H. A. Toliyat m = R + dψ R. O. C. Lya dt 1 4 Y 3 = u 1 u 2 u m T = i 1 i 2 i m T ψ = ψ 1 ψ 2 ψ m T R = E m m E m m m m 1. 2 b e 7 1 i

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1 ELECTR C MACHNES AND CONTROL Vol. 14 No. 9 Sep d-q- TM 343 A X Modelig ad imulatio of a multiphae cocetated iductio machie ZHANG Jig-wei ZH Hou-qua HANG Zhe-hua YANG Gao DA Yog The 712 Reeach titute CSC Wuha 4364 Chia Abtact Thi pape peet a mathematical model fo a multiphae cocetated iductio machie baed o multi-loop theoy ad deduce the iteelated mutual iductace accodig to the pace aagemet of coil. Compaed with taditioal mathematical model baed o d-q- tafomatio thi model ha ome chaacteitic of coideig the umbe of lot ad eaie calculatio of paamete which big ome beefit of commoality ad accuacy due to avoidig the eceay paamete-coveio i taditioal model ad coideig the effect of all hamoic. Thee meit make it uitable fo imulatio ad aalyi of the multiphae cocetated iductio machie while o-ie voltage powe i upplied. The model i alo veified by expeimetal eult. Key wod multi-loop theoy multiphae cocetated iductio machie mathematical model oie powe upply

2 H. A. Toliyat m = R + dψ R. O. C. Lya dt 1 4 Y 3 = u 1 u 2 u m T = i 1 i 2 i m T ψ = ψ 1 ψ 2 ψ m T R = E m m E m m m m 1. 2 b e 7 1 i d-q- = dψ i + 1 dt i i - b i i + i i - 1 = 2 b + e = R + dψ dt 2 2 = i 1 i 2 i ψ = ψ 1 ψ 2 ψ m - b - b - b - b m R = - b Y 3 - b 6 - i i-1 i i i i = R R + d ψ dt 1 ψ ψ ψ = L L L T L 4 L L Fig. 1 Cuet-loop i oto

3 9 77 L L σ L max 1. 4 L max = ψ = N φ = R R R R L L L T L + d dt + ω dl T dθ d dt L L ( L T L ) dl dθ + = 5 θ ω L max = N 1 μ N 1 πd 2 g ef 2p 2p l ef = N2 μ πd 4p 2 g 2 l ef 7 ef μ g ef D 2 l ef L F 驻兹 (a) 定子整距绕阻产生的气隙磁势仔 1 2p N 兹 2 -L max 驻兹 1 ~ 5 m (b) 定子绕组之间的互感与电角度差之间的关系 5 2 Fig. 2 Relatiohip betwee the mutual-iductace of 7-8 tato ad the diffeece of electical agle ψ 2. 1 L N 2 a 1 p 2 b 2 b 2 a Δθ Δθ = Δθ = π Δθ = 2π Δθ = Δθ 2π 2. 2 L Δθ 2 b i 3 a = 6 j L max + L σ i = j - 2L max Δθ L ij = π ( - π 2 ) i j Δθ < π 2L max Δθ π ( - 3π 2 ) i j π Δθ < 2π 6 Δθ 3 b Δθ Δθ i j

4 78 14 { L max + 2 L e + L b i = j L ij = L mi - L b i - j = 1 i - j = - 1 L mi 8 L e L b 15 L max L mi ( ) L max = 1-1 μ πd 2 g ef l ef L mi = 1 μ πd 2 g 2 l ef 9 ef F L max = ψ 1 驻兹 p μ = N πd 2 2pg ef l ef N 1 1 2p (a) 定子整距绕组和转子导条回路的相对位置 L 兹 12 F L max 仔 2 2 -L max p (b) 定转子互感与电角度差之间的关系驻兹 L 驻兹 (a) 转子导条回路产生的气隙磁势兹 Fig. 4 4 Mutual-iductace of tato widig ad oto loop elative to diffeece of electical agle L max 2 -L max 仔驻兹 (b) 转子导条回路的互感与电角度差之间的关系 dl { dl π - 2πp / Δθ < π = - dl 3 dθ 2π - 2πp / Δθ < 2π 13 Fig. 3 Mutual-iductace of oto elative to diffeece of electical agle dl 2. 3 dl = 2L max 2πp / = N μ D 2p 2 g 2 l ef ef 4 a dl %/dt dl Δθ Δθ 2π 4 b 仔 L max Δθ < π - 2πp / L max Δθ πp ( + πp - π) π - 2πp / Δθ < π L = - L max π Δθ < 2π - 2πp / - L max Δθ πp ( + πp - 2 π ) 2π - 2πp / Δθ < 2π Δθ Δθ t = Δθ + ω τ dτ b 5 Fig. 5 -dl 5 p 驻兹 14 Deivative of mutual-iductace of tato widig ad oto loop with epect to diffeece of electical agle F m F m = F δ + F t1 + F t2 + F j1 + F j2 Δθ ω F δ F t1 F t2 L max F j1 F j2 15

9 79 K = 1 + F t1 + F t2 F m F δ F δ 16 14 L = K F m g ef 17 K L' = K F δ g ef = K F δ F m F m g ef = K F m K g ef 18 14 K g ef (b) 转子导条电流 3 15 K 45 kw 4 %%%%%%.5%%%%%1.%%%%1.5%%%%%2.%%%%2.5%%%%%3.

5 9 79 K = 1 + F t1 + F t2 F m F δ F δ L = K F m g ef 17 K L' = K F δ g ef = K F δ F m F m g ef = K F m K g ef K g ef (b) 转子导条电流 3 15 K 45 kw 4 %%%%%%.5%%%%%1.%%%%1.5%%%%%2.%%%%2.5%%%%%3.%%%%3.5%%%%%4.%%%%4.5%%%%5. f 1 = (d) 电机转速 2 Hz 1 = 14 V 7 f 2 = 6 Hz 2 = V 2 = 1 /6 15 N m 2% Fig. 7 Simulatio of dyamic pefomace of pototype machie ude give voltage ad load toque T l = 15 N m t = 2 T l = 262 N m kw t = 3. 5 a b 1 T l = 388 N m kw 6 a 8 ~ u 1 b T l u1/v 2-2 %%%%%%.5%%%%%1.%%%%1.5%%%%%2.%%%%2.5%%%%%3.%%%%3.5%%%%%4.%%%%4.5%%%%5. (a) 定子第 1 相外加电压波形 4 Tl /(N m) 2 %%%%%%.5%%%%%1.%%%%1.5%%%%%2.%%%%2.5%%%%%3.%%%%3.5%%%%%4.%%%%4.5%%%%5. (b) 负载转矩波形 /mi 594 /mi %%%%%%%%1.84%%%%%%%%1.88%%%%%%%%1.92%%%%%%%%1.96%%%%%%%%2. Fig. 6 Cuve of voltage ad load toque applied o phae 1 i1/a Te /(N m) i1/a 7 a 1 b 8 c d Fig. 8 Meaued cuet ad imulative cuet o o-load 4-4 %%%%%%.5%%%%%1.%%%%1.5%%%%%2.%%%%2.5%%%%%3.%%%%3.5%%%%%4.%%%%4.5%%%%5. (a) 定子第 1 相电流 % -5% /( mi -1 ) 5 %%%%%%.5%%%%%1.%%%%1.5%%%%%2.%%%%2.5%%%%%3.%%%%3.5%%%%%4.%%%%4.5%%%%5. %%%%%%.5%%%%%1.%%%%1.5%%%%%2.%%%%2.5%%%%%3.%%%%3.5%%%%%4.%%%%4.5%%%%5. (c) 电磁转矩 kw kw i1/a i1/a %%%%%%%%%%%.4%%%%%%%%.8%%%%%%%%.12%%%%%%%%.16%%%%%%%% (a) 空载时的实测电流 (b) 空载时的仿真电流

8 14 i1/a i1/a i1/a i1/a 3 2 1-1 -2-3 %%%%%%%%%%%.4%%%%%%%%%.8%%%%%%%%%.12%%%%%%%%.16%%%%%%%%.2 (a)15.4%kw 时的实测电流 3 2 1-1 -2-3 3.3%%%%%%%%3.34%%%%%%%%3.38%%%%%%%%3.42%%%%%%%%3.46%%%%%%%%3.5 (b)15.

HO Liju S Yami CHEN Li et al. The developmet (a)23.2%kw 时的实测电流 tate ad applicatio popect of multiphae iductio moto dive 3 ytem J. Micomoto 21 34 5 42-44. 2 2 TOLYAT H A LPO T A WHTE J C.

6 8 14 i1/a i1/a i1/a i1/a %%%%%%%%%%%.4%%%%%%%%%.8%%%%%%%%%.12%%%%%%%%.16%%%%%%%%.2 (a)15.4%kw 时的实测电流 %%%%%%%%3.34%%%%%%%%3.38%%%%%%%%3.42%%%%%%%%3.46%%%%%%%%3.5 (b)15.4%kw 时的仿真电流 kw Fig. 9 Meaued cuet ad imulative cuet at beaig powe of kw %%%%%%%%%%%.4%%%%%%%%%.8%%%%%%%%%.12%%%%%%%%%.16%%%%%%%%.2 J HO Liju S Yami CHEN Li et al. The developmet (a)23.2%kw 时的实测电流 tate ad applicatio popect of multiphae iductio moto dive 3 ytem J. Micomoto TOLYAT H A LPO T A WHTE J C. Aalyi of a cocetated 1 widig iductio machie fo adjutable peed dive applica- tio Ⅰ Moto aalyi J. EEE Taactio Eegy Coveio TOLYAT H A LPO T A WHTE J C. Aalyi of a cocetated %%%%%%%%4.84%%%%%%%%4.88%%%%%%%%4.92%%%%%%%%4.96%%%%%%%%5. widig iductio machie fo adjutable peed dive applica- tio Ⅱ Moto deig ad pefomace J. EEE Taactio (b)23.2%kw 时的仿真电流 Eegy Coveio kw 4 LYRA R O C LPO T A. Toque deity impovemet i a ix-phae Fig. 1 Meaued cuet ad imulative cuet at beaig powe of kw iductio moto with thid hamoic cuet ijectio J. EEE Taactio o duty Applicatio M M J L Hui. Geealized modelig ad imulatio of iductio moto 2 takig the hamoic field effect ito accout J. Lage Electic 3 Machie ad Hydaulic Tubie Table 1 空载 15.4%kW 23.2%kW 负载 Hamoic aalyi eult of meaued ad imulative cuet ude diffeet load 实验值仿真值实验值仿真值实验值仿真值 4 幅值 /A 基波电流功率因数.81%7.92%.725%5.764%6.823%1.865%4 三次谐波电流幅值 /A 功率因数.69%3.93%3.414%6.428%4.58%5.537%3

8 9 8 Δ 9 = 1 Η Ι4 ϑ< Κ Λ 3ϑ 3 >1Ε Μ Ε 8 > = 8 9 =

!! % & ( & ),,., / 0 1. 0 0 3 4 0 5 3 6!! 7 8 9 8!! : ; < = > :? Α 4 8 9 < Β Β : Δ Ε Δ Α = 819 = Γ 8 9 8 Δ 9 = 1 Η Ι4 ϑ< Κ Λ 3ϑ 3 >1Ε 8 9 0 Μ Ε 8 > 9 8 9 = 8 9 = 819 8 9 =