hw1 - , McGraw-Hill, 2002, ISBN 0-07-229135-4. ~ ) ( t v )...

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EEL 3211 Basic Electrical Energy Engineering Homework 1 Starting from the complex power equation shown on Slide 28 of Lecture Set 1, derive all of the boxed equations on Slide 31. Book * Problems 1-19, 2-2, 2-5 SELECTED ANSWERS 1-19 a. 47.59 ANG -37.5 A; 0.793 lag; 4531 W; 3477 var; 5711 VA b. 38.08 ANG -7.5 A; 0.991 lag; 4531 W; 596 var; 4570 VA 2-2 a. 439 V b. 41.3 ANG 52 V c. 61.6 kW, 46.2 kvar, 108 kW, -39.5 kvar d. 13.7 kW, 24.3 kvar e. 184 kW, 31 kvar, 0.986 lagging 2-5 a. Vab=208 ANG 30 V, Vbc=208 ANG -90 V, Vca=208 ANG 150 V b. Iab=20.8 ANG 10 A, Ibc=20.8 ANG -110 A, Ica=20.8 ANG 130 A c. Ia=36 ANG -20 A, Ib=36 ANG -140 A, Ic=36 ANG 100 A SOLUTIONS Let t V t v ω cos 2 ) ( = ) cos( 2 ) ( L t I t i θ = Where V and I are rms values of voltage and current. (Recall, 2 pk rms A A = for a cosine wave with peak amplitude A pk ) The phasor voltage and current are: 0 2 ~ = V V = I I 2 ~ By direct substitution * Homework assignments are from the text, Chapman, Electrical Machinery and Power System Fundamentals
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Unformatted text preview: , McGraw-Hill, 2002, ISBN 0-07-229135-4. ~ ) ( t v ) ( t i L L L L L L Z Z jX R Z ∠ = + = ( ) ( ) ( ) ( ) ( ) ( ) L L L L L L VI I V I V Q VI I V I V P VI I V I V S S θ sin sin 2 2 2 1 sin ~ ~ 2 1 cos cos 2 2 2 1 cos ~ ~ 2 1 2 2 2 1 ~ ~ 2 1 ~ = = = = = = = = = = But L Z I V ~ ~ ~ = , so L IZ V = and ( ) ( ) L L L L L L L L L L Z I I IZ VI Q Z I I IZ VI P sin sin sin cos cos cos 2 2 = = = = = = And furthermore L L L L L jX R jZ Z Z + = + = sin cos ~ , so L L L L L L X I Z I Q R I Z I P 2 2 2 2 sin cos = = = = Note, these solutions are incorrect. θ L should be POSITIVE, and Q should also be positive. Note, these solutions are incorrect. θ L should be POSITIVE, and Q should also be positive....
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This note was uploaded on 06/22/2010 for the course EEL 3211 taught by Professor Staff during the Spring '08 term at University of Florida.

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hw1 - , McGraw-Hill, 2002, ISBN 0-07-229135-4. ~ ) ( t v )...

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