Determination of slot leakage inductance for three-phase induction motor winding using an analytical method
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1 ACHIVES OF EECTICA EGIEEIG VO 6 pp DOI 78/--6 Dtnton of ot ntn fo t-p nton oto wnn n n nt to JA STASZAK Dptnt of Et Mn n Mton St K Unvt of Tnoo Tą PP 7 K Pon -: j@tp v: v: 5 Att: T t nto o pon fo f- n t ot ntn of p wnn fo t tt o of n nton n n t nt p oont t n fo o n n n t oont f Cton of f- n t ot ntn v n pfo fo tp o- t n t-of wnn onnton Into pon f n t n of wnn n n t n of n tt of AC t n K wo: ot ntn f- n t ntn nton oto Intoton T n of n tt of nton n n ot n t nt t-p t [6 7] o n t oon t fn f T t of t ntn twn t tto n oto wnn n t nt oont f pn on t n twn of t tto n oto wnn Intoton of oon t fn f fo t tto n oto tt t t ntn t t offnt w n-npnnt on t oto otton In t to of t n w nt ntn of t tto n oto wnn ot wt t n nt f n t ntn ot wt f T of tnn t f- n t ntn ot wt t n f n w n t tt [ 7] T ntn tn n t now of t pt tton of t tto nt f n t p-tn [ ] Howv of t po v to t tnton of t ntn of wnn In t onoon o of t-p nton n t f of wnn ont of ot f -p f n wnn n w f T t ptpton n t tot f t oponnt ot wt t ot on So f to t t ot ntn n t op v [5 ] T w t ot ntn tn fo t tt Untntt Downo Dt /9/8 : AM
2 57 J Stz A Et En of n nton n T of op v o not ow to tnt of f- n t ntn of ot T oo [7] nto pnn t f- n t ntn of ot f fo t o- wnn n ntntno v of tto nt T oo pnt ow to tn t f- n t ntn of t ot f fo t tt o n nt t-p t n fo o n n t fn f Cton v n pfo fo t-p o t n t-of wnn In wnn t oon ot two of ffnt o n n o ot t on to ffnt p T po t ot ntn fo t n- wnn w to zo A tt o of t-p nton n fo t nt p t Annt of t tto n oto wnn n t t-p nton n wt on p of po own n F T-p nton n on t of nt op tto- n oto wnn T f nt fo t tto n t ottn nt of t oto ovn to ot wt n t vot ω T tto wnn nt n t tt t S t-p oto wnn ont of t nt tt wnn p n p t [6 7] F Annt of t-p wnn of t nton n n t fn tto n oto v wtn oon fn f Vot ton of t tto n oto wnn n t nt fn f n t t fo [6 7] Untntt Downo Dt /9/8 : AM
3 Vo 6 Dtnton of ot ntn fo t-p nton oto wnn 57 t t w: on vto of vot nt n f ot tto n oto wnn t of t tto n oto wnn tn Mt of tto n oto tn on w: tn of on p wnn of tto n oto Stto n oto n f n p t ntn t t foown ton 5 w: tto n oto f ntn t t of t ntn twn tto n oto wnn T t n twn t oto n tto F In t ov ton t n f to v n pt of tto t n n to v n pt of t oto t Mt of f ntn of tto n oto ont of t of f ntn ot wt t n f n t t ot wt t ntn ot wt f 6 w: t of f ntn of tto n oto onnt wt t n f n p t of ntn of tto n oto Mt of ntn of tto n oto of H non t t n ontn t f ntn f n t t ntn f Untntt Downo Dt /9/8 : AM
4 57 J Stz A Et En 7 w: f f ntn of on p of tto n oto wnn t ntn of f twn t tto wnn o oto wnn In t n- n f-pt o- wnn t tto n oto t ntn to zo Sf ntn t of tto n oto onnt wt t n f of H non t t wt ontnt offnt 8 w: ntzn ntn of t tto n oto wnn onnt wt t n f Mntzn ntn of tto n oto fn pon [6 9] δ p w w δ p n 9 w: nt pt of v v of p δ fftv tn of p fftv nt of t tto o n of onnt tn n wnn tto n oto p w w offnt of tto n oto wnn n tn to w n w w T t of t ntn twn t tto n oto wnn t wt offnt pnn on t n of oto otton o o o o o o o o o t ntn twn t tto n oto wnn tn ton [6 9] δ p w p w n Tn nto ont 5 twn t f ot wt t tto n oto wnn n Untntt Downo Dt /9/8 : AM
5 Vo 6 Dtnton of ot ntn fo t-p nton oto wnn 57 tto n oto nt t vot ton fo t tto n oto t t foown fo t t t t t t Tn nto onton t t vtv of t ntn ω ω t t t t t t Eton n wttn ω ω t t t t 5 In o to o t ton fo t n tt of n nton oto t tto n oto vot ton 5 o ppnt t ton of ovnt T T J t Ω 6 w: J ont of nt T tont to T o to Etont to of n nton oto n nt t-p fn f t fo pnn [6 8 9] T p T 7 A tt o of t-p nton oto n t t fn f In o to pf t n t onvnnt to t t oto v vot nt n f fo tto on to tn to n n n ψ ψ 8 Untntt Downo Dt /9/8 : AM
6 57 J Stz A Et En Conn pnn 8 t vot n f ton t t fo t t 9 n t n- Conn t pon 8 9 n wt oto tn t tn w otn n n n o o o o o o n o o o In o to otn ton wt ontnt offnt t n to ot t tnfoton of t tto n oto v to oon t fn f w ottn wt n n vot ω C C C 5 D D D T tnfoton t C of tto p to t t fn f of n t nv t C tn o o o C n n n 6 Untntt Downo Dt /9/8 : AM
7 Vo 6 Dtnton of ot ntn fo t-p nton oto wnn 575 n o n o n o C 7 Howv tnfoton t D of oto p to t t fn f of n t nv t D tn n n n o o o D 8 n o n o n o D 9 In t ov-nton t n n t n twn tto nt n t of oon t fn f Howv n t n twn t tto n oto T t vtv of t n n n nt n F v t t n vot ω n t fn f n t n p of oto ω t ω t ω T f-vot Eton 9 n to n t oon t fn f on to pnn 5 v t t D D D D C C C C D D C D D C C C Untntt Downo Dt /9/8 : AM
8 J Stz A Et En 576 Aft tnn t t Eton n on n otn D D D C C C C C D D 5 t t t t - - K D D K C C ω ω ω 6 w: K K Don t of ntn ontn tto ntn n oto on w tto ntn n t oto on 7 ntn of tto n oto t ffn of f ntn of pt wnn n t ntn twn t p wnn of t tto o oto S ntn wnn ntn of t oponnt of f Howv t tto ntn n oto wnn ntn fo zo f n oponnt It t of wnn f ntn n o t ntn of tto o oto wnn Untntt Downo Dt /9/8 : AM
9 Vo 6 Dtnton of ot ntn fo t-p nton oto wnn 577 Tn nto ont t pnn -6 t t ton of t tto n oto vot n f n t t of oont n t t fnf t t fo of t t ω ω ω 8 8 w F ow t vnt oponn to pon 8 n 8 F At fn-f vnt fo -p t nton n Untntt Downo Dt /9/8 : AM
10 578 J Stz A Et En Etont to n t oon fn f tn pnn [ 6 7] T p 9 Dtnton of ot ntn of o- wnn In t o- wnn t ot w tt n pp n ow t o On of t o ot n t otto of ot n t on of t o ot pp t ot In t of o- wnn w n tn t ot n w t ow n pp wt ffnt p F ow t tton of o w n t ot of tto of t t-p nton oto of tto wt ot n 8 t n of po p p t n of ot p po n p n ot pt 7/ F Annt of o of o- wnn wt ot pt 7/9 Sot ntn tn t foown pfn pton: C nt pt of font t onn t ot to nfnt C tton of t nt f n on t wt of ot tt Sot ntn tn fo t nt f n to n ot If t nt f tnt n on ot t tn nt f tnt on to t nton n F t fo t foown pnn H Mnt n of n nv ot t of nt n of ot pt F H H H H Untntt Downo Dt /9/8 : AM
11 Vo 6 Dtnton of ot ntn fo t-p nton oto wnn 579 F Co-ton of ot wt o fo o- wnn wt n non to t t ot ntn Mnt f tnt of ot pt f on wt p wnn to C n pt H fo C n pt H fo C n pt H fo C n pt H fo 5 T tot nt n of n ot f on wt p wnn to 6 Anoo pon otn f t ot f n on wt p wnn o of ot wt onto n t nt of t wnn p to Untntt Downo Dt /9/8 : AM
12 J Stz A Et En 58 Tfo t tot nt n ot wt ot w t o nt onn t p F 7 If t ot w ontn t of o wt ffnt p n ont wt ffnt ton wn t ow n p n t pp n t p t nt n of n ot t fo t foown pnn 8 S pnn otn f t ow ontn t p nt w t pp ontn t p nt 9 n t ow ontn t p nt n t top t p nt 5 T w n ot v t o oppot t n t o of pt p op on t ow T w n to T t nt n of ot wt ffnt p to Untntt Downo Dt /9/8 : AM
13 Vo 6 Dtnton of ot ntn fo t-p nton oto wnn 58 5 Tot nt n to n tto ot tn t pon 5 T tnt ot f ntn n t ntn n t fo t n n of t nt f n tto ot T n n pnt [7] { } 5 T opon of pnn 5 n 5 t n f- n t ntn of ot f wt o- ot pt wnn 5 55 Untntt Downo Dt /9/8 : AM
14 J Stz A Et En 58 Tn nto onton t pon 6 p p 56 n tn nto ont tt fo t o- wnn / w / t pon fo f- n t ot ntn n wttn p 57 p 58 w t offnt n tn t foown fo Sot ntn fo oponnt w t zo n oponnt on to pnn 7 n wttn p 6 p 6 w t offnt n n n vn t foown fo T v of t fto fo f ntn n n t ntn n of ot fo o- wnn vn n F 5 F 6 ow t v of fto n fo t oponnt n offnt n fo zo n oponnt Untntt Downo Dt /9/8 : AM
15 Vo 6 Dtnton of ot ntn fo t-p nton oto wnn 58 F 5 T fto n of o v t pn v F 6 T fto n fo o v t pn v Dtnton of ot ntn fo t wnn oton of t wnn n tto ot pnt n F 7 T wnn tz t tton of t n nt of t nt [] F 7 Annt of t o fo t wnn wt t n of ot p po n p n t n of po p p A t of ot wt o fo t onntn of t wnn wt n non to t t ot ntn own n F 8 T nt f tnt fo pt ot pt fo -of ot wn on to t nton n F 8 t fo t foown pnn Untntt Downo Dt /9/8 : AM
16 J Stz A Et En 58 C n pt ow pt of ot nt fow H fo 6 C n pt H fo 6 C n pt H fo 65 C n pt H fo 66 w: t t of t ot op o n t ot F 8 A t of ot wt o of t wnn wt n non to t t ot ntn T nt n of t -of ot w t of t n of nv ot pt tn fo t foown pon Untntt Downo Dt /9/8 : AM
17 Vo 6 Dtnton of ot ntn fo t-p nton oto wnn Mnt n fo ot - t n t w fo ot nn nt wt nt 68 Tot nt n fo -of ot n fo ot - to 69 T tot n of ot wt t nt n tn t foown pnn 7 Un pon of fnt of n [] Untntt Downo Dt /9/8 : AM
18 J Stz A Et En n pon 7 w otn t fn fo fo t tot n 6 7 S pnn fo nt n vn fo ot w ontn p of p nt n T tot nt n of ot wt t nt of ffnt p wt p of po to 6 75 T nt n fo ot w ontn on wnn wt nt of t p two ot of pt p fo on p of po n t n of o n ot n t fo 76 Untntt Downo Dt /9/8 : AM
19 Vo 6 Dtnton of ot ntn fo t-p nton oto wnn 587 n t wnn po n two n ot w otn 77 Tn nto ont t pnn 75 n 77 tot nt n of ot w tn t foown pnn p 78 Fo t opon of ton 5 n 78 n tn nto ont t pon 7 w n t t f- n t ot ntn fo t wnn p 79 p 8 w t offnt n n vn t foown pnn Howv ot ntn fo oponnt n zo n oponnt on to 79 n 8 n 7 ont to p 8 p 8 T offnt n vn t foown pon Untntt Downo Dt /9/8 : AM
20 588 J Stz A Et En t v of f ntn fto n w t fto fo t n ntn fo t ot of o- wnn vn n F 9 F ow t v of t fto n fo oponnt n offnt n fo zo n oponnt F 9 Fto n v t n of ot p po n p F Fto n v t n of ot p po n p 6 Dtnton of t-of ot ntn Spt tton of n nt of nt fo t wnn onnton o to t no p tn tt otn fo t o- wnn Dt wnn o not ow to nt n on t pt fn oponnt n t nt f tton Fo p t fft n vnt on oponnt n nt f Dtof wnn wo w n n ptnt n [] It tz nt on pt ontnt n ow fo nfnt ton n t fft n vnt on t ot nfnt T pt tton to t no on It otn fo tt wnn n t n of w n t o of t wnn w v t n It onn t o w p n ot n F 7 Dtton of t-of wnn op n wttn Untntt Downo Dt /9/8 : AM
21 Vo 6 Dtnton of ot ntn fo t-p nton oto wnn w: n of wnn n ot n of ot on t po n p T offnt n t fo 85 op n of < < wn fo wnn n t onnton w B t ton of offnt w otn tton of t nt f o to no tton fo t ton of offnt vn n t ptnt pton [] Mnt n of ot w t on wnn wt t p t ot of pt p p on p of po p n two wt t n of wnn n ot to 86 Tn nto ont t pnn 75 n 86 t tot nt n of ot fo t-of wnn tn t foown pon p 87 Fo opon of t ton 87 n 5 n tn nto ont pon 7 t t fo f- n t ntn ot wt t ot f fo tof wnn n p p 88 p 89 offnt n pon 9 owv offnt n nt n t wnn Sot ntn fo oponnt n zo n oponnt on to 88 n 89 n 7 w ont to Untntt Downo Dt /9/8 : AM
22 J Stz A Et En 59 p 9 p 9 offnt n T po fo tn of ot ntn n pf n ottn nt nton tn twn t two of t wnn n ot A t of pfton t ot ntn n t n t w fo n- wnn t on o t two fto tn nto ont t p nt oton on ot of t wnn n ot T offnt to t ot pt op t wnn n t offnt to t top of ot wtot wnn o tn nto ont T ot ntn tn tn fo t foown pon p p λ λ λ λ 9 p p λ λ λ λ 95 Mnt ontvt offnt λ n λ n t fo ov f to t n wnn of n p w n t offnt λ f to t ot pt opn t wnn n offnt λ f to t top of t ot wtot wnn T offnt t fo tn ot n o to t t ot ntn of ot p [ ] ottn on o Dpnn on nt ontvt offnt of n- wnn of n p ppn n fo 9 n 95 n fon n t wo [ 5 ] T ow t v of t offnt n fo ffnt tp of wnn fo Untntt Downo Dt /9/8 : AM
23 Vo 6 Dtnton of ot ntn fo t-p nton oto wnn 59 T Coffnt n fo ffnt tp of wnn Tp of wnn n o- 5/ t t-of Conon In t pp t ntn of t wnn fo nton oto v n t T pnn of t nt f n on t nnt of t oto o ovwttn Fo t t-p nt v t to v t fo fo t ot ntn of o- t n t-of wnn T to pnt n t pp ow to t f- n t ot ntn of n nton n n nt t of oont n ot ntn fo oponnt n zo oponnt Pnt pnn n p ow tt t pnt of t o n t ot w on to ffnt p ton n ot ntn n opon to n wnn Copn offnt own n T w n tt tt t tt ton n ntn ov fo t-of wnn tn t n t t on fo t o- wnn Dvop nt pnn f n t n of wnn n n t n of n tt of t AC t n fn [] Bo I SJ T Inton Mn Hnoo CC P Bo ton onon [] Czzt J S Et Mo-n toton n Po T zw 968 [] Dąow M Dn of AC t n n Po T zw 99 [] Głow A Etont ton of t-p nton oto n Po T zw 99 [5] Kń G Pzoow nn n pt of t n n Po Ofn wnz Potn zwj zw 998 [6] K PC nz O Soff SD An of Et Mn n Dv St n IEEE P Jon & Son w Yo [7] Pz Dn of t tntn nt n n Po T zw 986 [8] Pńow K An n onto of tto wnn nton oto Av of Et Ennn 6: -8 [9] Soz TJ Mtooo pt of tt on of nton n n Po T zw [] Stz J o nn of ow pt on n t nt f P 957 B Ptnt p of Pon [] Śwń T Mto fo tn t nton oto T An wntwo ow P zw 8 [] Zwn D Stn Mtt T n Fo Cpn & H/CC Bo ton onon w Yo nton Untntt Downo Dt /9/8 : AM
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