lecture11

lecture11 - Balanced 3-Phase Short Circuit Consider a...

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(c) Feb 2004 Power Systems I 1 Balanced 3-Phase Short Circuit ( ) ( ) ( ) ( ) ( ) ( ) () 0 0 0 0 0 0 0 0 0 0 0 0 0 = = = → = = = = = = = = = = + + + + + + + q d Park c b a F F F q d Park c b a v v v v v v r V i i i i i i i Consider a synchronous generator operating at 60 Hz with constant excitation Examine the impact on the stator currents when a three- phase short circuit is applied to the generator terminals The initial currents The voltage after applying the fault
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(c) Feb 2004 Power Systems I 2 Balanced 3-Phase Short Circuit = Q q D F d Q Q Q q D R D R F F D F d Q q D F d Q D F d D F Q q q F d i i i i i dt d L M M L L M M M L M M M L i i i i i r r M M L r r M L r v v v 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ω Rearranging the equation and neglecting the zero sequence term
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(c) Feb 2004 Power Systems I 3 Balanced 3-Phase Short Circuit () 3 2 3 2 3 2 3 2 0 1 1 1 sin cos sin cos sin cos π θ + + + = + = + = = = = q d c q d b q d a dq abc i i i i i i i i i dt d dt d i P i v L Ri L i i L Ri v In matrix form (or state space form) the equation can be rewritten Using the Laplace transform or integrating the equation results in
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(c) Feb 2004 Power Systems I 4 Example
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lecture11 - Balanced 3-Phase Short Circuit Consider a...

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