please give the answer asap our-unit hydro plant serves a remote load through tw
ID: 2291128 • Letter: P
Question
please give the answer asap
our-unit hydro plant serves a remote load through two transmission lines. The four hydro units are connected to a single step-up transformer which is then connected to the two lines. The remote load has a daily peak load variation curve which is a straight line from the 100% to the 60% point. Calculate the annual loss of load expectation for a forecast peak of 70 MW using the following data. Hydro units Transformer Transmission lines 25 MW. Forced outage rate 2%. 1. Co 0.2% 40 l 110 MVA. Forced outage rate Carrying capability 50 MW each line Failure rate 2 f/year Average repair time 24 hoursExplanation / Answer
LOLE - Loss of Load Expectation
100 MW installed capacity, 70 MW peak load at 80% load factor Calculate LOLE for the following system:
G G G G
| | | |
------------
|
X
|
---------
| |
L L
| |
-------
|
D
where G represents a 25 MW generator unit, X represents a 110 MVA transformer, L represents a 50 MW transmission line, and D represents a 70 MW peak load.
LOLE for generation only
Cap Out Cap Avail Cumulative Prob Time Interval Prob Curtail (day)
0 100 1.000e+000 0.00 0.000e+000
25 75 7.763e-002 0.00 0.000e+000
50 50 2.336e-003 260.71 6.092e-001
75 25 3.152e-005 104.29 3.287e-003
100 0 1.600e-007 0.00 0.000e+000
LOLE 6.124e-001
LOLE for transformer only
Cap Out Cap Avail Cumulative Prob Time Interval Prob Curtail (day)
0 110 1.000e+000 0.00 0.000e+000
110 0 2. 000e-003 365.00 7.300e-001
LOLE 7.300e-001
U=MTTR/(MTTF+MTTR)=1/(365/2 + 1)=0.0054
LOLE for trans. lines only
Cap Out Cap Avail Cumulative Prob Time Interval Prob Curtail (day)
0 100 1.000e+000 0.00 0.000e+000
50 50 1.087e-002 260.71 2.834e+000
100 0 2.970e-005 104.29 3.097e-003
LOLE 2.837e+000
The "union" of cumulative probabilities yields
Pr(G&Xout >= 0) = Pr(Gout >= 0) + Pr(Xout >= 0) - Pr(Gout >= 0)*Pr(Xout >= 0)
Pr(G&Xout >= 100) = Pr(Gout >= 100) + Pr(Xout >= 100) - Pr(Gout >= 100)*Pr(Xout >= 100)
Cumulative Probability for gen and xfmr
Cap Out Cap Avail Cumulative Prob
0 100 1.000e+000
25 75 7.948e-002
50 50 4.332e-003
75 25 2.031e-003
100 0 2.000e-003
Combine G&X subsystem above with transmission line subsystem via the union of cumulative probabilities.
LOLE for entire system
Cap Out Cap Avail Cumulative Prob Time Interval Prob Curtail (day)
0 100 1.000e+000 0.00 0.000e+000
25 75 8.948e-002 0.00 0.000e+000
50 50 1.515e-002 260.71 3.951e+000
75 25 2.061e-003 104.29 2.149e-001
100 0 2.030e-003 0.00 0.000e+000
LOLE 4.166e+000
sum of individual LOLEs
0.6124+0.73+2.837 = 4.179
is greater than actual system LOLE, since independent systems (e.g., generation, transformer and transmission lines) can have outages at the same time.
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