lect22 - + = = t N dt d N e ( 29 2 max 2 2 2 cos + = = t N...

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Lecture 22 - EE743 Lecture 22 - EE743 3-Phase Induction Machines Steady-state model. Equivalent Circuit Professor: Ali Keyhani Professor: Ali Keyhani
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2 Equivalent circuit Assumption Both stator and rotor have 3-phase Y connected windings The staotr is fed from a 3-phase source The subscript “1” refers to the stator and “2” to the rotor Stand still condition Suppose the rotor is at stand still (stationary rotor ϖ m =0). Using transformer theory, the eq circuit for 1 phase to ground
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3 Equivalent circuit Normally X m and R m are very large and net Z m acts as open circuit. Therefore, they are ignored and I 1 =I' 2 ( 29 ( 29 2 2 2 2 1 1 1 1 ~ ~ ~ ~ ~ L j R R I E E L j R I V s ext s ϖ + + = + + = Stand still
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4 Equivalent circuit Rotor is free to rotate suppose rotor speed is ϖ m . Let R 2 =R rotor +R ext ( 29 ( 29 0 , ~ ~ ~ ~ ~ 2 2 2 2 1 1 1 1 = + = + + = ext r R L j R I E E jX R I V ϖ
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5 Equivalent circuit R 1 : stator resistance / φ X 1 = ϖ s L 1 stator reactance / φ I 1 : stator current (line) E 1 : induced emf / φ Note that Therefore Let then s r s ϖ ϖ= ( 29 2 2 2 2 ~ ~ L js R I E s + = 2 2 L X s = ( 29 2 2 2 2 ~ ~ jsX R I E + =
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6 Relationship between I 1 and I 2 , E 1 and E 2 Define 2 1 N N a = 1 2 ~ ~ I a I = ( 29 1 max 1 1 1 cos
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Unformatted text preview: + = = t N dt d N e ( 29 2 max 2 2 2 cos + = = t N dt d N e 2 ~ max 1 1 N E = 2 ~ max 1 2 sN E = a E s N N E s N E sN E 1 2 1 1 1 1 2 2 ~ ~ ~ ~ = = = a E s E 1 2 ~ ~ = 7 Reduced circuit model Multiply both side by a divide by s ( 29 2 2 2 2 ~ ~ jsX R I E + = a E s E 1 2 ~ ~ = 1 2 ~ ~ I a I = ( 29 ( 29 1 2 2 1 ~ ~ I a jsX R a E s + = ( 29 1 2 2 2 2 1 ~ ~ I a jsX a R E s + = 1 2 2 2 2 1 ~ ~ I a jX s R a E + = 8 Reduced circuit model But from the stator side Lets define ( 29 1 1 1 1 ~ ~ E I jX R V + + = ( 29 1 2 2 2 2 1 1 1 ~ ~ I a jX s R a I jX R V + + + = 2 2 ' 2 R a R = 2 2 ' 2 X a X = ( 29 + + + = ' 2 1 ' 2 1 1 ~ X X j s R R I V 9 Reduced circuit model The induction machine reduced equivalent circuit is...
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lect22 - + = = t N dt d N e ( 29 2 max 2 2 2 cos + = = t N...

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