The fuel-cost curves for a two generator system are given as follows:
C1(PG1) = 2000 + 45 * PG1 + 0.05 * (PG1)2
C2(PG2) = 500 + 50 * PG2 + 0.03 * (PG2)2
Generator limits are: 0 ?PG1 ?200
200 ?PG2 ? 800
For a load of 600 MW, use the lambda iteration method to determine the values of ?M, PG1(?M) and P G2(?M) after two iterations. Show the values of all variables at each iteration. Use starting values of ?L = 60 and ?H = 80. Be sure to consider the generator limits; you may ignore any penalty factors.
P(60) = 150 + 200 – 600 = -300 (PG2 at low limit)
P(80) = 200 +500 – 600 = 100 (PG1 at high limit)
Initial values bound the solution
Set ?m = (60+80)/2 = 70
P(70) = 200+333.3-600 = -66.7
Less than zero so ?L =?m; new ?m = (70+80)/2 = 75
P(75) = 200+416.7 - 600 = 16.7
Greater than zero so ?H = ?m; new ?m = (70+75)/2 = 72.5
Note, after the first iteration it is clear that PG1 = 200 MW at the solution so PG2 = 400 meaning ? will be $ 74/MWh
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