2009-10-08 Energy Management Systems III

2009-10-08 Energy Management Systems III - Energy...

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Energy Management Systems III Jovan Ilić ECE 18-418 Fall 2009
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Decoupled Power Flow 11 12 11 21 22 22 0 Small and small 0 ki k i J J J G J J J  11 22 || l l l l l l JP J V Q     Decoupled and of smaller dimensions 1 1 1. All | | approximately equal 2. small shunts 3. Because of 2, | | | | k N ii ik k N ik ii k V BB 
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2 2 2 22 1 1 | | | | | | | | | | | | | | || N i i ii i i k ik ii i i k i N i k ik i ii i ii k i P Q B V VV B B V V B Q V B V B V B V         22 2 2 2 0 0 N RI N NN N B B V BV B B V
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11 22 I R I I R J V B V J V B           || ll I R I l l l I R l l V B V P V B V Q                       1 1 1 1 | | | | l l l I R I l l l R I l I R l l l R I l V B V P B V P V B V Q V B V Q                 
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DC Power Flow     1. All voltages, | | 1.0 2. Line resistances are neglected , 0.0 3. cos 1 and sin k ik ik ik ik k i k i k i V Y G jB G R PB     1 N i ik k i k ki   
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Distribution Factors (DF) approximation of line power flows BUS1 BUS2 BUS3 BUS4
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Define incidence matrix A: and the reduced incidence matrix A 1 2 1 3 2 3 2 4 3 4 1 1 1 0 0 0 A= 2 1 0 1 1 0 3 0 1 1 0 1 4 0 0 0 1 1 line line line line line bus bus bus bus     1 0 1 1 0 0 1 1 0 1 0 0 0 1 1 R A
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12 12 23 24 13 13 23 24 23 34 24 24 34 1 0 1 1 0 0 1 1 0 1 0 0 0 1 1 R F F F F F P F F F F A F F F F F      12 12 12 13 13 13 23 23 23 24 24 24 34 34 34 0 0 0 0 0 0 0 0 0 0 0 0 = diag(b) 0 0 0 0 0 0 0 0 is the ij Fb   
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This note was uploaded on 09/20/2010 for the course ECE 18418 taught by Professor Illic during the Fall '09 term at Carnegie Mellon.

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2009-10-08 Energy Management Systems III - Energy...

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