General Theory of Electric Machines 2017 Shiraz University of Technology Dr. A. Rahideh
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1 In The ame o Go The Mot Compaonate, The Mot Mecul Geneal Theoy o Electc Machne 7 Shaz Unety o Technoloy D. A. Raheh
2 Tale o Content. Intoucton. Tanome. Reeence Fame Theoy 4. Inucton Machne 5. Synchonou Machne 7 Shaz Unety o Technoloy D. A. Raheh
3 Chapte 5 Synchonou Machne 5.. Intoucton 5.. Moelln o Woun Roto Synchonou Machne 5.. Smulaton o Woun Roto Synchonou Machne 5.4. Pe Unt Sytem 5.5. Woun Roto Synchonou Machne Paamete 5.6. Pemanent Manet Synchonou Machne 7 Shaz Unety o Technoloy D. A. Raheh
4 Intoucton The contucton o phae ynchonou machne elately moe epene than that o nucton machne. Synchonou machne ae moe ecent compae to the nucton machne. The tato o ynchonou machne mla to that o nucton machne. The ynchonou machne ae e n tem o the oto tuctue a alent oto an cylncal oto machne. The ynchonou machne ae alo cateoze a: Woun oto (electcally ecte oto ynchonou machne, Pemanent manet ynchonou machne, Reluctance ynchonou machne. 7 Shaz Unety o Technoloy D. A. Raheh 4
5 5 Vaou Type o Synchonou Machne Woun oto (electcally ecte oto ynchonou machne Cylncal oto Salent oto Pemanent manet ynchonou machne Suace mounte PM (cylncal oto Suace net PM (alent oto Bue PM (Salent oto Raally place Aally place nclne Reluctance ynchonou machne Semental oto Flu ae oto Aally lamnate oto c' a' a' a c c ' c' a' a a' c ' c c' c' a a' ' c ' c' ' a a 7 Shaz Unety o Technoloy D. A. Raheh
6 (a ( (c PM Synchonou Machne Clacaton n tem o Manet tuctue Deent tuctue o PM n aal lu PM ynchonou moto: ( ( (e (h ( ( (a uace mounte manet ( uace mounte wth paallel ee (c uace mounte n manet ( uace mounte ea loa manet (e uace net manet ( uace net manet wth apace etween manet an on nte pole ( ue o nteo manet (h poke manet ( mult ement nteo manet (j multlaye nteo manet (j 6 7 Shaz Unety o Technoloy D. A. Raheh
7 Woun Roto Synchonou Machne Ccut Repeentaton a -a c' ' a ampe -a -a a' c Fel wnn a ampe -a a-a c a a c a a-a c 7 Shaz Unety o Technoloy D. A. Raheh 7
8 Woun Roto Synchonou Machne Ccut Repeentaton The tato ha a et o thee nuoally tute wnn. a -a The oto ha nomally one el wnn whch epeente on the a o the ame e to the oto. c' ' Fo alent oto machne, the ampe can e epeente a two hot ccute ampe wnn alon the an a o the ame e to the oto. a' -a c Anothe wnn conee on the a to epeent the eect o cuent low n the oto on. 8 7 Shaz Unety o Technoloy D. A. Raheh
9 Woun Roto Synchonou Machne Ccut Repeentaton a ampe -a a el a el -a a-a c a a c a a-a c a ampe 7 Shaz Unety o Technoloy D. A. Raheh 9
10 Woun Roto Synchonou Machne Mathematcal moel: Voltae euaton The tato oto oltae euaton can e epee a: a -a t t t t -a c' a' ' -a c a c a c a c t t t -a a-a c a a c a a-a c 7 Shaz Unety o Technoloy D. A. Raheh
11 Woun Roto Synchonou Machne 7 Shaz Unety o Technoloy D. A. Raheh Mathematcal moel: Voltae euaton The oltae euaton can e ewtten n mat om a ollow: whee ac ac ac ac t λ λ ac c a ac c a ac c a ac λ λ
12 alo Woun Roto Synchonou Machne Mathematcal moel: Voltae euaton tato o amatue wnn etance a el wnn etance a el wnn etance a ampe wnn etance a ampe wnn etance -a a -a c' a' ' -a c a-a -a c a a c a a-a c 7 Shaz Unety o Technoloy D. A. Raheh
13 Woun Roto Synchonou Machne Mathematcal moel: Flu lnkae euaton In mat om, the lu lnkae o the tato an oto wnn n tem o the wnn nuctance an cuent ae epee -a a λ λ ac ac ac whee c c -a ac tato wnn nuctance mat oto wnn nuctance mat T the mat o mutual nuctance etween tato an oto wnn 7 Shaz Unety o Technoloy D. A. Raheh a-a a a a a-a c
14 Woun Roto Synchonou Machne Mathematcal moel: Flu lnkae euaton ow the nuctance matce hae to e epeente. Fo alent oto machne, the tato wnn nuctance n ac ytem ay wth the oto poton. So t moe conenent to otan the tato wnn nuctance alon the an a o the ame e to the oto. Alo t aume that the aaton o the tato wnn nuctance nuoally. aa aa aa m co co 4 7 Shaz Unety o Technoloy D. A. Raheh
15 Woun Roto Synchonou Machne Mathematcal moel: Flu lnkae euaton Aume the tato wnn nuctance mat n ac ytem ac aa a ca a c ac c cc In the ollown le, the tato phae a el nuctance ( aa wthout the leakae nuctance an the mutual nuctance etween phae a an phae ( a wll e otane. The othe nuctance can e etemne n the ame manne. 5 7 Shaz Unety o Technoloy D. A. Raheh
16 Woun Roto Synchonou Machne Mathematcal moel: Flu lnkae euaton The tato phae a el nuctance ( aa can e calculate un the ollown epeon Sel nuctance aa aa a whee aa the manetc lu pouce y only the cuent o phae a ( a, lnke wth the wnn o phae a an otane a aa a whee a the manetc lu o phae a an the nume o tun o the wnn o phae a. 7 Shaz Unety o Technoloy D. A. Raheh 6
17 Woun Roto Synchonou Machne Mathematcal moel: Flu lnkae euaton a nomally calculate y the multplcaton o the MMF o phae a (F a = a an the pemeance. But the pemeance a uncton o the oto poton. Sel nuctance Theeoe the MMF eole alon the an a a: -a F a -a F a F a n a n F a a-a F a F a co a co F a -a c-a 7 Shaz Unety o Technoloy D. A. Raheh 7
18 Woun Roto Synchonou Machne Mathematcal moel: Flu lnkae euaton ow a an a can e calculate y the multplcaton o the coeponn MMF (F a an F a epectely an the elate pemeance (P an P epectely: Sel nuctance a P F a P F a n -a -a a P F a P F a co F a a a now calculate y the pojecton o a an a on a a: a F a F a a-a a a n a co c-a -a 7 Shaz Unety o Technoloy D. A. Raheh 8
19 Woun Roto Synchonou Machne Mathematcal moel: Flu lnkae euaton Sel nuctance a P F a n a P F a co a F a P n P co a a n a co whee F a a aa a a P n P co aa aa P n P co a 9 7 Shaz Unety o Technoloy D. A. Raheh
20 Woun Roto Synchonou Machne Mathematcal moel: Flu lnkae euaton Sel nuctance aa P n P co n ( co co ( co aa P P P P co P P aa aa m co co m 7 Shaz Unety o Technoloy D. A. Raheh
21 a Woun Roto Synchonou Machne P Mathematcal moel: Flu lnkae euaton F a n a P Smlaly the lnkae o the lu component ( a an a y phae wnn that / electcal aan ahea can e wtten a: a a n F a co co a Mutual nuctance a a P n n P co co a a a P n n P co co 7 Shaz Unety o Technoloy D. A. Raheh
22 Woun Roto Synchonou Machne Mathematcal moel: Flu lnkae euaton Mutual nuctance a P n n P co co a a P P P P co 4 co 4 a m co m P P 7 Shaz Unety o Technoloy D. A. Raheh
23 Woun Roto Synchonou Machne Mathematcal moel: Flu lnkae euaton Theeoe the tato nuctance mat wth conen the leakae nuctance wtten a: ac l m co m co( m co( l m m m co( co( co( l m m m co( co( co( The oto nuctance mat can e epee a: l m l m l m l m Why? 7 Shaz Unety o Technoloy D. A. Raheh
24 Woun Roto Synchonou Machne Mathematcal moel: Flu lnkae euaton The mutual nuctance mat etween the oto an tato wnn : n n( n( n n( n( co co( co( co co( co( T Why? ac Snce oth an ae uncton o the oto poton, the tato uantte ae tanome to the oto RF. 4 7 Shaz Unety o Technoloy D. A. Raheh
25 l l l l l m m m Woun Roto Synchonou Machne Mathematcal moel: Flu lnkae euaton tato o amatue wnn leakae nuctance a el wnn leakae nuctance a el wnn leakae nuctance a ampe wnn leakae nuctance a ampe wnn leakae nuctance a tato manetzn nuctance a tato manetzn nuctance a el wnn manetzn nuctance a el wnn manetzn nuctance a ampe wnn manetzn nuctance m a ampe wnn manetzn nuctance 5 7 Shaz Unety o Technoloy D. A. Raheh
26 Woun Roto Synchonou Machne Mathematcal moel: Flu lnkae euaton mutual nuctance etween a el wnn an a ampe wnn. mutual nuctance etween a el wnn an a ampe wnn. peak alue o mutual nuctance etween tato wnn an a el wnn. peak alue o mutual nuctance etween tato wnn an a ampe wnn. peak alue o mutual nuctance etween tato wnn an a el wnn. peak alue o mutual nuctance etween tato wnn an a ampe wnn. 7 Shaz Unety o Technoloy D. A. Raheh 6
27 Woun Roto Synchonou Machne tato oltae euaton ote that only the tato uantte nee to e tanome to oto eeence ame. The tanomaton one un: T T ( ac ac ( whee T co co co n n n ( co co n ( co n T n 7 7 Shaz Unety o Technoloy D. A. Raheh
28 Woun Roto Synchonou Machne tato oltae euaton The tato oltae euaton n ac ytem ae ac ac ac pλ ac whee p Applyn the tanomaton T ( to the oltae, cuent an lu yel ac T ( T ( T ( p λ t T ac ( Multplyn oth e y the tanomaton mat yel ac T ( T ( T ( T ( p λ 8 7 Shaz Unety o Technoloy D. A. Raheh
29 9 Woun Roto Synchonou Machne 7 Shaz Unety o Technoloy D. A. Raheh tato oltae euaton Suttutn the ollown elaton n the aoe epeon yel ( ( ( ( ac p λ T T T T ac ( ( p p λ λ λ T T p λ λ
30 Woun Roto Synchonou Machne tato oltae euaton Ohmc op λ Rotatonal EMF p p p p λ Tanome EMF λ 7 Shaz Unety o Technoloy D. A. Raheh
31 Woun Roto Synchonou Machne tato lu lnkae euaton The tato lu lnkae euaton n ac ytem epee a: λ ac ac ac Applyn the tanomaton T ( to the tato uantte yel Multplyn oth e y T ( yel ac T ( λ T ( T ac ( ac T T ( T ( λ ( 7 Shaz Unety o Technoloy D. A. Raheh
32 Woun Roto Synchonou Machne tato lu lnkae euaton λ ac T T ( T ( ( λ The nuctance matce an n eeence ame nee to e otane. 7 Shaz Unety o Technoloy D. A. Raheh
33 Woun Roto Synchonou Machne tato lu lnkae euaton ac l m co m co( m co( l m m m co( co( co( l m m m co( co( co( ac whee T ( T ( the tato el nuctance mat n eeence ame l ( m l ( m l Daonal mat an nepenent o. 7 Shaz Unety o Technoloy D. A. Raheh
34 Woun Roto Synchonou Machne tato lu lnkae euaton n n( n( n n( n( co co( co( co co( co( an T ( the tato to oto mutual nuctance mat n eeence ame Mat nepenent o. 4 7 Shaz Unety o Technoloy D. A. Raheh
35 Woun Roto Synchonou Machne oto lu lnkae euaton The oto lu lnkae euaton n RF epee a: λ ac Applyn the tanomaton T ( to the tato cuent yel T ac ( λ λ T ( T 5 7 Shaz Unety o Technoloy D. A. Raheh
36 Woun Roto Synchonou Machne lu lnkae euaton λ & λ l l l l m whee ( m P an ( m P ae the eualent manetzn nuctance o the an a tato wnn epectely. 7 Shaz Unety o Technoloy D. A. Raheh l m l m l m 6
37 Woun Roto Synchonou Machne lu lnkae euaton A eent, the nuctance mat non ymmetc ue to the peence o / acto. Replacn the actual oto cuent wth the ollown eualent cuent yel ˆ ˆ ˆ ˆ l l l ( l m ( l m ( l m ( l m ˆ ˆ ˆ ˆ 7 Shaz Unety o Technoloy D. A. Raheh 7
38 Woun Roto Synchonou Machne Reen oto uantte to the tato e ow all the oto uantte an paamete ae eee to the tato e: ˆ ˆ ˆ ˆ 8 7 Shaz Unety o Technoloy D. A. Raheh
39 Woun Roto Synchonou Machne Reen oto uantte to the tato e P P Un the aoe elaton, the nuctance ae epee a: Mutual nuctance etween oto an tato wnn: P P P P Manetzn nuctance o the m P oto wnn: m P m P 7 Shaz Unety o Technoloy D. A. Raheh m P 9
40 Woun Roto Synchonou Machne Reen oto uantte to the tato e P P Un the aoe elaton, the nuctance ae epee a: Mutual nuctance etween a oto wnn (etween an : P Mutual nuctance etween a oto wnn (etween an : P 4 7 Shaz Unety o Technoloy D. A. Raheh
41 Woun Roto Synchonou Machne Reen oto uantte to the tato e The emann oto paamete ae eee to the tato e: l l l l The an a ynchonou nuctance ae ene a: l l 4 7 Shaz Unety o Technoloy D. A. Raheh
42 4 Woun Roto Synchonou Machne 7 Shaz Unety o Technoloy D. A. Raheh lu lnkae euaton eee to the tato e l l l l l l l
43 Woun Roto Synchonou Machne Summay: euaton eee to the tato e t t t c' a a' -a ' -a c t t t t l 4 7 Shaz Unety o Technoloy D. A. Raheh
44 Woun Roto Synchonou Machne a eualent ccut + _ l t + _ ( l l l + _ l + _ l ( ( t t 44 7 Shaz Unety o Technoloy D. A. Raheh
45 Woun Roto Synchonou Machne a eualent ccut + _ l t _ + ( l l l + _ l + _ l ( ( t t 45 7 Shaz Unety o Technoloy D. A. Raheh
46 Woun Roto Synchonou Machne Zeo component eualent ccut t a -a l c' ' l -a + c _ a' 46 7 Shaz Unety o Technoloy D. A. Raheh
47 Woun Roto Synchonou Machne Toue Euaton The ntantaneou nput powe otane a P n a a c c In tem o uantte, the ntantaneou nput powe P n Suttutn the oltae euaton n the aoe epeon yel P n p p p p p 7 Shaz Unety o Technoloy D. A. Raheh 47
48 Woun Roto Synchonou Machne Toue Euaton P n p p p p p The ohmc loe ( tem an the ate o echane o manetc el eney etween wnn (p tem o not contute to electomanetc (EM toue eelopment. Hence the powe tem contute to EM toue eneaton ae: P T 48 7 Shaz Unety o Technoloy D. A. Raheh
49 Woun Roto Synchonou Machne P T Toue Euaton The electomanetc toue otane y n the aoe powe y the mechancal pee. T em P whee P the nume o pole. The elaton etween the mechancal pee an the electcal pee a ollow: m P 49 7 Shaz Unety o Technoloy D. A. Raheh
50 Woun Roto Synchonou Machne Mechancal Dynamc Euaton Bae on ewton n law o otatonal moement, the mechancal ynamc euaton otane: T J t m T T t whee T mech the etenally apple mechancal toue, T amp the ampn toue, J the moment o neta an m the mechancal otatonal elocty. 7 Shaz Unety o Technoloy D. A. Raheh T T em em T mech mech T amp amp J J t m m 5
51 Woun Roto Synchonou Machne Cuent n tem o lu lnkae Synchonou machne can e mulate un the lu lnkae a the tate aale. Hence t eue to otan the cuent n tem o lu lnkae. et ene the ollown mutual lu lnkae n the an a a: ( c' -a ' ( -a c a' 5 7 Shaz Unety o Technoloy D. A. Raheh
52 Woun Roto Synchonou Machne Cuent n tem o lu lnkae The ollown epeon o a cuent can e otane: l ( ( l ( l ( ( l ( l ( ( l ( 5 7 Shaz Unety o Technoloy D. A. Raheh
53 Woun Roto Synchonou Machne Cuent n tem o lu lnkae The ollown epeon o a cuent can e otane: l ( ( l ( l ( ( l ( l ( ( l ( 5 7 Shaz Unety o Technoloy D. A. Raheh
54 Woun Roto Synchonou Machne Cuent n tem o lu lnkae Suttutn the epeon o the a wnn cuent n the a mutual lu lnkae yel: ( l l ( ( MQ l l l l ( whee MQ l l l 54 7 Shaz Unety o Technoloy D. A. Raheh
55 Woun Roto Synchonou Machne Cuent n tem o lu lnkae Suttutn the epeon o the a wnn cuent n the a mutual lu lnkae yel: ( l l ( ( MD l l l l ( whee MD l l l 55 7 Shaz Unety o Technoloy D. A. Raheh
56 Woun Roto Synchonou Machne Cuent n tem o lu lnkae MQ l l l Suttutn the aoe epeon n the a wnn cuent yel ( ( ( l ( MQ l l l MQ MQ l l l l ( l MQ l l MQ MQ ( 7 Shaz Unety o Technoloy D. A. Raheh l l l l l MQ l MQ MQ l l l l 56
57 Woun Roto Synchonou Machne Cuent n tem o lu lnkae MD l l l Suttutn the aoe epeon n the a wnn cuent yel ( ( ( l l l ( MD l l l MD MD l l l ( MD MD l l l MD l l l ( l MD l MD l MD l l l 57 7 Shaz Unety o Technoloy D. A. Raheh
58 Smulaton o Woun Roto Synchonou Machne The wnn euaton o the ee moel mplemente n a mulaton that ue oltae a nput an cuent a output. State a c m Input a c -phae Woun Roto Synchonou Machne Moel a c Output T mech T em 58 7 Shaz Unety o Technoloy D. A. Raheh
59 Smulaton o Woun Roto Synchonou Machne Su ytem: Tanomaton o tato oltae om ac ytem to RF e to the oto T ac a c ac to Tanomaton It can e one n two tep (: ac ytem to tatonay RF; : tatonay RF to oto RF o n nle tep Shaz Unety o Technoloy D. A. Raheh
60 Smulaton o Woun Roto Synchonou Machne Su ytem: Voltae & lu lnkae euaton Voltae & Flu nkae Euaton The tato an oto euaton ae couple. 6 7 Shaz Unety o Technoloy D. A. Raheh
61 Smulaton o Woun Roto Synchonou Machne Su ytem: Toue euaton Toue Euaton T em T T em o em P P whee 6 7 Shaz Unety o Technoloy D. A. Raheh
62 Smulaton o Woun Roto Synchonou Machne Su ytem: Mechancal euaton T em T mech Mechancal Euaton m T em T mech T amp J t m T em T mech T amp J t m 6 7 Shaz Unety o Technoloy D. A. Raheh
63 Smulaton o Woun Roto Synchonou Machne Su ytem: Tanomaton o tato cuent om oto RF to ac ytem T ac to ac Tanomaton a c It can e one n two tep (: oto RF to tatonay RF; : tatonay RF to ac ytem o n nle tep. 6 7 Shaz Unety o Technoloy D. A. Raheh
64 Smulaton o Woun Roto Synchonou Machne Tanomaton (Stato oltae Tanomaton o the tato oltae om tato ac ytem to the oto RF. T co co co n n n co co( 4 c co( a n n( 4 c n( a T ac ( a c 64 7 Shaz Unety o Technoloy D. A. Raheh
65 Smulaton o Woun Roto Synchonou Machne Flu lnkae an oltae euaton The eactance ue ntea o the nuctance y y. a tato euaton l t y ( l y whee ( t ( l 65 7 Shaz Unety o Technoloy D. A. Raheh
66 Smulaton o Woun Roto Synchonou Machne. a tato euaton l t ( l Flu lnkae an oltae euaton whee ( t. Zeo component tato euaton l ( t l l t 66 7 Shaz Unety o Technoloy D. A. Raheh
67 Smulaton o Woun Roto Synchonou Machne 4. a oto el wnn euaton ( l t l Flu lnkae an oltae euaton 5. a oto ampe euaton t l l ( t ( l l ( t 67 7 Shaz Unety o Technoloy D. A. Raheh
68 Smulaton o Woun Roto Synchonou Machne Flu lnkae an oltae euaton 6. a oto ampe euaton t ( l l l ( t 68 7 Shaz Unety o Technoloy D. A. Raheh
69 Smulaton o Woun Roto Synchonou Machne Flu lnkae an oltae euaton A eoe, to hanle the cut et o nucto, the ollown epeon ae ue: MD l l l MD l l l MQ l l MQ l l 69 7 Shaz Unety o Technoloy D. A. Raheh
70 Smulaton o Woun Roto Synchonou Machne Flu lnkae an oltae euaton: a lock aam Shaz Unety o Technoloy D. A. Raheh
71 Smulaton o Woun Roto Synchonou Machne Flu lnkae an oltae euaton: a lock aam Shaz Unety o Technoloy D. A. Raheh
72 Smulaton o Woun Roto Synchonou Machne Step Tanomaton o the Stato Cuent Tanomaton om the oto RF to the tato RF: co n n co Tanomaton om the tato RF to ac ytem: a c 7 7 Shaz Unety o Technoloy D. A. Raheh
73 Pe Unt Sytem Bae uantte The ae uantte wth peak athe than m alue o a P pole, thee phae ynchonou machne wth ate lne to lne m oltae, V ate, an ate olt ampee, S ate, ae a ollow: V V ate S S ate I S /(V Z V / I T S / m whee m / P 7 7 Shaz Unety o Technoloy D. A. Raheh
74 Pe Unt Sytem T em P Toue Euaton T S m m / P T P S I S /(V T P V I T T em whee P ( pu V P V I ( pu V T em ( pu ( pu ( pu ( pu ( pu ( pu I ( pu I 74 7 Shaz Unety o Technoloy D. A. Raheh
75 Pe Unt Sytem Mechancal Euaton J t m T m / em P T mech T amp J ( / P t T em T mech T amp T S / m m / P ( / H Tem( pu Tmech( pu Tamp( pu t whee H J /( the neta contant. m S 75 7 Shaz Unety o Technoloy D. A. Raheh
76 Machne Paamete The ollown machne paamete ae eue o the mulaton l tato o amatue wnn leakae eactance l a el wnn leakae eactance eee to tato a ampe wnn leakae eactance eee to tato l a ampe wnn leakae eactance eee to tato l a manetzn eactance a manetzn eactance tato o amatue wnn etance a el wnn etance eee to tato a ampe wnn etance eee to tato a ampe wnn etance eee to tato 76 7 Shaz Unety o Technoloy D. A. Raheh
77 Machne Paamete Othe paamete/uantte eue o mulaton ae: J oto moment o neta P nume o pole ate S ae T mech oto ae pee ate lne to lne m oltae o tato ate olt ampee mechancal loa toue pole 77 7 Shaz Unety o Technoloy D. A. Raheh
78 Machne Paamete The machne ata om manuactue ae uually n the om o eactance, tme contant, an etance. Mot o them ae ee om meauement taken om the tato wnn. Roto wnn paamete can e otane om tato meauement, ecaue the eecte tme contant o aou oto cuent ae ncantly eent. A common appoach the hot ccut oclloam o the tato cuent, when a phae hot ccut apple to the machne whoe tato ntally open ccut an t el hel contant. 7 Shaz Unety o Technoloy D. A. Raheh 78
79 Machne Paamete The hot ccut cuent cont o: DC oet Su tanent peo Tanent peo Steay tate peo Dun the u tanent peo the cuent ecay ey ap, ue to the chane n the cuent o ampe wnn. The cuent ecay lowe un the tanent peo an attute to chane n the cuent o the el wnn Shaz Unety o Technoloy D. A. Raheh
80 Machne Paamete The lu path o a un eent peo (a ( ' (c '' 8 7 Shaz Unety o Technoloy D. A. Raheh
81 Machne Paamete The lu path o a un eent peo (a ( ' (c '' 8 7 Shaz Unety o Technoloy D. A. Raheh
82 Machne Paamete Synchonou Inuctance l l l l l l l 8 l 7 Shaz Unety o Technoloy D. A. Raheh
83 Machne Paamete Tanent Inuctance l l l l l l l l l l 8 l l l l l l 7 Shaz Unety o Technoloy D. A. Raheh
84 Machne Paamete Tanent Inuctance Dun the tanent peo an whch the ame a l l l 84 Smlaly o the a 7 Shaz Unety o Technoloy D. A. Raheh
85 Machne Paamete Su tanent Inuctance l l l l l l l l l l l l 85 7 Shaz Unety o Technoloy D. A. Raheh
86 Machne Paamete Su tanent Inuctance Dun the u tanent peo n a an Wtn an n tem o an uttutn n yel 86 ( l l whch the ame a l l l l l ( l l 7 Shaz Unety o Technoloy D. A. Raheh
87 Machne Paamete Su tanent Inuctance Dun the u tanent peo n a an Wtn an n tem o an uttutn n yel 87 ( l l whch the ame a l l l l l ( l l 7 Shaz Unety o Technoloy D. A. Raheh
88 Machne Paamete Open ccut tanent tme contant When the tato open ccute an the eect o hhe wnn etance, ampe wnn, ae nelecte, the openccut tme contant o the el wnn ae ene a: l l T o l l l l T o T o l l 88 T o 7 Shaz Unety o Technoloy D. A. Raheh
89 Machne Paamete Shot ccut tanent tme contant When the tato hot ccute an the eect o hhe wnn etance, ampe wnn, ae nelecte, the hotccut tme contant o the el wnn ae ene a: l l T l l l l l T T l l l 89 T 7 Shaz Unety o Technoloy D. A. Raheh
90 Machne Paamete Tanent tme contant The ato o the tme contant o the el wnn wth hotccute tato wnn to that wth open ccut tato wnn eual to the ato o the appaent nuctance een y the tato cuent wth el hot ccute to that wth el open ccute: T T o whee an l l l l T T o whee an l l l l 9 Why? 7 Shaz Unety o Technoloy D. A. Raheh
91 Machne Paamete Open ccut u tanent tme contant The open ccut u tanent tme contant ae the tme contant o the ampe wnn cuent when the tato open ccute an the el wnn hot ccute. T o l l l l l T o T o l l l l l T o 9 7 Shaz Unety o Technoloy D. A. Raheh
92 Machne Paamete Shot ccut u tanent tme contant The hot ccut u tanent tme contant ae the tme contant o the ampe wnn cuent when the tato an the el wnn ae oth hot ccute. l T l l l l l T T l l l l l l T 9 7 Shaz Unety o Technoloy D. A. Raheh
93 Machne Paamete Calculaton o Machne Paamete Aume the ollown paamete ae en y the manuactue:,,,,,,,, T, T, T, T, T, l o o o T Bae on the aoe en paamete, the ollown paamete ae calculate:,,,,,,,. l l l The amatue leakae eactance nomally en; ut t not en, the alue o the zeo euence eactance may e ue ntea: l 9 7 Shaz Unety o Technoloy D. A. Raheh
94 Machne Paamete Calculaton o Machne Paamete (,, The ect an uaatue manetzn eactance ae otane: l l l The el leakae eactance otane un: l l l l ( l ( l I : l l l 94 7 Shaz Unety o Technoloy D. A. Raheh
95 Machne Paamete Calculaton o Machne Paamete ( The leakae eactance o the a ampe wnn calculate un: l l l l l l l l l l ( ( l l ( l l I l l ( l ( l l l 95 7 Shaz Unety o Technoloy D. A. Raheh
96 Machne Paamete Calculaton o Machne Paamete ( Han no wnn n the a ( l, the leakae eactance o the a ampe wnn calculate un: l l l l ( ( l l l I l l l The tme contant ae ue to calculate the etance o the oto wnn Shaz Unety o Technoloy D. A. Raheh
97 Machne Paamete Calculaton o Machne Paamete ( The el etance calculate om the a tanent openccut tme contant: T o ( l T o ( l l l l T o 97 7 Shaz Unety o Technoloy D. A. Raheh
98 Machne Paamete Calculaton o Machne Paamete ( The a ampe etance calculate om the a utanent open ccut tme contant: T o ( l l l o T o ( l l l T o ( l l l l T o 98 7 Shaz Unety o Technoloy D. A. Raheh
99 Machne Paamete Calculaton o Machne Paamete ( The a ampe etance calculate om the a utanent open ccut tme contant: T o ( l T o ( l l l T o l 99 7 Shaz Unety o Technoloy D. A. Raheh
100 Machne Paamete Calculaton o Machne Paamete Altenately, the hot ccut tme contant can e ue to calculate the oto etance: T ( l l l T ( l l l l l l l T ( l l l 7 Shaz Unety o Technoloy D. A. Raheh
101 Pemanent Manet Synchonou Machne (a ( (c ( (e ( ( (h ( (j 7 Shaz Unety o Technoloy D. A. Raheh
102 PM Synchonou Machne The DC ectaton o the el wnn n a ynchonou machne can e poe y pemanent manet. So the oto coppe loe ae elmnate. PMSM can oe mple contucton, lowe weht an ze, euce loe an thu hhe ecency. The aantae o PMSM ae the hhe pce aeeath manet ae ue. Stato ackon Stato teeth A-ap Dampe Roto on PM on-manet hu Shat 7 Shaz Unety o Technoloy D. A. Raheh
103 PM Synchonou Machne euaton eee to the tato e t t t t t l m m whee m the eualent manetzn cuent o the PM. 7 Shaz Unety o Technoloy D. A. Raheh
104 PM Synchonou Machne a eualent ccut t t l ( l ( + _ + _ l l 4 7 Shaz Unety o Technoloy D. A. Raheh
105 PM Synchonou Machne a eualent ccut t t l ( m l ( m + + l l c m The PM eluctance can e epeente y a tual nuctance enote y c, that aocate wth t ecol lope c 5 7 Shaz Unety o Technoloy D. A. Raheh
106 PM Synchonou Machne Zeo component eualent ccut t l + _ l 6 7 Shaz Unety o Technoloy D. A. Raheh
107 PM Synchonou Machne Toue Euaton Smla to woun oto ynchonou machne, the electomanetc toue o PMSM otane y T em P whee P the nume o pole. It can e ewtten a: T em P P m P Reluctance toue Inucton toue Ectaton toue whee l an l 7 7 Shaz Unety o Technoloy D. A. Raheh
108 PM Synchonou Machne Mechancal Dynamc Euaton Bae on ewton n law o otatonal moement, the mechancal ynamc euaton otane: T J t m T T t whee T mech the etenally apple mechancal toue, T amp the ampn toue, J the moment o neta an m the mechancal otatonal elocty. 7 Shaz Unety o Technoloy D. A. Raheh T T em em T mech mech T amp amp J J t m m 8
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