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View File - University of Engineering and Technology, Taxila

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Calculate (1) the probability that one solar cell goes (a) short-circuit <strong>and</strong> (b)open circuit in a one-year period, (2) the probability that the three cells in onearm short-circuit, <strong>and</strong> (3) the reliability <strong>of</strong> the solar power system for a oneyearperiod.SolutionThe solution to Example 2.5 uses the equations derived in (2.32)through (2.36). SoN s ¼ 80dN f ¼ 6 for short-circuitdN f ¼ 9 for open circuitdt ¼ 10 8 hrt ¼ð365 24Þ ¼8760 hr for nonleap year1. To obtain the probability <strong>of</strong> the open <strong>and</strong> short-circuit cases, eachcase’s failure rate <strong>and</strong> reliability must be established since theirprobability P ¼ 1 reliability. Hence for(a)A short-circuit cell, using (2.35) the average failure rate isgiven byl rðs=cÞ ¼ 1 N sdN fdtUsing (2.37), the reliability isR ¼ e l rðs=cÞt ¼ 0:99999343¼ 1 680 10 8 ¼ 0:75*10 9Hence, the probability <strong>of</strong> a short circuit within a calendar yearisP s=c ¼ 1 R s=c ¼ 6:75*10 6(b)Similarly, for an open circuit celll rðo=cÞ ¼ 1 N sdN fdt¼ 1 980 10 8 ¼ 1:13*10 9Its reliability R o=c ¼ 0:99999015. The probability <strong>of</strong> an opencircuit within the calendar year P o=c ¼ 9:85*10 6 .2. The probability <strong>of</strong> the cells array in one arm short-circuiting isP array ¼ N s *P s=c ¼ 80*6:57*10 6 ¼ 5:26*10 4Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.

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