EEE591Ch13-2

# EEE591Ch13-2 - Power System Stability Chapter 13-2 1 EQUAL...

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1 Power System Stability Chapter 13-2

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2 EQUAL AREA CRITERIA For one machine against a infinite bus X e X’d P E E I / δ E 2 / 0 2 Power angle equation δ sin ' 2 e I E x d x E E P + = δ P E P max δ 0 π δ 0 is for steady state condition with constant P M.
3 EQUAL AREA CRITERIA 2 2 2 dt d H P P P M SM Eu Mu Au δ ϖ = - = For a 3-phase fault at the generator terminals, P E = 0. δ P E P max δ 0 δ C δ 2 A 1 A 2

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4 δ P E P max δ 0 δ C δ 2 A 1 A 2 Can show that for stability to exist: 0 ) ( 2 0 = - δ d P P Eu Mu In parts: 0 ) ( ) ( 2 0 = - + - d P P d P P Eu Mu Eu Mu C C Or A 1 + A 2 = 0 (radians)
5 EXAMPLE 13.4 - + E g / δ X’d=.3 pu j.1 I j.2 j.1 j.2 1/ 0 1 2 3 S 2 3-Phase fault at X on Bus 1, Fault cleared in 3 cycles by Breaker b, H = 3. Find: a) If stable b) Maximum δ swing δ P E P max δ 0 δ C δ 2 A 1 A 2 UEP X b

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6 EXAMPLE 13.4 δ P E P max δ 0 δ C δ 2 A 1 A 2 If we can find δ 0 and δ C we will know A 1 and since A 2 = A 1 we can find δ M . P E = 2.464 Sin δ P E = 1.0 for δ 0 . so Sin δ 0 = 1/2.464, δ 0 =.4178 radians 2 2 2 dt d H P P P M SM Eu Mu Au δ ϖ = - = 2 2 377 ) 3 )( 2 ( 0 . 1 dt d = so 2 2 2 sec / 83 . 62 rad dt d =
7 Example 13.4 2 2 2 sec / 83 . 62 rad dt d = δ + = = 83 . 62 83 . 62 ϖ t dt dt d 0 4178 . 2 ) 05 (. 83 , 62 2 83 . 62 83 . 62 2 0 2 + = + = = t dt C δ C = .4963 radians A 1 = (.4963 - .4178)(1.0) = 0.785 radians - - = - = = cos 464 . 2 ) 1 sin 464 . 2 ( 4963 . 2 1 M d A A δ M .4963 A 1 = A 2 = -2.464cosδ M –δ M + 2.167 +.4963 = .0785 2.464Cosδ M + δ M = 2.584 By iteration: δ M = 0.7 radians = 40.12 o . δ(uep) = π – δ 0 = π -.4178 = 2.272 > 0.7 (STABLE)

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8 EXAMPLE 13.5 3-Phase fault at X on Bus 1, Fault cleared by Breaker b, H = 3. Find the critical clearing time for Breaker b for stability. - + E g / δ X’d=.3 pu j.1 I j.2 j.1 j.2 1/ 0 1 2 3 S 2 X b δ P E P max δ 0 δ C δ 2 A 1 UEP A 2
9 δ P E P max δ 0 δ C δ 2 A 1 UEP A 2 δ d P P A d P P A M E E M CR CR

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## This note was uploaded on 02/21/2010 for the course EEE ??? taught by Professor Farmer during the Spring '10 term at ASU.

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EEE591Ch13-2 - Power System Stability Chapter 13-2 1 EQUAL...

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