5) Consider the following power system in which we want to transmit 200MW from p

Question

5) Consider the following power system in which we want to transmit 200MW from point A to point C. Bl to B9 indicate buses of the system. Bl to B8 are 100% reliable, and B9 has a reliability of 0.94. Lines l 0, 1 1, 12, 13, and 14 (i.e., L 10, LI I, L 12, L 13, L 14) arc 100% reliable. The reliability of each line Li, L2, L3, L4, L5, L6, L7, L8, and, L9 is 0.94. Assume that switch Sl has a probability of failing to changeover of 0.06. Evaluate reliability of the system if: a) the capacity of each line is 200MW (10 pts) b) the capacity of L-L2-L3-L4-L5-LI 0-LI I =LI 2=LI 3-LI 4-200 Mw, and the capacity of L6-L7-Ls-L9-1 00MW ( 1 0 pts) b) the capacity of LI-L2-L3-L4-L5-LI 0-LI-LI 2-LI3-LI 4-200MW, and the capacity of L6-L7-L8-L9-50MW (10 pts) L4 S1 B4 0 11 L5 82 L2 81 L1 10 L6 12 14 L8 L9 B7

Explanation / Answer

A) when capacity of each line is 200MW

Reliability between B5 to B6 and B7 to B8

=0.94×0.06+0.94*0.94= 0.94

and

=0.94/4=0.235

Total reliability = 0.94×0.47×1+0.94/5=0.629×200=125.961MW

b) 200×0.94×.47= 88.36MW +{200×0.94+100×0.94/4}/2=194.11MW

c) 88.36MW+{200×0.94+50×0.94/4}/2= 188.235MW

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