Recitation1 - 1 Electric Energy Processing: Fundamentals...

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Unformatted text preview: 1 Electric Energy Processing: Fundamentals and Applications 18-418: Recitation #1 Dr. Nermeen T. Mahmoud ( ntalaat@andrew.cmu.edu ) August 26,2009 Circuit concept, Circuit Laws and Analysis Methods 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 - + = + = 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 A piece of equipment i(t) i(t) +- e(t) 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 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...
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Recitation1 - 1 Electric Energy Processing: Fundamentals...

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