IGEE402_Galiana_Fall_2010_Midterm_Solutions

IGEE402_Galiana_Fall_2010_Midterm_Solutions - POWER SYSTEM...

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POWER SYSTEM ANALYSIS MID-TERM TEST SOLUTIONS WEDNESDAY, NOVEMBER 3, 2010 PROF. F.D. GALIANA 9:30 TO 12:00 YOU MAY BRING INTO THE TEST ROOM A SINGLE 8.5 BY 11 INCH PAGE WITH NOTES ALL QUESTIONS HAVE EQUAL WEIGHT FOR A MAXIMUM OF 70 POINTS SI VOUS PRÉFÉREZ, RÉPONDEZ EN FRANCAIS (1) Consider a power plant supplying 1000 MW to a power system. The power generated by the plant has to pass through 5 step-up transformers, each one rated at 200 MVA. The unavailability of each transformer is 0.1. Find the loss of load probability. Find the probability of the power plant being able to supply only 200 MW. Solution: The transformers are in parallel. Then LOLP = Probability that one or more transformers will be unavailable = 1-Probability that all transformers are available = 1 A 5 = 1 (0.9) 5 = 0.4095. The probability of supplying only 200 MW is the probability of only one transformer being available and 4 being unavailable, that is, 5AU 4 = 5(0.9)(0.1) 4 = 4.5x10 -4 .
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