Comparison between Induction Motor and Transformer An induction motor is considered as a transformer with a rotating short-circuited secondary.

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Eugene Byrd
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1 Comparion between Induction Motor and Tranformer An induction motor i conidered a a tranformer with a rotating hort-circuited econdary. The tator winding correpond to tranformer primary and the rotor winding correpond to tranformer econdary. However, there are difference: (i) The induction motor ha an air gap, but the tranformer ha a core. Therefore, the magnetizing current in an induction motor i much larger than that of the tranformer. For example, in induction motor i about % of rated current wherea it i only 1-5% of rated current in a tranformer. (ii) In an induction motor, the tator and rotor winding are ditributed around the periphery of the air gap rather than concentrated on a core a in a tranformer (i.e., in the motor: leakage flux pae eaily through the air gap) (i.e., in tranformer: mall amount of leakage flux pae away from the core). Therefore, the leakage reactance of tator and rotor winding quite large compared to that of a tranformer. (iii) In an induction motor, the input i electrical but output i mechanical. However, in a tranformer, input a well a output are electrical. (iv) Unlike the tranformer, in the induction motor the rotor voltage, reactance and frequency are proportional to the lip. At any lip, rotor value: e.m.f/phae (E =E) reactance/phae (X =X) frequency (f =f ) 68

2 Equivalent Circuit of 3-Phae Induction Motor at any Slip In a 3-phae IM, the tator winding i connected to 3- phae upply and the rotor winding i hort-circuited. The energy i tranferred magnetically from the tator winding to the hortcircuited rotor winding. Therefore, an induction motor may be conidered a a tranformer with a rotating econdary (hort-circuited). Then the tator winding correpond to tranformer primary and the rotor winding correpond to tranformer econdary. So, the equivalent circuit of an induction motor will be imilar to that of a tranformer. Figure how the equivalent circuit per phae for an induction motor. The applied voltage V1 produce a magnetic flux which link the tator winding (i.e., primary) a well a the rotor winding (i.e., econdary). Thu; elf-induced e.m.f. E1 i induced in the tator winding and mutually induced e.m.f. E i induced in the rotor winding (where: E = E = ke1 k i a tranformation ratio). Why we draw the branch of magnetization a hown in the above figure ee MagBranch.MP4 69

3 Stator circuit of the Equivalent Circuit Fig. 1: equivalent circuit of induction motor per phae at any lip V1 : upply voltage or tator terminal voltage/phae. 1 : tator reitance/phae. X1 : tator leakage reactance/phae. I1 : upply current or tator current/phae. E1 : induced emf voltage/phae in the tator winding (by elf-induction). V1 E1 I1( 1 jx 1) 70

4 Stator circuit of the Equivalent Circuit Fig. 1: equivalent circuit of induction motor per phae at any lip Io : no-load current/phae (pae at when the motor ha no-load). Iw : working or iron lo current component/phae (which caue the no-load motor loe). Im : magnetization current component/phae (which etup the magnetic flux in the core and the airgap). Io Iw Im Alo, Io Io coo ji o ino o angle between E 1 & Io 71

5 Stator circuit of the Equivalent Circuit Fig. 1: equivalent circuit of induction motor per phae at any lip From the magnetization branch: E 1 Io.( c // jx m) Io. Zmag. E I. w c E I. jx 1 1 m m 7

6 otor circuit of the Equivalent Circuit Fig. 1: equivalent circuit of induction motor per phae at any lip Since the rotor winding i hort-circuited, the whole of induced e.m.f/phae E i ued to etup a circulating rotor current I. E : induced emf voltage/phae in the rotor winding (by mutual-induction). I : rotor current/phae. : rotor reitance/phae. X : rotor leakage reactance/phae. E E E I ( jx ) I i.e.: X ( X ) 73

74 Equivalent Circuit of the otor We hall now ee how mechanical load of the motor i replaced by the equivalent electrical load. The rotor phae current i given by; 1 1 1 ) ( 1)) ( ( ) ( ) (.

7 74 Equivalent Circuit of the otor We hall now ee how mechanical load of the motor i replaced by the equivalent electrical load. The rotor phae current i given by; ) ( 1)) ( ( ) ( ) (. ) ( X E X E X E X E I From above equation: We now have a rotor circuit that ha a fixed reactance X connected in erie with a variable reitance / and upplied with contant voltage E. The rotor circuit can be repreented by the following figure. (all figure here are the ame)

8 Equivalent Circuit of the otor 1 ( 1 L ) The rotor reitance in above equation ha two component: 1- The firt part i the rotor reitance itelf and repreent the rotor Cu loe. - The econd part ( 1 1) i the load reitance L i the electrical equivalent of the mechanical load on the motor. In other word, the mechanical load on the induction motor can be electrically repreented by ( 1 L 1). 75

9 Tranformer Equivalent Circuit of Induction Motor Fig. : eqt. circuit of induction motor per phae at any lip Fig. : eqt. circuit of induction motor per phae at any lip referred to tator ide 76

10 Equivalent Circuit of Induction Motor eferred to Stator Side Fig. : eqt. circuit of induction motor per phae at any lip referred to tator ide eferring to tator ide i made baed on the tranformation ratio k. E E1 E k rotor induced emf/phae referred to tator ide I ki rotor current/phae referred to tator ide k E E 1 X k X rotor leakage reactance/phae referred to tator ide ( ) k (rotor reitance/phae + load reitance/phae) referred to tator ide 77

Equivalent Circuit of Induction Motor eferred to Stator Side Fig. 3: eqt. circuit of induction motor per phae at any lip referred to tator ide (Fig. 3 i the ame a Fig.

11 Equivalent Circuit of Induction Motor eferred to Stator Side Fig. 3: eqt. circuit of induction motor per phae at any lip referred to tator ide (Fig. 3 i the ame a Fig. ) Earlier we ay that: E rotor induced emf/phae at any lip.... (E = E) X rotor leakage reactance/phae at any lip. (X = E) I rotor current/phae at any lip... (I = E /Z ) In tudying the equivalent circuit (from Fig. 3): E rotor induced emf/phae at any lip referred to tator ide. (E = E/k) X rotor reactance/phae at any lip referred to tator ide.. (X = X/k ) I rotor current/phae at any lip referred to tator ide... (I = E /Z ) From Fig. 3. Z = ( +L )+jx 78

12 Equivalent Circuit of Induction Motor eferred to Stator Side Fig. 3: eqt. circuit of induction motor per phae at any lip referred to tator ide (Fig. 3 i the ame a Fig. ) Note that: the element L i the equivalent electrical reitance related to the mechanical load on the motor. The following point may be noted from the equivalent circuit of the induction motor: At no-load (where N N), the lip i practically zero and the load L i infinite. Thi condition look like a tranformer whoe econdary winding i open-circuited. At tandtill (N=0), the lip i unity and the load L i zero. Thi condition look like a tranformer whoe econdary winding i hort-circuited. When the motor i running under load, the value of L will depend upon the value of the lip. Thi condition reemble that in a tranformer whoe econdary i upplying variable and purely reitive load. L depend on lip. If the lip increae, the load L decreae and the rotor current increae and motor will develop more mechanical power. Thi i expected becaue the lip of the motor increae with the increae of load. 79

13 Power elation from Equivalent Circuit of Induction Motor (i) Stator input power : P in 3V 1I1 co 1 (ii) Stator Cu loe : P cu ( tator ) 3I1 1 (iii) otor input power 3( I ) : P rotor (iv) otor Cu loe : P cu ( rotor ) 3( I ) or Pcu ( rotor ) Protor (v) Total mechanical power developed by rotor 1 : P mech 3( I ) ( 1) 3 ( I ) 1 Or Pmech Protor Pcu( rotor) 3( I ) 3( I ) ( 1) (vi) Total or gro torque developed by rotor : T gro P rotor 3( I ) N 60 3( I ) 9.55 N 9.55 N i the ynchronou peed in rpm Note: the haft torque Th le than Tgro by friction and windage loe. P rotor N 80

Approximate Equivalent Circuit of Induction Motor A in cae of a tranformer, the approximate equivalent circuit of an induction motor i obtained by hifting the hunt branch (cjxm) to the input terminal

14 Approximate Equivalent Circuit of Induction Motor A in cae of a tranformer, the approximate equivalent circuit of an induction motor i obtained by hifting the hunt branch (cjxm) to the input terminal a hown in Figure (Fig.: approximate eqt. circuit of IM per phae referred to tator ide). Thi tep ha been taken on the aumption that voltage drop in 1 and X1 i mall and the terminal voltage V1 doe not appreciably differ from the induced voltage E1. From the above approximate circuit, we note that: (i) Unlike a power tranformer, the magnetic circuit of induction motor ha an air-gap. Therefore, the exciting current of induction motor (30 to 40% of full-load current) i much higher than that of the tranformer. Conequently, the exact equivalent circuit mut be ued for accurate reult. (ii) The value of X 1 and X in an induction motor are larger than the correponding one to be found in the tranformer. Thi fact doe not jutify the ue of approximate equivalent circuit. (iii) In a tranformer, the winding are concentrated wherea in an induction motor, the winding are ditributed. Thi affect the tranformation ratio. (iv) Depite the above drawback of approximate equivalent circuit, thi approximate circuit i atifactory for large motor but not preferred for mall motor. 81

Example on Equivalent Circuit of Induction Motor [An: I1

15 Example on Equivalent Circuit of Induction Motor [An: I A, pf co 1 co lag ] [An: (a) (e) A (b) A (c) lag (d) Pgro 3I L 3067Watt Pgro 4.9Nm (f) P in 3473Watt (g) % P % ] in 8

Equivalent Circuit of Induction Motor Referred to Stator Side

Electrical Machine IV Code: CECE 437 http://bu.edu.eg/taff/emadattwa3 Equivalent Circuit of Induction Motor Referred to Stator Side Fig. 3: eqt. circuit of induction motor per phae at any lip referred