# HW 02 - Spring2011 Homework 2 Solutions 2.1(10 pt We need...

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ELEN 3441 – Fundamentals of Power Engineering Spring 2011 Page | 1 Homework 2 – Solutions 2.1. (10 pt.) We need to show that ( ) ( ) ( ) ( ) 3 cos t o t abc pt p t p t V I θ = ++= starting from () ( ) cos cos 2 ( ) cos cos 2 240 ( ) cos cos 2 480 a b c pt V I t I t I t θω ωθ =− ⎡⎤ ⎣⎦ ° ° Apparently, it implies that the sum of three cosine terms in the right-hand side must be zero… ( ) ( ) ( ) ( ) {} ( ) ( ) ( ) cos 2 cos 2 240 cos 2 480 c o s2 c o 2 4 0 c o 1 2 0 2 cos cos 120 cos 240 cos cos cos120 sin sin120 cos cos240 sin sin 240 cos (1 cos120 cos240 ) sin (cos1 tt t t t ω ωα α αααα αα −+ ° ° +− ° ° = = ° ° = + °+ ° =+° + 20 cos240 ) cos (1 2cos180 cos( 60 )) sin (2cos180 cos( 60 )) cos (1 2 ( 1) 0.5) sin (2 0) 0 ° = + °− ° + ° =+ +⋅ = 2.2. (15 pt.) 2.3. (25 pt.) First, we need to convert two deltas (generator and one load) to Y and find the per-phase equivalent diagram.

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ELEN 3441 – Fundamentals of Power Engineering Spring 2011 Page | 2
ELEN 3441 – Fundamentals of Power Engineering

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HW 02 - Spring2011 Homework 2 Solutions 2.1(10 pt We need...

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