lecture16

# lecture16 - Power Systems I Fault Analysis l Fault types: u...

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Unformatted text preview: Power Systems I Fault Analysis l Fault types: u balanced faults Percentage of total faults n three-phase <5% u unbalanced faults n single-line to ground 60-75% n double-line to ground 15-25% n line-to-line faults 5-15% l Unbalance fault analysis requires new tools u symmetrical components u augmented component models Power Systems I Symmetrical Components l Allow unbalanced three-phase phasor quantities to be replaced by the sum of three separate but balanced symmetrical components u applicable to current and voltages u permits modeling of unbalanced systems and networks l Representative symmetrical components I a1 I b1 I c1 120 ° 120 ° 120 ° ° I a0 I b0 I c0 I a2 I b2 I c2 120 ° 120 ° 120 ° I a I c abc sequence positive sequence acb sequence negative sequence zero sequence Power Systems I Symmetrical Components ( ) ( ) ( ) 1 1 1 866 . 5 . 240 1 866 . 5 . 120 1 120 240 2 3 2 1 1 1 1 2 1 1 1 1 1 = + + + = ° ∠ = − − = ° ∠ = + − = ° ∠ = = ° + ∠ = = ° + ∠ = = ° + ∠ = a a j a j a j a I a I I I a I I I I I a a c a a b a a a δ δ δ l Positive sequence phasors l Operator a identities Power Systems I Symmetrical Components ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 240 120 a a c a a b a a a a a c a a b a a a I I I I I I I I I I a I I I a I I I I I = ° + ∠ = = ° + ∠ = = ° + ∠ = = ° + ∠ = = ° + ∠ = = ° + ∠ = δ δ δ δ δ δ l Negative sequence phasors l Zero sequence phasors Power Systems I l Relating unbalanced phasors to symmetrical components l In matrix notation Symmetrical Components 2 2 1 2 1 2 1 2 2 1 2 1 2 1 a a a c c c c a a a b b b b a a a a a a a I a I a I I I I I I a I a I I I I I I I I I I I I + + = + + = + + = + + = + + = + + = = 2 1 2 2 1 1 1 1 1 a a a c b a I I I a a a a I I I Power Systems I l [A] is known as the symmetrical components transformation matrix...
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## This note was uploaded on 10/13/2011 for the course EEL 4213 taught by Professor Thomasbaldwin during the Spring '11 term at FSU.

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lecture16 - Power Systems I Fault Analysis l Fault types: u...

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