34 RLC Circuit and instantaneous real or reactive power

34 RLC Circuit and instantaneous real or reactive power -...

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Lecture 3 RLC Circuit and instantaneous real/reactive power Sep. 8 th , 2003 RLC Circuits RLC circuits driven by sinusoidal sources can be analyzed in steady-state through a set of algebraic instead of differential equations; v(t) R, L, C Transformer () ()() p tv t i t = where p t is the total instantaneous power consumed. 11 2 2 () () () () . . . pt v ti t = ++ 1 n kk k vt it = = . 1 2 3 4 () n 1 2 3 4 n
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cos VI ϕ Consuming Generating t p(t) INSTANTANEOUS, REAL AND REACTIVE POWER The instantaneous power consumed by a load with voltage v(t) and current i(t) , () ()() p tv t i t = (1.1) If the load is R,L,C and the input voltage is sinusoidal with 2 s in vt V t ω = (1.2) then, the output current is also sinusoidal, ( ) it I t = (1.3) In terms of phasors, these two sinusoids become, 0 VV = (1.4) and, II = ∠− (1.5) For sinusoidal inputs the instantaneous power can be expressed as, () 2 s in s ( ) 2c o s ( ) c o s ( 2 ) / 2 cos( ) cos(2 ) pt V I t t VI t VI VI t ωϕ ϕω =− (1.6) P = average power per cycle = 0 1 () () T ptdt T ; Also P = real power = active power.
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This note was uploaded on 01/27/2011 for the course ECSE 361 taught by Professor Franciscodgaliana during the Spring '09 term at McGill.

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34 RLC Circuit and instantaneous real or reactive power -...

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