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Recitation1

# Recitation1 - Electric Energy Processing Fundamentals and...

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1 Electric Energy Processing: Fundamentals and Applications 18-418: Recitation #1 Dr. Nermeen T. Mahmoud ( [email protected] ) August 26,2009 Circuit concept, Circuit Laws and Analysis Methods

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2 Outline •Time domain representation •Instantaneous power flow in steady state. •Phasor Domain. •Circuit Laws and connections. •Three phase.
3 Time Domain Representation )) ( ) ( cos( ) ( 2 ) ( )) ( cos( ) ( 2 ) ( t t t t I t i t t t E t e ϕ δ ω δ ω - + = + = The time-domain representation for AC voltage and current for equilibrium steady state condition : Where E: the rms for voltage. I: the rms for current. : the peak value of voltage. :the peak value of current. : the power factor angle. E 2 I 2 ϕ A piece of equipment i(t) i(t) + - e(t)

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4 Instantaneous Power Flow in steady state 1/3 ) sin( ) cos( ) cos( ) sin( ) sin( ) sin( ) sin( ) cos( ) cos( ) cos( )) ( ) ( cos( )) ( cos( ) ( ) ( 2 ) ( )) ( ) ( cos( ) ( 2 ) ( )) ( cos( ) ( 2 ) ( : ) ( ) ( ) ( y x y x y x y x y x y x t t t t t t I t E t p t t t t I t i t t t E t e where t i t e t p ± = ± = ± - + + = - + = + = = m ϕ δ ω δ ω ϕ δ ω δ ω A piece of equipment i(t) i(t) + - e(t)
5 ))] ( cos( * )) ( ))[sin( ( sin( ) ( ) ( 2 ))] ( cos( * )) ( ))[cos( ( cos( ) ( ) ( 2 ) ( ))] ( sin( * )) ( ))[sin( ( cos( ) ( ) ( 2 ))] ( cos( * )) ( ))[cos( ( cos( ) ( ) ( 2 ) ( ))] ( sin( * )) ( sin( )) ( cos( * )) ( ))[cos( ( cos( ) ( ) ( 2 ) ( t t t t t t I t E t t t t t t I t E t p t t t t t t I t E t t t t t t I t E t p t t t t t t t t t I t E t p δ ω δ ω ϕ δ ω δ ω ϕ ϕ δ ω δ ω ϕ δ ω δ ω ϕ δ ω ϕ δ ω δ ω + + + + + = + + + + + = + + + + = Instantaneous Power Flow in steady state 2/3

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6 ) ( ) ( ) ( ))} ( ( 2 )){sin ( sin( ) ( ) ( ) ( ))} ( ( 2 cos 1 )){ ( cos( ) ( ) ( ) ( ))} ( ( 2 )){sin ( sin( ) ( ) ( ))} ( ( 2 cos 1 )){ ( cos( ) ( ) ( ) ( t q t t p t
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Recitation1 - Electric Energy Processing Fundamentals and...

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