords: Prticle swrm optimiztion technique, synchronous motor (SM). I. INTRODUCTION Synchronous motors re being incresingly used in dierent industry sectors in new pplictions or s lterntives to induction motors in current pplictions. This is due to their mny dvntges including high eiciency, compctness, st dynmics nd high torque to inerti rtio. Synchronous motors with extr etures o mechnicl robustness, cpbility o lux weening nd high speed opertion re prticulrly suitble s vrible speed drives. The reliztion o these merits depends gretly on motor conigurtion. Thereore, gret del o ttention hs been ocused on the optiml design o synchronous motors in recent yers. In the literture, dierent optimiztion procedures were crried with dierent objectives, depending on the prospective ppliction o the motor nd the user s desire. Comprtive studies o minimiztion techniques or optimiztion o c mchines design ws presented with greet progress in mthemticl tools leds to use these optimiztion tools or the electric mchines design in reerence [-]. The optimiztion procedures re pplied or IM []. The prcticl considertion ws presented or the IM design in []. The SM optiml design using Immune lgorithm [3], genetic [4-6] inite element [7]. The optimized design problem in [8] considered the torque cpbility nd low mgnetic volume while in [9] multi-objective optiml design procedure or the interior permnent SM with improved core ormul ws presented. A design optimiztion 795 is perormed on interior type permnent mgnet synchronous motors to chieve high torque development cpbility with low permnent mgnet consumption. A multi-objective optimiztion is perormed in serch or optimum mgnet dimensions nd loction. The design optimiztion results in motor structure superior to originl motor speciictions. For mny resons, experience bsed design methods cnnot ind optiml design solutions when deling with nonliner systems. Also, these methods do not gurntee globl solution or nonliner systems; stochstic serch lgorithms my provide promising lterntive to these trditionl pproches. An intelligent model prmeter identiiction method using prticle swrm optimiztion (PSO). PSO is reltively new stochstic optimiztion technique developed in the mid-99s. The prticle swrm optimiztion procedure ws presented in [-] or IM design in [] nd or the prmeter identiiction o the SM. In pst severl yers, PSO hs been successully pplied in mny reserch nd ppliction res []. It is demonstrted tht PSO gets better results in ster, cheper wy compred with other methods. Another reson tht PSO is ttrctive is tht there re ew prmeters to djust. One version, with slight vritions, wors well in wide vriety o pplictions. Prticle swrm optimiztion hs been used or pproches tht cn be used cross wide rnge o pplictions, s well s or speciic pplictions ocused on speciic requirement. In this pper, multistge design procedure o synchronous motor is proposed. In the irst stge, the sttor prmeters re optimized using prticle swrm optimiztion technique or two objective unctions. These objective unctions re the motor volume minimiztion nd mximiztion o the developed pprent power. Ater the SM sttor prmeters re optimized, the rotor iled nd dmper re designed. Two studied cses re considered nd compred with the experience bsed SM design method. The eect o the in ed voltge o dmper nd ield windings re considered or their dimeter nd their number o conductors per slot. II. RPOBLEM FORMULATION A. Synchronous Motor Output Eqution

2 The output eqution or synchronous mchine cn be expressed in term o its min dimensions, speciic mgnetic nd electric lodings nd speed; the eqution describing this reltionship is nown s output eqution s: S (VA) = C D L n o s () Where, 3 C = B ck w () o v L=sttor core length m, B v =mgnetic loding, c=electric loding, D: sttor conductor dimeter in mm. nd w = winding ctor. The SM volume cn be written s: V(m) = D L (3 ) B. SM DESIGN AS AN OPTIMIZATION PROBLEM The SM design problem cn be expressed s n optimiztion problem s: Min ( x ) st.. g( x) = (4) hx ( ) Where, (x) is the objective unction, g(x), h(x) represent the equlity nd inequlity constrints, respectively nd x is the vector o the control vribles o the SM. These control vribles re the sttor dimeter, length, lux density, the rtio o pole length to pole pitch ( γ ) ) SM design Objectives There re two suggested optiml bsed design procedures, The irst design procedure imed t minimizing the motor volume (Eqution 3) while the second procedure imed t mximizing the pprent power t the ir gp (Equtions nd ). Both objectives re chieved while the motor constrints re considered. ) SM design Constrints ) Air gb length constrint The length o ir gp (l g ) gretly inluences the perormnce o synchronous mchine. A lrge ir gp oers lrge reluctnce to the pth o lux produced by the rmture mm nd thus reduces the eect o rmture rection. This leds to smll vlue o synchronous rectnce nd high vlue o SCR. The rtio o lg to pole pitch should stisy the ollowing constrint: l g τ p. (5) b) Armture Slot constrint π D The slot pitch τ s ( τ = ) depends upon the voltge s s o the mchine. For high voltge mchines which re normlly built in lrge cpcities, it is desirble to use lrge slot pitch. The slot pitch should be less thn 5 mm or low voltge mchines. For slient pole mchines, the number o slots /pole/ phse is usully in the rnge -4. c) Armture conductor constrint The rmture conductor size is dependent on the current psses through it. The conductor current cn be computed rom: S( VA) 3 Iz = I ph = (6) 3E ph I there is set o prllel bths, the permissible current density in the rmture conductor is ssumed to be with 3-5 A/mm. The cross-section re or rmture conductors is computed rom: q s = I z / J mm. s Where, J s = current density in rmture conductors, A/mm. The conductor dimeter (dc) cn be computed s: dcs = qc π (7) C. SM ROTOR DESGIN PROCEDURE The rotor contins the dmper nd ield windings. The design o these windings is crried out s ollows: ) Filed winding The rotor winding is distributed in slots. The pole pitch is so chosen tht undesirble hrmonics re not produced in the lux density wve. The width o rotor slots is limited by stresses t the root o the teeth nd by hoop stress in the end retining rings. Rotor current density my be bout.5 A/mm or cooled mchines. However, in modern direct cooled genertors the rotor current densities my be s high s 9.5 to 4 A/mm. Rotor winding design steps: Computing the Armture mm per pole s: K Tph A T.7 w I = p ph A (8) The Full lod ield mm cn clculted rom: AT = AT (9) For certin excittion voltge V, About 5 to % o this voltge is ept in reserve. Then, the voltge cross ech ield coil is: (.8 to.85)v E = () p The men turn length o iled winding is obtined s : Lm = L +.3τ + 4cm () pr Where, τ =eective spn o coils. p The voltge cross ech ield coil is computed rom: 796

3 E = I R = I L T ρ m L AT = ρ m l Where, I = ield current A, T = number o turns in ech ield coil, = re o ield conductors mm, nd () ρ = resistively ohm /m The re o ield conductors cn be clculted rom: L AT = ρ m l mm (3) E For the ield current density J, the ield winding conductors re cn be computed rom the ollowing eqution: E t ( ) = ATl R = ( pa T l ) ( I ) (4) = ( pa T l ) ( T ) The number o ield conductor is computed rom: pat Z = l (5) J And the number o ield conductor per slot is computed by: pat Z = l (6) s J s r ) Dmper winding The design o dmper winding is dependent on the purpose or which it is provided. In synchronous genertor, it is provided to suppress the negtive sequence ield nd to dmp the oscilltions when the mchine strts hunting, while in synchronous motor its unction is to provide strting torque nd to develop dmping power when the mchine strts hunting. The rotor voltge on open circuit between slip rings should not exceed 5 voltges or smll mchine. The dmper turns T is computed s ollows: E ω T = T ph (7) E ω Where, E is the sttor voltge per phse nd E is rotor voltge per phse t stndstill. The rotor current per phse ( I ) is computed rom considering the ull lod rotor mm is bout 85% o sttor mm s: T I.85 = I T (8) The re o the rotor conductors is ound out by ssumes suitble vlue or current density. The current density ( J ) in the rotor is chosen lmost equl to tht in the sttor. Rotor conductor re is computed rom: = I J mm. The dmper dimeter o conductor is then computed rom: d =. π mm (9) Where, J =current density in rotor conductors. Round conductor re used or smll motors. But or lrge motor it becomes necessry to use br conductors. III. PARTICLE SWARM OPTIMIZATION TECHNIQUE Prticle Swrm Optimiztion (PSO) ws invented by Kennedy nd Eberhrt in 995 while ttempting to simulte the choreogrphed, grceul motion o swrms o birds s prt o study investigting the notion o collective intelligence in biologicl popultions. Prticle swrm optimiztion (PSO) is popultion bsed stochstic optimiztion technique developed by Dr. Eberhrt nd Dr. Kennedy in 995 [], inspired by socil behvior o bird locing or ish schooling. PSO shres mny similrities with evolutionry computtion techniques such s Genetic Algorithms (GA). The system is initilized with popultion o rndom solutions nd serches or optim by updting genertions. However, unlie GA, PSO hs no evolution opertors such s crossover nd muttion. In PSO, the potentil solutions, clled prticles, ly through the problem spce by ollowing the current optimum prticles. In PSO, set o rndomly generted solutions (initil swrm) propgtes in the design spce towrds the optiml solution over number o itertions bsed on lrge mount o inormtion bout the design spce tht is ssimilted nd shred by ll members o the swrm. Modiiction o the swrm gent positions is relized by the position nd trnsition inormtion. Ech gent trnsition cn be simulted by two dimensionl reerred to the vilble inormtion's bout sel nd group experiences. A bsic PSO version bsed on the collected inormtion o sel nd group experience ccording to the gents positions. The bsic PSO version ws presented s [, 3]: best best Δ x = v. Δ x + cr (x x) + cr(gx x) () x+ = x +Δx Where, x is the vector o control vribles t itertion. x best is the vector o personl best o control vribles t itertion. 797

4 best gx is the vector o globl best o control vribles t itertion. x + is the vector o control vribles t itertion +. The velocity is updted t itertion or the control vribles using eqution () s: mx mx min mx v = v ( v v ) Iter () The lrge number o inerti coeicient (v) leds to more globl solution. The lerning coeicients c nd c re the ctors which PSO technique optimizes dierent objective unctions on the bsis o personl nd group experiences nd ech gent tries to modiy its position the updting ormul (). The updting ormul in () or gent position nd trnsition inormtion is limited by the minimum nd mximum trnsition vlues s: min mx T Δx T () Where the mximum nd the minimum trnsition in () re computed rom: mx mx min T = m( x x ), (3) min mx min T = m( x x ) IV. PROPOSED SOLUTION METHODOLOGY The PSO-bsed design procedure steps re:. Deining the motor limits nd constrints nd the PSO lgorithm coeicients (lerning inerti).. Solving the sttor side problem by solving the PSO-bsed design problem to obtin the best sttor design considering two objectives nmely, developed power (pprent power) nd the sttor volume. For the motor volume minimiztion, Eqution is considered s n objective unction with the sttor constrints (Equtions 5-7). For the developed pprent power mximiztion, Eqution 3 is considered s n objective unction with the sttor constrints (Equtions 5-7). 3. For ech studied cse, design the ield/dmper windings re perormed bsed on the optiml sttor prmeters in the previous step. 4. Agin, redesign the dmper/ield windings or dierent in ed voltges bsed on the sttor results obtined in step. 5. Perorming comprison with the experience bsed design or the synchronous motor or vried rnge. V. NUMERICAL EXAMPLE Three studied cses re considered in this pper to design the SM or 4-pole proto-type synchronous mchines which is produced t 7 militry production ctory by modiying the rotor o 4-pole 38V, str connection, 5Hz, squirrel-cge induction motor. The modiied SM strts s n IM nd the continuous opertion will be synchronous. Three studied cses re considered: Cse ) Design o the SM using conventionl method. Cse ) Designs o the SM using the proposed MPSO procedure bsed on minimize the motor volume. Cse ) Design o the SM using MPSO method bsed on mximizes the output power. Tble shows the results obtined using the experience bsed design procedure (cse ) compred to the other two optimized cses or the tested motor. In this tble, Cses nd leds to more reduction in the motor volume with reduction o.84 % compred with the cse. Cse increses the output power compred to the other two cses. Also, cses nd leds to more reduction in the required totl mpere conductor (AC) with reduction o.88%. The ield nd dmper prmeters re vried ccording the objective unctions considered in the irst stge o the design bsed on PSO technique. For the irst studied cse (Cse ), Figures nd show the vrition o ield winding dimeter nd ield conductor per slot versus the ield voltge, respectively. It is clered tht, the ield winding dimeters increse linerly with the ield voltge while, the ield winding conductor per slot decreses with the ield voltge incresed. This mens tht: the higher ield voltge leds to decrese the ield conductor per slot. Figures 3-4 show the vrition o dmper conductor per slot nd dmper dimeter versus dmper voltge, respectively. It is clered tht rom these igures, the dmper conductor per slot increse linerly with the dmper voltge while, the dmper winding conductor per slot decreses with the dmper voltge incresed. This mens tht: the higher dmper voltge leds to decrese the dmper dimeter. For the second studied cse (Cse ), Figures 5 nd 6 show the vrition o dmper conductor per slot nd dmper dimeter versus the dmper voltge or Cse. It is clered tht, the dmper winding turns nd conductor per slot increse linerly with the dmper voltge while, the dmper winding conductor per slot decreses with the dmper voltge incresed. This mens tht: the higher dmper voltge leds to decrese the dmper dimeter The ield winding dimeter increse linerly with the ield voltge s shown in Figure 7 while, the ield winding conductor per slot decreses with the ield voltge incresed s shown in Figure 8. This mens tht: the higher ield voltge leds to decrese the ield conductor per slot. TABLE A COMPARISON BETWEEN SM DESIGN RESULTS USING DIFFERENT OPTIMIZATION TECHNIQUES FOR THE TESTED MOTOR studied cses Vribles cse cse cse γ B (web/m ) Control D (m) vribles AC L (m)...3 Rted power S VA Volume Vm Ts Dmper E (V) winding Tr

5 ield winding dimeter Field winding dimeter mm Zs dmper 56 7 V (V) 3.38 dimeter mm Zs Z ield voltge (volt) Figure : Field winding dimeter verses ield voltge or Cse.5 ield conductor per slot dmper winding dimeter ield voltge (volt) Figure : Field conductor per slot versus ield voltge or Cse dmper voltge per phse (volt) Figure 3: Dmper winding dimeter versus dmper voltge or Cse dmper conductor per slot dmper voltge per phse (volt) Figure 4 Dmper conductors per slot versus dmper voltge or Cse 5 dmper conductor per slot dmper voltge per phse (volt) Figure 5 Dmper conductors per slot versus dmper voltge or Cse dmper winding dimeter dmper voltge per phse (volt) Figure 6: Dmper winding dimeter versus ield voltge or Cse ield winding dimeter ield voltge (volt) Figure 7: Field winding dimeter versus ield voltge or Cse 799

6 ield conductor per slot ield voltge (volt) Figure 8: Field conductors per slot versus ield voltge or Cse [8] S. Vez-Zdeh, A.R. Ghsemi, " Design optimiztion o permnent mgnet synchronous motors or high torque cpbility nd low mgnet volume," Electric Power Systems Reserch 74 (5) [9] D. Hyeo, H. Kyo, D. Joon, "Multiobjective optiml design o interior permnent mgnet synchronous motors considering improved core ormul," IEEE Trns. Energy Conv. 4 (999) [] R. Knnn, R. Bhuvneswri, nd S. Subrmnin, "Optiml Design o Three-Phse Induction Motor Using Prticle Swrm Optimiztion," Irnin Journl o Electricl nd Computer Engineering 6 (7) 5-. [] L. Liu, W. Liu, D. A. Crtes, "Prticle swrm optimiztion-bsed prmeter identiiction pplied to permnent mgnet synchronous motors," Engineering Applictions o Artiicil Intelligence (8) 9-. [] [3] A. A. Abou El-El, R. A. El-Sehiemy," Optimized Genertion Costs Using Modiied Prticle Swrm Optimiztion Version," WSEAS Trnsctions on Power Systems (8) 5-3. VI. CONCLUSIONS This pper hs been eiciently solved the problem o synchronous motor design using prticle swrm optimiztion technique. The results obtined with the designed procedure re compred with experience-bsed method. The proposed PSO technique oers some dvntges over deterministic methods s: ) Minimizing the motor volume rom 87 cm 3 using the conventionl method to 68 cm 3 using the proposed optimized design procedure. ) Mximizing the pprent power compred to the conventionl design method. 3) The totl mpere conductor using the proposed optimiztion technique is sved by.88%. 4) The incresed dmper voltge leds to more reduction in dmper winding dimeter. While, The incresed ield voltge leds to more reduction in the ield conductor per slot. REFERENCES [] J. Appelbum, E.F. Fuchs, J.C. White, I.A. Khn, "Optimiztion o Three Phse Induction Motor Design, " Prt I + II, IEEE Trns. EC, (987) [] C. Singh, D. Srs, "Prcticl Considertions in the Optimiztion o Induction Motor Design," Proc.IEE, Vol.B 49 (99) [3] J. Chun, J. Lim, J. Yoon, "Optiml Design o Synchronous Motor with Prmeter Correction Using Immune Algorithm," IEEE Trnsctions on Energy Conversion 4 (999) [4] D.-H. Cho, H.-K. Jung, T.-K. Chung, C.-G. Lee, "Design o shorttime rting interior permnent mgnet synchronous motor using niching genetic lgorithm," IEEE Trns. Mgn. 36 () [5] D.-J. Sim, H.-K. Jung, "Appliction o vector optimiztion employing modiied genetic lgorithm to permnent mgnet motor design," IEEE Trns. Mgn. 33 (997) [6] D. Joon, D. Hyeo, J. Sung, "Eiciency optimiztion o interior permnent mgnet synchronous motor using genetic lgorithms," IEEE Trns. Mgn. 33 (997) [7] T. Ohnishi, N. Thshi, "Optiml design o eicient IPM motor using inite element method," IEEE Trns. Mgn. 36 ()