T e = K 1 Φ m I 2 cosθ K 1 Φ m I cosθ 2 1 T 12 e Φ / 13 m I 4 2 Φ m Φ m 14 I 2 Φ m I 2 15 dq0 T e = K 2 ΦI a 2 16

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纶位胥
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1 Vol. 23 No. 5 JOURNAL OF HARBIN UNIVERSITY OF SCIENCE AND TECHNOLOGY Oct αβ0 MT0 ABC DOI /j. jhst TM351 A Indcton Motor Hybrd Coordnate Transformaton Model and Its Applcaton LIANG Yan-png WAN Yn-long WANG Chen-gang School of Electrcal and Electronc Engneerng Harbn Unversty of Scence and Technology Harbn Chna Abstract For the strong coplng problem between the rotor crrent and the ar gap flx n the expresson of the electromagnetc torqe expresson of the ndcton motor the hybrd coordnate transformaton s adopted by the αβ0 transformaton and the MT0 transformaton and the electromagnetc torqe expresson of the ndcton motor s decopled. The hybrd coordnate transformaton s dedced and the mathematcal model of hybrd coordnate transformaton of ndcton motor s gven. The smlaton model of the ndcton motor s respectvely establshed nder the hybrd coordnate system and the ABC coordnate system. The mathematcal model of the hybrd coordnate transformaton n the ndcton motor s verfed by comparng the smlaton reslts. In the applcaton of the hybrd coordnate transformaton the ndrect vector control smlaton system based on flx lnkage open-loop and speed closed loop s taken as an example. The smlaton reslts show that the stator crrent of the ndcton motor s decopled nto the stator crrent component generatng the magnetc feld and the stator crrent component generatng torqe by the hybrd coordnate transformaton so the valdty of the hybrd coordnate transformaton s verfed. Keywords electromagnetc torqe hybrd coordnate transformaton decoplng E E-mal @ qq. com.

2 T e = K 1 Φ m I 2 cosθ K 1 Φ m I cosθ 2 1 T 12 e Φ / 13 m I 4 2 Φ m Φ m 14 I 2 Φ m I 2 15 dq0 T e = K 2 ΦI a 2 16 K 2 Φ PI I /F I a dq 17 dq0 Φ I a Φ I a Φ 18 I a αβ0 MT0 αβ0 MT0 αβ0 1 ABC 1

3 ABC αβ cosθ snθ 0 N 3 A B C C 2s/2r = - snθ cosθ 0 N 2 α β A α 1 N 2 α = N 3 A - ( N 3 B - N 3 C ) cos60 = N 3 ( A B C ) 3 N 2 β = N 3 B sn60 - N 3 C sn60 = N 3 槡 3 2 B - 槡 3 ( 2 ) 4 C 3 ~ 4 [ α ] = N A N B 5 2 β 2 0 槡 3 - 槡 C = K N 3 ( N A + B + C ) ~ 6 3 N 3 2 = N 2 槡 3 K = 1 A B C A 7 槡 2 a b c a A 5 ~ 7 φ ω 1 α A β = C 3s/2s B 8 0 C C 3s/2s = 0 槡 3 - 槡 3 槡槡 2 槡 2 槡 2 MT0 2 αβ MT α β m t ω 1 F s θ M α 3 2 A = R s A + pψ A [ m cosθ snθ ] = [ t - snθ cosθ] [ α ] 9 B = R s B + pψ B β C = R s C + pψ C 11 m a = R r a + pψ a α t = C 2s/2r β b = R r b + pψ b 10 c = R r c + pψ c 0 0

4 5 49 A A ψ A A A A αβ0 MT0 M A α θ s θ r ( ) A A = 槡 2 R s R r p 3 smcosθ s - st snθ s + 1 槡 2 s0 A = 槡 2 3 smcosθ s - st snθ s + 1 槡 2 s0 ( ) 16 ψ A L AA L AB L AC L Aa L Ab L Ac A ψ ψ B L BA L BB L BC L Ba L Bb L Bc A = 槡 2 3 ψ smcosθ s - ψ st snθ s + 1 B 槡 2 s0 ( ) ψ C L CA L CB L CC L Ca L Cb L Cc C 16 A = R s A + pψ A = ψ a L aa L ab L ac L aa L ab L ac a sm = R s sm + pψ sm - ω 1 ψ st } ψ b L ba L bb L bc L ba L bb L bc b st = R s rt + pψ st + ω 1 ψ sm 17 ψc L ca L cb L cc L ca L cb Lcc c s0 = R s s0 + pψ s0 12 L AA A sm = R s sm + pψ sm - ω 1 ψ st L AB B A st = R s rt + pψ st + ω 1 ψ sm 18 rm = R r rm + pψ rm - ω s ψ rt T e = n p L ms [ ( A a + B b + C c ) snφ + rt = R r rt + pψ rt + ω s ψ rm ( A b + B c + C a ) sn( φ + 2π / 3 ) + ( A c + B a + C b ) sn( φ - 2π / 3) ] 13 ω s n p L ms 12 ψ [ s ψ ] r I [ ] [ s ] = L ss L sr L ψ s = [ ψ A ψ B ψ ] T C ψ r = [ ψ a ψ b ψ ] T c C s3s/2r = C 3s/2s C 2s/2r = I s = [ A B ] T C I r = [ a b ] T c cosθ s cos( θ s - 2π / 3) cos( θ s + 2π / 3) 2 - snθ 槡 s - sn( θ s - 2π / 3) - sn( θ s + 2π / 3) L AA L AB L AC L Aa L Ab L Ac 3 L ss = L BA L BB L BC L 1 / 槡 2 1 / 槡 2 1 / 槡 2 sr = L Ba L Bb L Bc L CA L CB LCC L Ca L Cb LCc 14 L aa L ab L ac L aa L ab L ac C - 1 s2r /3s = C T s3s/2r L rs = L ba L bb L bc L rr = L ba L bb L bc L ca L cb LcC L ca L cb Lcc C r3s/2r = C 3s/2s C 2s/2r = cosθ r cos( θ r - 2π / 3) cos( θ r + 2π / 3) 2 - snθ 槡 r - sn( θ r - 2π / 3) - sn( θ r + 2π / 3) ψ sm sm 3 ψ st 1 / 槡 2 1 / 槡 2 1 / 槡 2 st ψ s0 15 = C s3s/2rl ss C - 1 s2r /3s C s3s/2r L sr C - 1 r2r /3s C - 1 r2r /3s = C T ψ r3s/2r rm [ C r3s/2r L rs C - 1 s2r /3s C r3s/2r L rr C ] s0 = - 1 r2r /3s rm ψ rt rt ψr0 r0 L rs rr I r 19

5 50 23 L s 0 0 L m L s 0 0 L m L s L m 0 0 L r L m 0 0 L r L r0 sm st s0 rm rt r0 20 L s = 1. 5L ms + L ls L ls L s0 = L ls L m = 1. 5L ms L r = 1. 5L ms + L lr L lr L r0 = L lr C - 1 s2r /3s C - 1 r2r /3s φ = θ s - θ r T e = n p L m L r ( st rm - sm ) rm = ( ψ rm - L m sm ) /L r rt = ( ψ rt - L m st ) /L } r rt MT0 M ψ r ψ rm = ψ r ψ rt = 0 23 rm = rt = 0 22 ~ T r = L r /R r L m ψ r = T r p + 1 sm ψ r 200 N m sm sm ψ r 22 ~ T e = n p L m L r st ψ r ψ r T e st A 75 A Smlnk N m 4 Smlnk

6 r /mn r /mn 0. 1 s 10 ABC ABC Smlnk ABC N m 9 ABC Smlnk 9 ABC N m 13 ABC r /mn r /mn 11 ABC 0. 2 s 30 A A ABC 13

7 Smlnk 14 IGBT 3s /2s 2s /2r PI 16 sm ψ r N m sm ψ r st T e 17 st T e s 1 s 16 sm sm ψ r T r 17 3 s st 0 T e N m sm 3 st T e ψ r

8 J J J J Matlab 15. d-q J M J HUANG Xan HUANG Y. Modelng and Smlaton of Vector Control and Varable-freqency Reglatng Speed System of Asynchronos Motor Based on Matlab C / / 2011 Internatonal Conference on Consmer Electroncs Commncatons and Networks CECNet XanNng STATCOM Performance Drect torqe Control Method wth PWM Approach of J PMSMs C / / 2014 IEEE Internatonal Conference on Indstral 5. Technology ICIT Bsan J J J J J J J J J J YUN Chang Kwak AHN Jn-Woo LEE D. Dong-Hee An Hgh

3 9 1 V α = R s + pl α pl αβ α - snθ r + ωλ m V pl β αβ R s + plβ β cosθ r 1 V λ L α β α β R s p ω λ m θ r 3 V αs s 8 N /S V αs p λ α s λ β λ α λ 5 -

3 9 1 V α = R s + pl α pl αβ α - snθ r + ωλ m V pl β αβ R s + plβ β cosθ r 1 V λ L α β α β R s p ω λ m θ r 3 V αs s 8 N /S V αs p λ α s λ β λ α λ 5 - 1 3 1 3 ELECTRI C MACHINES AND CONTROL Vol. 1 No. 3 Mar. 1 1191 -q N /S N /S TM 351 A 17-9X 1 3-8- 5 Intal rotor poston nspecton of PMSM base on rotatng hgh frequency voltage sgnal njecton ZHOU Yuan-jun