# Lecture 9 - leading. current , 2 /-If < − < i v π...

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CF Video on Linear Machine UCF Linear Motor http://www.youtube.com/watch?v=a4KUwFP42yo German Maglev Linear Motion vs Ball Screw http://www.youtube.com/watch?v=aEdvuc2Qxyw http://www.youtube.com/watch?v=eSi6J-QK1lw Bose Active Suspension

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CF Time-harmonic Signal UCF ) cos( 2 ) ( t V t v θ ω+ = V and I are rms values. ) cos( 2 ) ( i v t I t i = ) ( t i ] 2 Re[ ) ( t j j e Ve t v v ω = Z + - ) ( t v Phasor Domain v j Ve V = rms V V = or ] 2 Re[ ) ( t j j e Ie t i i = v i j Ie I = rms i I I = or
CF Instantaneous Power UCF Definition: ) ( ) ( ) ( t i t v t p = + ) ( t i Time-harmonic Case: Z - ) ( t v ] 2 Re[ ) ( t j j e Ve t v v ω θ = ] 2 Re[ ) ( t j j e Ie t i i = ) 2 2 ( 1 ) ( t j j t j j e Ve e Ve t p v v + = 1 2 t j j t j j v v ) 2 2 ( 2 e Ie e Ie +

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CF Average Power UCF ] [ 1 ) ( ) ( ) ( j j VIe VIe t p i v i v θ + = 1 2 2 ) ( 2 ) ( t j j t j j Ie Ie ω + + ] [ 2 e VIe e VIe i v i v + + verage Power: Average Power: ] [ 1 ) ( 1 ) ( ) ( j j T VIe VIe dt t p P i v i v + = = ) cos( 2 0 VI T θ− = i v 0 : Note 0 2 = ± dt e T t j
CF Power Factor UCF pf ) cos( = = VI VI P θ Unit: Watt = (volt . amp) i v Power Factor: ) cos( pf i v θ− = lways positive for passive load lagging. current , 2 / 0 If < < i v π Always positive for passive load.

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Unformatted text preview: leading. current , 2 /-If < − < i v π j j e Z e I V I Z V i v | | , From ) ( = = − + I Lagging – inductive load Leading – capacitive load Z i v − =-V CF Reactive and Apparent Power UCF ) cos( VI P θ − = Average Power: i v Reactive (or Quadrature) Power: ) sin( i v VI Q − = pparent Power: Unit: Var = (volt . amp) Apparent Power: VI S = Unit: VA = (volt . amp) i v − = Power angle: Q S P CF Complex Power UCF Complex Power: VIe Ie Ve I V S j j j i v i v = = ⋅ = − ) )( ( ) ( * * θ jVI VI i v i v − + − = ) sin( ) cos( jQ P + = Q S P...
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## This document was uploaded on 11/03/2009.

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Lecture 9 - leading. current , 2 /-If < − < i v π...

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